%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU774^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:17 AM UTC 2026
% Result : Theorem 13.85s 2.46s
% Output : Refutation 14.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU774^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.21 % Computer : n009.cluster.edu
% 0.14/0.21 % Model : x86_64 x86_64
% 0.14/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.21 % Memory : 8046.5625MB
% 0.14/0.21 % OS : Linux 6.8.0-71-generic
% 0.14/0.21 % CPULimit : 300
% 0.14/0.21 % WCLimit : 300
% 0.14/0.21 % DateTime : Tue Sep 29 14:27:52 UTC 2026
% 0.14/0.21 % CPUTime :
% 0.14/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.27 Running higher-order theorem proving
% 0.37/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.56 % (4075570)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.41/0.56 % (4075580)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1790149911:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.41/0.56 % (4075581)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.41/0.56 % (4075581)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.41/0.56 % (4075578)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2961677780:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.41/0.56 % (4075581)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=92836885:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.41/0.56 % (4075579)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4067702838:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.41/0.56 % (4075576)lrs+10_16_si=on:nwc=1.5:random_seed=2354180844:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.41/0.56 % (4075575)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1412794972:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.41/0.56 % (4075577)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2656291847:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.41/0.56 % (4075577)Instruction limit reached!
% 0.41/0.56 % (4075577)------------------------------
% 0.41/0.56 % (4075577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.56 % (4075577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.56 % (4075577)CaDiCaL version: 2.1.3
% 0.41/0.56 % (4075577)Termination reason: Instruction limit
% 0.41/0.56 % (4075577)Termination phase: shuffling
% 0.41/0.56 % (4075577)Time elapsed: 0.003 s
% 0.41/0.56 % (4075577)Peak memory usage: 10 MB
% 0.41/0.56 % (4075577)Instructions burned: 3 (million)
% 0.41/0.56 % (4075580)Instruction limit reached!
% 0.41/0.56 % (4075580)------------------------------
% 0.41/0.56 % (4075580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.56 % (4075580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.56 % (4075580)CaDiCaL version: 2.1.3
% 0.41/0.56 % (4075580)Termination reason: Instruction limit
% 0.41/0.56 % (4075580)Termination phase: Preprocessing 3
% 0.41/0.56 % (4075580)Time elapsed: 0.024 s
% 0.41/0.56 % (4075580)Peak memory usage: 12 MB
% 0.41/0.56 % (4075580)Instructions burned: 90 (million)
% 0.41/0.56 % (4075579)Instruction limit reached!
% 0.41/0.56 % (4075579)------------------------------
% 0.41/0.56 % (4075579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.56 % (4075579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.56 % (4075576)Instruction limit reached!
% 0.41/0.56 % (4075576)------------------------------
% 0.41/0.56 % (4075576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.56 % (4075579)CaDiCaL version: 2.1.3
% 0.41/0.56 % (4075579)Termination reason: Instruction limit
% 0.41/0.56 % (4075579)Termination phase: shuffling
% 0.41/0.56 % (4075576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.56 % (4075579)Time elapsed: 0.012 s
% 0.41/0.56 % (4075579)Peak memory usage: 11 MB
% 0.41/0.56 % (4075576)CaDiCaL version: 2.1.3
% 0.41/0.56 % (4075579)Instructions burned: 25 (million)
% 0.41/0.56 % (4075576)Termination reason: Instruction limit
% 0.41/0.56 % (4075576)Termination phase: shuffling
% 0.41/0.56 % (4075576)Time elapsed: 0.011 s
% 0.41/0.56 % (4075576)Peak memory usage: 10 MB
% 0.41/0.56 % (4075576)Instructions burned: 19 (million)
% 0.41/0.56 % (4075591)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.41/0.56 % (4075591)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=257583883:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.30/0.60 % (4075589)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2905526792:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.30/0.60 % (4075591)Instruction limit reached!
% 1.30/0.60 % (4075591)------------------------------
% 1.30/0.60 % (4075591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.60 % (4075591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.60 % (4075591)CaDiCaL version: 2.1.3
% 1.30/0.60 % (4075591)Termination reason: Instruction limit
% 1.30/0.60 % (4075591)Termination phase: shuffling
% 1.30/0.60 % (4075591)Time elapsed: 0.002 s
% 1.30/0.60 % (4075591)Peak memory usage: 10 MB
% 1.30/0.60 % (4075591)Instructions burned: 8 (million)
% 1.30/0.60 % (4075589)Instruction limit reached!
% 1.30/0.60 % (4075589)------------------------------
% 1.30/0.60 % (4075589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.60 % (4075589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.60 % (4075589)CaDiCaL version: 2.1.3
% 1.30/0.60 % (4075589)Termination reason: Instruction limit
% 1.30/0.60 % (4075589)Termination phase: shuffling
% 1.30/0.60 % (4075589)Time elapsed: 0.002 s
% 1.30/0.60 % (4075589)Peak memory usage: 10 MB
% 1.30/0.60 % (4075589)Instructions burned: 2 (million)
% 1.30/0.60 % (4075592)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1813342515:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.30/0.60 % (4075590)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3076639936:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.30/0.60 % (4075597)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.30/0.60 % (4075597)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.30/0.60 % (4075590)Instruction limit reached!
% 1.30/0.60 % (4075590)------------------------------
% 1.30/0.60 % (4075590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.60 % (4075590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.60 % (4075590)CaDiCaL version: 2.1.3
% 1.30/0.60 % (4075590)Termination reason: Instruction limit
% 1.30/0.60 % (4075590)Termination phase: shuffling
% 1.30/0.60 % (4075590)Time elapsed: 0.004 s
% 1.30/0.60 % (4075590)Peak memory usage: 10 MB
% 1.30/0.60 % (4075590)Instructions burned: 6 (million)
% 1.30/0.60 % (4075597)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2624959911:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.30/0.60 % (4075592)Instruction limit reached!
% 1.30/0.60 % (4075592)------------------------------
% 1.30/0.60 % (4075592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.60 % (4075592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.60 % (4075592)CaDiCaL version: 2.1.3
% 1.30/0.60 % (4075592)Termination reason: Instruction limit
% 1.30/0.60 % (4075592)Termination phase: shuffling
% 1.30/0.60 % (4075592)Time elapsed: 0.006 s
% 1.30/0.60 % (4075592)Peak memory usage: 10 MB
% 1.30/0.60 % (4075592)Instructions burned: 12 (million)
% 1.30/0.60 % (4075575)Instruction limit reached!
% 1.30/0.60 % (4075575)------------------------------
% 1.30/0.60 % (4075575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.60 % (4075575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.60 % (4075575)CaDiCaL version: 2.1.3
% 1.30/0.60 % (4075575)Termination reason: Instruction limit
% 1.30/0.60 % (4075575)Termination phase: Preprocessing 3
% 1.30/0.60 % (4075575)Time elapsed: 0.040 s
% 1.30/0.60 % (4075575)Peak memory usage: 12 MB
% 1.30/0.60 % (4075575)Instructions burned: 87 (million)
% 1.30/0.60 % (4075597)Instruction limit reached!
% 1.30/0.60 % (4075597)------------------------------
% 1.30/0.60 % (4075597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.60 % (4075597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.60 % (4075597)CaDiCaL version: 2.1.3
% 1.30/0.60 % (4075597)Termination reason: Instruction limit
% 1.30/0.63 % (4075597)Termination phase: shuffling
% 1.30/0.63 % (4075597)Time elapsed: 0.007 s
% 1.30/0.63 % (4075597)Peak memory usage: 11 MB
% 1.30/0.63 % (4075597)Instructions burned: 31 (million)
% 1.30/0.63 % (4075598)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1909312149:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.30/0.63 % (4075604)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.30/0.63 % (4075606)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2454448098:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.30/0.63 % (4075603)lrs+10_1_si=on:cs=on:random_seed=1548414858:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.30/0.63 % (4075604)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3683228249:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.30/0.63 % (4075604)Instruction limit reached!
% 1.30/0.63 % (4075604)------------------------------
% 1.30/0.63 % (4075604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.63 % (4075604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.63 % (4075604)CaDiCaL version: 2.1.3
% 1.30/0.63 % (4075604)Termination reason: Instruction limit
% 1.30/0.63 % (4075604)Termination phase: shuffling
% 1.30/0.63 % (4075604)Time elapsed: 0.002 s
% 1.30/0.63 % (4075604)Peak memory usage: 10 MB
% 1.30/0.63 % (4075604)Instructions burned: 3 (million)
% 1.30/0.63 % (4075603)Instruction limit reached!
% 1.30/0.63 % (4075603)------------------------------
% 1.30/0.63 % (4075603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.63 % (4075603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.63 % (4075603)CaDiCaL version: 2.1.3
% 1.30/0.63 % (4075603)Termination reason: Instruction limit
% 1.30/0.63 % (4075603)Termination phase: shuffling
% 1.30/0.63 % (4075603)Time elapsed: 0.004 s
% 1.30/0.63 % (4075603)Peak memory usage: 10 MB
% 1.30/0.63 % (4075603)Instructions burned: 8 (million)
% 1.30/0.63 % (4075605)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=129183255:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.30/0.63 % (4075581)Instruction limit reached!
% 1.30/0.63 % (4075581)------------------------------
% 1.30/0.63 % (4075581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.63 % (4075581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.63 % (4075581)CaDiCaL version: 2.1.3
% 1.30/0.63 % (4075581)Termination reason: Instruction limit
% 1.30/0.63 % (4075581)Termination phase: Property scanning
% 1.30/0.63 % (4075581)Time elapsed: 0.073 s
% 1.30/0.63 % (4075581)Peak memory usage: 13 MB
% 1.30/0.63 % (4075581)Instructions burned: 158 (million)
% 1.30/0.63 % (4075605)Instruction limit reached!
% 1.30/0.63 % (4075605)------------------------------
% 1.30/0.63 % (4075605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.63 % (4075605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.63 % (4075605)CaDiCaL version: 2.1.3
% 1.30/0.63 % (4075605)Termination reason: Instruction limit
% 1.30/0.63 % (4075605)Termination phase: Property scanning
% 1.30/0.63 % (4075605)Time elapsed: 0.017 s
% 1.30/0.63 % (4075605)Peak memory usage: 11 MB
% 1.30/0.63 % (4075605)Instructions burned: 39 (million)
% 1.30/0.63 % (4075612)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2257167883:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.30/0.63 % (4075613)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=55057170:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.30/0.63 % (4075613)Instruction limit reached!
% 1.30/0.63 % (4075613)------------------------------
% 1.30/0.63 % (4075613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.63 % (4075613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.63 % (4075613)CaDiCaL version: 2.1.3
% 1.30/0.63 % (4075613)Termination reason: Instruction limit
% 1.30/0.63 % (4075613)Termination phase: shuffling
% 1.30/0.63 % (4075613)Time elapsed: 0.007 s
% 1.62/0.68 % (4075613)Peak memory usage: 10 MB
% 1.62/0.68 % (4075613)Instructions burned: 15 (million)
% 1.62/0.68 % (4075598)Instruction limit reached!
% 1.62/0.68 % (4075598)------------------------------
% 1.62/0.68 % (4075598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.68 % (4075598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.68 % (4075598)CaDiCaL version: 2.1.3
% 1.62/0.68 % (4075598)Termination reason: Instruction limit
% 1.62/0.68 % (4075598)Termination phase: Property scanning
% 1.62/0.68 % (4075598)Time elapsed: 0.040 s
% 1.62/0.68 % (4075598)Peak memory usage: 11 MB
% 1.62/0.68 % (4075598)Instructions burned: 87 (million)
% 1.62/0.68 % (4075612)Instruction limit reached!
% 1.62/0.68 % (4075612)------------------------------
% 1.62/0.68 % (4075612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.68 % (4075612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.68 % (4075612)CaDiCaL version: 2.1.3
% 1.62/0.68 % (4075612)Termination reason: Instruction limit
% 1.62/0.68 % (4075612)Termination phase: shuffling
% 1.62/0.68 % (4075612)Time elapsed: 0.011 s
% 1.62/0.68 % (4075612)Peak memory usage: 10 MB
% 1.62/0.68 % (4075612)Instructions burned: 26 (million)
% 1.62/0.68 % (4075614)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1934300933:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.62/0.68 % (4075615)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=401575346:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.62/0.68 % (4075615)Instruction limit reached!
% 1.62/0.68 % (4075615)------------------------------
% 1.62/0.68 % (4075615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.68 % (4075615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.68 % (4075615)CaDiCaL version: 2.1.3
% 1.62/0.68 % (4075615)Termination reason: Instruction limit
% 1.62/0.68 % (4075615)Termination phase: shuffling
% 1.62/0.68 % (4075615)Time elapsed: 0.007 s
% 1.62/0.68 % (4075615)Peak memory usage: 10 MB
% 1.62/0.68 % (4075615)Instructions burned: 16 (million)
% 1.62/0.68 % (4075621)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=292441248:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.62/0.68 % (4075606)Instruction limit reached!
% 1.62/0.68 % (4075606)------------------------------
% 1.62/0.68 % (4075606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.68 % (4075606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.68 % (4075606)CaDiCaL version: 2.1.3
% 1.62/0.68 % (4075606)Termination reason: Instruction limit
% 1.62/0.68 % (4075606)Termination phase: Saturation
% 1.62/0.68 % (4075606)Time elapsed: 0.056 s
% 1.62/0.68 % (4075606)Peak memory usage: 15 MB
% 1.62/0.68 % (4075606)Instructions burned: 250 (million)
% 1.62/0.68 % (4075625)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.62/0.68 % (4075625)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.62/0.68 % (4075621)Instruction limit reached!
% 1.62/0.68 % (4075621)------------------------------
% 1.62/0.68 % (4075621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.68 % (4075621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.68 % (4075621)CaDiCaL version: 2.1.3
% 1.62/0.68 % (4075621)Termination reason: Instruction limit
% 1.62/0.68 % (4075621)Termination phase: shuffling
% 1.62/0.68 % (4075621)Time elapsed: 0.010 s
% 1.62/0.68 % (4075621)Peak memory usage: 10 MB
% 1.62/0.68 % (4075621)Instructions burned: 23 (million)
% 1.62/0.68 % (4075625)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2297207504:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.62/0.68 % (4075623)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=166369477:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.62/0.68 % (4075618)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=961392439:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.70/0.74 % (4075625)Instruction limit reached!
% 1.70/0.74 % (4075625)------------------------------
% 1.70/0.74 % (4075625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.74 % (4075625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.74 % (4075625)CaDiCaL version: 2.1.3
% 1.70/0.74 % (4075625)Termination reason: Instruction limit
% 1.70/0.74 % (4075625)Termination phase: shuffling
% 1.70/0.74 % (4075625)Time elapsed: 0.004 s
% 1.70/0.74 % (4075625)Peak memory usage: 10 MB
% 1.70/0.74 % (4075625)Instructions burned: 17 (million)
% 1.70/0.74 % (4075618)Instruction limit reached!
% 1.70/0.74 % (4075618)------------------------------
% 1.70/0.74 % (4075618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.74 % (4075618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.74 % (4075618)CaDiCaL version: 2.1.3
% 1.70/0.74 % (4075618)Termination reason: Instruction limit
% 1.70/0.74 % (4075618)Termination phase: shuffling
% 1.70/0.74 % (4075618)Time elapsed: 0.002 s
% 1.70/0.74 % (4075618)Peak memory usage: 10 MB
% 1.70/0.74 % (4075618)Instructions burned: 3 (million)
% 1.70/0.74 % (4075619)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2588016577:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.70/0.74 % (4075626)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.70/0.74 % (4075630)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=4199998632:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.70/0.74 % (4075626)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=593221224:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.70/0.74 % (4075619)Instruction limit reached!
% 1.70/0.74 % (4075619)------------------------------
% 1.70/0.74 % (4075619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.74 % (4075619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.74 % (4075619)CaDiCaL version: 2.1.3
% 1.70/0.74 % (4075619)Termination reason: Instruction limit
% 1.70/0.74 % (4075619)Termination phase: shuffling
% 1.70/0.74 % (4075619)Time elapsed: 0.013 s
% 1.70/0.74 % (4075619)Peak memory usage: 11 MB
% 1.70/0.74 % (4075619)Instructions burned: 28 (million)
% 1.70/0.74 % (4075630)Instruction limit reached!
% 1.70/0.74 % (4075630)------------------------------
% 1.70/0.74 % (4075630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.74 % (4075630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.74 % (4075630)CaDiCaL version: 2.1.3
% 1.70/0.74 % (4075630)Termination reason: Instruction limit
% 1.70/0.74 % (4075630)Termination phase: shuffling
% 1.70/0.74 % (4075630)Time elapsed: 0.007 s
% 1.70/0.74 % (4075630)Peak memory usage: 11 MB
% 1.70/0.74 % (4075630)Instructions burned: 31 (million)
% 1.70/0.74 % (4075626)Instruction limit reached!
% 1.70/0.74 % (4075626)------------------------------
% 1.70/0.74 % (4075626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.74 % (4075626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.74 % (4075626)CaDiCaL version: 2.1.3
% 1.70/0.74 % (4075626)Termination reason: Instruction limit
% 1.70/0.74 % (4075626)Termination phase: shuffling
% 1.70/0.74 % (4075626)Time elapsed: 0.004 s
% 1.70/0.74 % (4075626)Peak memory usage: 10 MB
% 1.70/0.74 % (4075626)Instructions burned: 8 (million)
% 1.70/0.74 % (4075623)Instruction limit reached!
% 1.70/0.74 % (4075623)------------------------------
% 1.70/0.74 % (4075623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.74 % (4075623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.74 % (4075623)CaDiCaL version: 2.1.3
% 1.70/0.74 % (4075623)Termination reason: Instruction limit
% 1.70/0.74 % (4075623)Termination phase: Preprocessing 3
% 1.70/0.74 % (4075623)Time elapsed: 0.027 s
% 1.70/0.74 % (4075623)Peak memory usage: 12 MB
% 1.70/0.74 % (4075623)Instructions burned: 60 (million)
% 1.70/0.74 % (4075636)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2148854421:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.70/0.80 % (4075636)Instruction limit reached!
% 1.70/0.80 % (4075636)------------------------------
% 1.70/0.80 % (4075636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.80 % (4075636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.80 % (4075636)CaDiCaL version: 2.1.3
% 1.70/0.80 % (4075636)Termination reason: Instruction limit
% 1.70/0.80 % (4075636)Termination phase: shuffling
% 1.70/0.80 % (4075636)Time elapsed: 0.005 s
% 1.70/0.80 % (4075636)Peak memory usage: 10 MB
% 1.70/0.80 % (4075636)Instructions burned: 23 (million)
% 1.70/0.80 % (4075635)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=491635139:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.70/0.80 % (4075632)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2471979269:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.70/0.80 % (4075637)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1105429340:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.70/0.80 % (4075638)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3703106327:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.70/0.80 % (4075632)Instruction limit reached!
% 1.70/0.80 % (4075632)------------------------------
% 1.70/0.80 % (4075632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.80 % (4075632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.80 % (4075632)CaDiCaL version: 2.1.3
% 1.70/0.80 % (4075632)Termination reason: Instruction limit
% 1.70/0.80 % (4075632)Termination phase: shuffling
% 1.70/0.80 % (4075632)Time elapsed: 0.007 s
% 1.70/0.80 % (4075632)Peak memory usage: 10 MB
% 1.70/0.80 % (4075632)Instructions burned: 7 (million)
% 1.70/0.80 % (4075635)Instruction limit reached!
% 1.70/0.80 % (4075635)------------------------------
% 1.70/0.80 % (4075635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.80 % (4075635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.80 % (4075635)CaDiCaL version: 2.1.3
% 1.70/0.80 % (4075635)Termination reason: Instruction limit
% 1.70/0.80 % (4075635)Termination phase: shuffling
% 1.70/0.80 % (4075635)Time elapsed: 0.010 s
% 1.70/0.80 % (4075635)Peak memory usage: 10 MB
% 1.70/0.80 % (4075635)Instructions burned: 24 (million)
% 1.70/0.80 % (4075641)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3002195093:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.70/0.80 % (4075645)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3233326260:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.70/0.80 % (4075646)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.70/0.80 % (4075645)Instruction limit reached!
% 1.70/0.80 % (4075645)------------------------------
% 1.70/0.80 % (4075645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.80 % (4075645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.80 % (4075645)CaDiCaL version: 2.1.3
% 1.70/0.80 % (4075645)Termination reason: Instruction limit
% 1.70/0.80 % (4075645)Termination phase: Property scanning
% 1.70/0.80 % (4075645)Time elapsed: 0.011 s
% 1.70/0.80 % (4075645)Peak memory usage: 11 MB
% 1.70/0.80 % (4075645)Instructions burned: 46 (million)
% 1.70/0.80 % (4075646)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1797282133:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.70/0.80 % (4075646)Instruction limit reached!
% 1.70/0.80 % (4075646)------------------------------
% 1.70/0.80 % (4075646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.80 % (4075646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.80 % (4075646)CaDiCaL version: 2.1.3
% 1.70/0.80 % (4075646)Termination reason: Instruction limit
% 1.70/0.80 % (4075646)Termination phase: shuffling
% 1.70/0.80 % (4075646)Time elapsed: 0.004 s
% 1.70/0.80 % (4075646)Peak memory usage: 10 MB
% 1.70/0.80 % (4075646)Instructions burned: 8 (million)
% 1.70/0.80 % (4075652)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1416497980:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.46/0.88 % (4075655)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2314181827:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.46/0.88 % (4075638)Instruction limit reached!
% 2.46/0.88 % (4075638)------------------------------
% 2.46/0.88 % (4075638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.88 % (4075638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.88 % (4075638)CaDiCaL version: 2.1.3
% 2.46/0.88 % (4075638)Termination reason: Instruction limit
% 2.46/0.88 % (4075638)Termination phase: Twee Goal Transformation
% 2.46/0.88 % (4075638)Time elapsed: 0.060 s
% 2.46/0.88 % (4075638)Peak memory usage: 12 MB
% 2.46/0.88 % (4075638)Instructions burned: 144 (million)
% 2.46/0.88 % (4075614)Instruction limit reached!
% 2.46/0.88 % (4075614)------------------------------
% 2.46/0.88 % (4075614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.88 % (4075614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.88 % (4075614)CaDiCaL version: 2.1.3
% 2.46/0.88 % (4075614)Termination reason: Instruction limit
% 2.46/0.88 % (4075614)Termination phase: Saturation
% 2.46/0.88 % (4075614)Time elapsed: 0.143 s
% 2.46/0.88 % (4075614)Peak memory usage: 16 MB
% 2.46/0.88 % (4075614)Instructions burned: 327 (million)
% 2.46/0.88 % (4075652)Instruction limit reached!
% 2.46/0.88 % (4075652)------------------------------
% 2.46/0.88 % (4075652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.88 % (4075652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.88 % (4075652)CaDiCaL version: 2.1.3
% 2.46/0.88 % (4075652)Termination reason: Instruction limit
% 2.46/0.88 % (4075652)Termination phase: Saturation
% 2.46/0.88 % (4075652)Time elapsed: 0.040 s
% 2.46/0.88 % (4075652)Peak memory usage: 13 MB
% 2.46/0.88 % (4075652)Instructions burned: 181 (million)
% 2.46/0.88 % (4075673)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.46/0.88 % (4075673)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=638447958:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 2.46/0.88 % (4075680)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3145267401:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.46/0.88 % (4075676)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1356036338:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.46/0.88 % (4075673)Instruction limit reached!
% 2.46/0.88 % (4075673)------------------------------
% 2.46/0.88 % (4075673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.88 % (4075673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.88 % (4075673)CaDiCaL version: 2.1.3
% 2.46/0.88 % (4075673)Termination reason: Instruction limit
% 2.46/0.88 % (4075673)Termination phase: shuffling
% 2.46/0.88 % (4075673)Time elapsed: 0.004 s
% 2.46/0.88 % (4075673)Peak memory usage: 10 MB
% 2.46/0.88 % (4075673)Instructions burned: 8 (million)
% 2.46/0.88 % (4075641)Instruction limit reached!
% 2.46/0.88 % (4075641)------------------------------
% 2.46/0.88 % (4075641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.88 % (4075641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.88 % (4075641)CaDiCaL version: 2.1.3
% 2.46/0.88 % (4075641)Termination reason: Instruction limit
% 2.46/0.88 % (4075641)Termination phase: Property scanning
% 2.46/0.88 % (4075641)Time elapsed: 0.080 s
% 2.46/0.88 % (4075641)Peak memory usage: 12 MB
% 2.46/0.88 % (4075641)Instructions burned: 193 (million)
% 2.46/0.88 % (4075680)Instruction limit reached!
% 2.46/0.88 % (4075680)------------------------------
% 2.46/0.88 % (4075680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.88 % (4075680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.88 % (4075680)CaDiCaL version: 2.1.3
% 2.46/0.88 % (4075680)Termination reason: Instruction limit
% 2.46/0.88 % (4075680)Termination phase: shuffling
% 2.46/0.88 % (4075680)Time elapsed: 0.005 s
% 2.85/0.99 % (4075680)Peak memory usage: 10 MB
% 2.85/0.99 % (4075680)Instructions burned: 22 (million)
% 2.85/0.99 % (4075676)Instruction limit reached!
% 2.85/0.99 % (4075676)------------------------------
% 2.85/0.99 % (4075676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.99 % (4075676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.99 % (4075676)CaDiCaL version: 2.1.3
% 2.85/0.99 % (4075676)Termination reason: Instruction limit
% 2.85/0.99 % (4075676)Termination phase: shuffling
% 2.85/0.99 % (4075676)Time elapsed: 0.010 s
% 2.85/0.99 % (4075676)Peak memory usage: 10 MB
% 2.85/0.99 % (4075676)Instructions burned: 23 (million)
% 2.85/0.99 % (4075688)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=982850399:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.85/0.99 % (4075694)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=412600173:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.85/0.99 % (4075695)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1808601737:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.85/0.99 % (4075699)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2448472965:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.85/0.99 % (4075655)Instruction limit reached!
% 2.85/0.99 % (4075655)------------------------------
% 2.85/0.99 % (4075655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.99 % (4075655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.99 % (4075655)CaDiCaL version: 2.1.3
% 2.85/0.99 % (4075655)Termination reason: Instruction limit
% 2.85/0.99 % (4075655)Termination phase: Property scanning
% 2.85/0.99 % (4075655)Time elapsed: 0.071 s
% 2.85/0.99 % (4075655)Peak memory usage: 12 MB
% 2.85/0.99 % (4075655)Instructions burned: 169 (million)
% 2.85/0.99 % (4075695)Instruction limit reached!
% 2.85/0.99 % (4075695)------------------------------
% 2.85/0.99 % (4075695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.99 % (4075695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.99 % (4075695)CaDiCaL version: 2.1.3
% 2.85/0.99 % (4075695)Termination reason: Instruction limit
% 2.85/0.99 % (4075695)Termination phase: Property scanning
% 2.85/0.99 % (4075695)Time elapsed: 0.020 s
% 2.85/0.99 % (4075695)Peak memory usage: 11 MB
% 2.85/0.99 % (4075695)Instructions burned: 47 (million)
% 2.85/0.99 % (4075710)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3074252334:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.85/0.99 % (4075715)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.85/0.99 % (4075710)Instruction limit reached!
% 2.85/0.99 % (4075710)------------------------------
% 2.85/0.99 % (4075710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.99 % (4075710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.99 % (4075710)CaDiCaL version: 2.1.3
% 2.85/0.99 % (4075710)Termination reason: Instruction limit
% 2.85/0.99 % (4075710)Termination phase: shuffling
% 2.85/0.99 % (4075710)Time elapsed: 0.010 s
% 2.85/0.99 % (4075710)Peak memory usage: 10 MB
% 2.85/0.99 % (4075710)Instructions burned: 23 (million)
% 2.85/0.99 % (4075715)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=462160591:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.85/0.99 % (4075578)Instruction limit reached!
% 2.85/0.99 % (4075578)------------------------------
% 2.85/0.99 % (4075578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.99 % (4075578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.99 % (4075578)CaDiCaL version: 2.1.3
% 2.85/0.99 % (4075578)Termination reason: Instruction limit
% 2.85/0.99 % (4075578)Termination phase: Saturation
% 5.03/1.17 % (4075578)Time elapsed: 0.323 s
% 5.03/1.17 % (4075578)Peak memory usage: 21 MB
% 5.03/1.17 % (4075578)Instructions burned: 635 (million)
% 5.03/1.17 % (4075727)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2269008538:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 5.03/1.17 % (4075727)Instruction limit reached!
% 5.03/1.17 % (4075727)------------------------------
% 5.03/1.17 % (4075727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.03/1.17 % (4075727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.17 % (4075727)CaDiCaL version: 2.1.3
% 5.03/1.17 % (4075727)Termination reason: Instruction limit
% 5.03/1.17 % (4075727)Termination phase: shuffling
% 5.03/1.17 % (4075727)Time elapsed: 0.004 s
% 5.03/1.17 % (4075727)Peak memory usage: 11 MB
% 5.03/1.17 % (4075727)Instructions burned: 17 (million)
% 5.03/1.17 % (4075729)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1300889700:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 5.03/1.17 % (4075739)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=114918979:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 5.03/1.17 % (4075739)Instruction limit reached!
% 5.03/1.17 % (4075739)------------------------------
% 5.03/1.17 % (4075739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.03/1.17 % (4075739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.17 % (4075739)CaDiCaL version: 2.1.3
% 5.03/1.17 % (4075739)Termination reason: Instruction limit
% 5.03/1.17 % (4075739)Termination phase: Property scanning
% 5.03/1.17 % (4075739)Time elapsed: 0.012 s
% 5.03/1.17 % (4075739)Peak memory usage: 11 MB
% 5.03/1.17 % (4075739)Instructions burned: 52 (million)
% 5.03/1.17 % (4075750)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1402187151:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 5.03/1.17 % (4075729)Instruction limit reached!
% 5.03/1.17 % (4075729)------------------------------
% 5.03/1.17 % (4075729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.03/1.17 % (4075729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.17 % (4075729)CaDiCaL version: 2.1.3
% 5.03/1.17 % (4075729)Termination reason: Instruction limit
% 5.03/1.17 % (4075729)Termination phase: Property scanning
% 5.03/1.17 % (4075729)Time elapsed: 0.028 s
% 5.03/1.17 % (4075729)Peak memory usage: 11 MB
% 5.03/1.17 % (4075729)Instructions burned: 66 (million)
% 5.03/1.17 % (4075750)Instruction limit reached!
% 5.03/1.17 % (4075750)------------------------------
% 5.03/1.17 % (4075750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.03/1.17 % (4075750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.17 % (4075750)CaDiCaL version: 2.1.3
% 5.03/1.17 % (4075750)Termination reason: Instruction limit
% 5.03/1.17 % (4075750)Termination phase: shuffling
% 5.03/1.17 % (4075750)Time elapsed: 0.007 s
% 5.03/1.17 % (4075750)Peak memory usage: 11 MB
% 5.03/1.17 % (4075750)Instructions burned: 32 (million)
% 5.03/1.17 % (4075757)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3410256591:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 5.03/1.17 % (4075754)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3643657650:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 5.03/1.17 % (4075757)Instruction limit reached!
% 5.03/1.17 % (4075757)------------------------------
% 5.03/1.17 % (4075757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.03/1.17 % (4075757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.17 % (4075757)CaDiCaL version: 2.1.3
% 5.03/1.17 % (4075757)Termination reason: Instruction limit
% 5.03/1.17 % (4075757)Termination phase: shuffling
% 5.03/1.17 % (4075757)Time elapsed: 0.008 s
% 5.03/1.17 % (4075757)Peak memory usage: 11 MB
% 5.03/1.17 % (4075757)Instructions burned: 37 (million)
% 5.03/1.17 % (4075715)Instruction limit reached!
% 5.03/1.17 % (4075715)------------------------------
% 5.03/1.17 % (4075715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.03/1.17 % (4075715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.23 % (4075715)CaDiCaL version: 2.1.3
% 5.32/1.23 % (4075715)Termination reason: Instruction limit
% 5.32/1.23 % (4075715)Termination phase: Saturation
% 5.32/1.23 % (4075715)Time elapsed: 0.084 s
% 5.32/1.23 % (4075715)Peak memory usage: 14 MB
% 5.32/1.23 % (4075715)Instructions burned: 200 (million)
% 5.32/1.23 % (4075767)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3602195518:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.32/1.23 % (4075688)Instruction limit reached!
% 5.32/1.23 % (4075688)------------------------------
% 5.32/1.23 % (4075688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.23 % (4075688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.23 % (4075688)CaDiCaL version: 2.1.3
% 5.32/1.23 % (4075688)Termination reason: Instruction limit
% 5.32/1.23 % (4075688)Termination phase: Saturation
% 5.32/1.23 % (4075688)Time elapsed: 0.140 s
% 5.32/1.23 % (4075688)Peak memory usage: 16 MB
% 5.32/1.23 % (4075688)Instructions burned: 317 (million)
% 5.32/1.23 % (4075771)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.32/1.23 % (4075767)Instruction limit reached!
% 5.32/1.23 % (4075767)------------------------------
% 5.32/1.23 % (4075767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.23 % (4075767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.23 % (4075767)CaDiCaL version: 2.1.3
% 5.32/1.23 % (4075767)Termination reason: Instruction limit
% 5.32/1.23 % (4075767)Termination phase: Property scanning
% 5.32/1.23 % (4075767)Time elapsed: 0.015 s
% 5.32/1.23 % (4075767)Peak memory usage: 11 MB
% 5.32/1.23 % (4075767)Instructions burned: 67 (million)
% 5.32/1.23 % (4075771)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=2075292263:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 5.32/1.23 % (4075779)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=492946103:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 5.32/1.23 % (4075778)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=751010396:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 5.32/1.23 % (4075754)Instruction limit reached!
% 5.32/1.23 % (4075754)------------------------------
% 5.32/1.23 % (4075754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.23 % (4075754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.23 % (4075754)CaDiCaL version: 2.1.3
% 5.32/1.23 % (4075754)Termination reason: Instruction limit
% 5.32/1.23 % (4075754)Termination phase: Twee Goal Transformation
% 5.32/1.23 % (4075754)Time elapsed: 0.057 s
% 5.32/1.23 % (4075754)Peak memory usage: 12 MB
% 5.32/1.23 % (4075754)Instructions burned: 137 (million)
% 5.32/1.23 % (4075779)Instruction limit reached!
% 5.32/1.23 % (4075779)------------------------------
% 5.32/1.23 % (4075779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.23 % (4075779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.23 % (4075779)CaDiCaL version: 2.1.3
% 5.32/1.23 % (4075779)Termination reason: Instruction limit
% 5.32/1.23 % (4075779)Termination phase: Property scanning
% 5.32/1.23 % (4075779)Time elapsed: 0.021 s
% 5.32/1.23 % (4075779)Peak memory usage: 12 MB
% 5.32/1.23 % (4075779)Instructions burned: 96 (million)
% 5.32/1.23 % (4075793)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=28275195:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.32/1.23 % (4075789)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2947562236:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 5.32/1.23 % (4075771)Instruction limit reached!
% 5.32/1.23 % (4075771)------------------------------
% 5.32/1.23 % (4075771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.23 % (4075771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.23 % (4075771)CaDiCaL version: 2.1.3
% 5.32/1.23 % (4075771)Termination reason: Instruction limit
% 5.32/1.23 % (4075771)Termination phase: Saturation
% 5.32/1.23 % (4075771)Time elapsed: 0.073 s
% 5.32/1.23 % (4075771)Peak memory usage: 13 MB
% 5.32/1.23 % (4075771)Instructions burned: 181 (million)
% 5.32/1.23 % (4075810)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2583771934:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.86/1.31 % (4075699)Instruction limit reached!
% 5.86/1.31 % (4075699)------------------------------
% 5.86/1.31 % (4075699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.31 % (4075699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.31 % (4075699)CaDiCaL version: 2.1.3
% 5.86/1.31 % (4075699)Termination reason: Instruction limit
% 5.86/1.31 % (4075699)Termination phase: Saturation
% 5.86/1.31 % (4075699)Time elapsed: 0.238 s
% 5.86/1.31 % (4075699)Peak memory usage: 19 MB
% 5.86/1.31 % (4075699)Instructions burned: 486 (million)
% 5.86/1.31 % (4075778)Instruction limit reached!
% 5.86/1.31 % (4075778)------------------------------
% 5.86/1.31 % (4075778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.31 % (4075778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.31 % (4075778)CaDiCaL version: 2.1.3
% 5.86/1.31 % (4075778)Termination reason: Instruction limit
% 5.86/1.31 % (4075778)Termination phase: Saturation
% 5.86/1.31 % (4075778)Time elapsed: 0.104 s
% 5.86/1.31 % (4075778)Peak memory usage: 14 MB
% 5.86/1.31 % (4075778)Instructions burned: 246 (million)
% 5.86/1.31 % (4075828)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=15698982:st=1.5:i=130:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/130Mi)
% 5.86/1.31 % (4075840)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3042583405:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 5.86/1.31 % (4075840)Instruction limit reached!
% 5.86/1.31 % (4075840)------------------------------
% 5.86/1.31 % (4075840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.31 % (4075840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.31 % (4075840)CaDiCaL version: 2.1.3
% 5.86/1.31 % (4075840)Termination reason: Instruction limit
% 5.86/1.31 % (4075840)Termination phase: shuffling
% 5.86/1.31 % (4075840)Time elapsed: 0.020 s
% 5.86/1.31 % (4075840)Peak memory usage: 11 MB
% 5.86/1.31 % (4075840)Instructions burned: 44 (million)
% 5.86/1.31 % (4075828)Instruction limit reached!
% 5.86/1.31 % (4075828)------------------------------
% 5.86/1.31 % (4075828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.31 % (4075828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.31 % (4075828)CaDiCaL version: 2.1.3
% 5.86/1.31 % (4075828)Termination reason: Instruction limit
% 5.86/1.31 % (4075828)Termination phase: Property scanning
% 5.86/1.31 % (4075828)Time elapsed: 0.054 s
% 5.86/1.31 % (4075828)Peak memory usage: 12 MB
% 5.86/1.31 % (4075828)Instructions burned: 132 (million)
% 5.86/1.31 % (4075854)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=492106731:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 5.86/1.31 % (4075855)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=348781899:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 5.86/1.31 % (4075789)Instruction limit reached!
% 5.86/1.31 % (4075789)------------------------------
% 5.86/1.31 % (4075789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.31 % (4075789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.31 % (4075789)CaDiCaL version: 2.1.3
% 5.86/1.31 % (4075789)Termination reason: Instruction limit
% 5.86/1.31 % (4075789)Termination phase: Saturation
% 5.86/1.31 % (4075789)Time elapsed: 0.196 s
% 5.86/1.31 % (4075789)Peak memory usage: 16 MB
% 5.86/1.31 % (4075789)Instructions burned: 427 (million)
% 5.86/1.31 % (4075858)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1078697588:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/95Mi)
% 5.86/1.31 % (4075793)Instruction limit reached!
% 5.86/1.31 % (4075793)------------------------------
% 5.86/1.31 % (4075793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.86/1.31 % (4075793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.31 % (4075793)CaDiCaL version: 2.1.3
% 5.86/1.31 % (4075793)Termination reason: Instruction limit
% 5.86/1.31 % (4075793)Termination phase: Saturation
% 5.86/1.31 % (4075793)Time elapsed: 0.224 s
% 5.86/1.31 % (4075793)Peak memory usage: 17 MB
% 5.86/1.31 % (4075793)Instructions burned: 874 (million)
% 6.49/1.45 % (4075860)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=1192328160:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 6.49/1.45 % (4075860)Instruction limit reached!
% 6.49/1.45 % (4075860)------------------------------
% 6.49/1.45 % (4075860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.45 % (4075860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.45 % (4075860)CaDiCaL version: 2.1.3
% 6.49/1.45 % (4075860)Termination reason: Instruction limit
% 6.49/1.45 % (4075860)Termination phase: Property scanning
% 6.49/1.45 % (4075860)Time elapsed: 0.015 s
% 6.49/1.45 % (4075860)Peak memory usage: 11 MB
% 6.49/1.45 % (4075860)Instructions burned: 68 (million)
% 6.49/1.45 % (4075694)Instruction limit reached!
% 6.49/1.45 % (4075694)------------------------------
% 6.49/1.45 % (4075694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.45 % (4075694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.45 % (4075694)CaDiCaL version: 2.1.3
% 6.49/1.45 % (4075694)Termination reason: Instruction limit
% 6.49/1.45 % (4075694)Termination phase: Saturation
% 6.49/1.45 % (4075694)Time elapsed: 0.443 s
% 6.49/1.45 % (4075694)Peak memory usage: 23 MB
% 6.49/1.45 % (4075694)Instructions burned: 853 (million)
% 6.49/1.45 % (4075858)Instruction limit reached!
% 6.49/1.45 % (4075858)------------------------------
% 6.49/1.45 % (4075858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.45 % (4075858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.45 % (4075858)CaDiCaL version: 2.1.3
% 6.49/1.45 % (4075858)Termination reason: Instruction limit
% 6.49/1.45 % (4075858)Termination phase: Property scanning
% 6.49/1.45 % (4075858)Time elapsed: 0.040 s
% 6.49/1.45 % (4075858)Peak memory usage: 12 MB
% 6.49/1.45 % (4075858)Instructions burned: 95 (million)
% 6.49/1.45 % (4075862)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=3264782281:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2992 on theBenchmark for (2992ds/105Mi)
% 6.49/1.45 % (4075863)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=50184298:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 6.49/1.45 % (4075864)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=439403635:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 6.49/1.45 % (4075637)Instruction limit reached!
% 6.49/1.45 % (4075637)------------------------------
% 6.49/1.45 % (4075637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.45 % (4075637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.45 % (4075637)CaDiCaL version: 2.1.3
% 6.49/1.45 % (4075637)Termination reason: Instruction limit
% 6.49/1.45 % (4075637)Termination phase: Saturation
% 6.49/1.45 % (4075637)Time elapsed: 0.583 s
% 6.49/1.45 % (4075637)Peak memory usage: 20 MB
% 6.49/1.45 % (4075637)Instructions burned: 1241 (million)
% 6.49/1.45 % (4075862)Instruction limit reached!
% 6.49/1.45 % (4075862)------------------------------
% 6.49/1.45 % (4075862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.45 % (4075862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.45 % (4075862)CaDiCaL version: 2.1.3
% 6.49/1.45 % (4075862)Termination reason: Instruction limit
% 6.49/1.45 % (4075862)Termination phase: Property scanning
% 6.49/1.45 % (4075862)Time elapsed: 0.023 s
% 6.49/1.45 % (4075862)Peak memory usage: 12 MB
% 6.49/1.45 % (4075862)Instructions burned: 106 (million)
% 6.49/1.45 % (4075810)Instruction limit reached!
% 6.49/1.45 % (4075810)------------------------------
% 6.49/1.45 % (4075810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.45 % (4075810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.45 % (4075810)CaDiCaL version: 2.1.3
% 6.49/1.45 % (4075810)Termination reason: Instruction limit
% 6.49/1.45 % (4075810)Termination phase: Saturation
% 6.49/1.45 % (4075810)Time elapsed: 0.235 s
% 7.18/1.54 % (4075810)Peak memory usage: 16 MB
% 7.18/1.54 % (4075810)Instructions burned: 516 (million)
% 7.18/1.54 % (4075869)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3151215695:cond=on:i=34:hud=10:nm=10:rtra=on_2991 on theBenchmark for (2991ds/34Mi)
% 7.18/1.54 % (4075868)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1906819035:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/495Mi)
% 7.18/1.54 % (4075869)Instruction limit reached!
% 7.18/1.54 % (4075869)------------------------------
% 7.18/1.54 % (4075869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.18/1.54 % (4075869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.54 % (4075869)CaDiCaL version: 2.1.3
% 7.18/1.54 % (4075869)Termination reason: Instruction limit
% 7.18/1.54 % (4075869)Termination phase: shuffling
% 7.18/1.54 % (4075869)Time elapsed: 0.008 s
% 7.18/1.54 % (4075869)Peak memory usage: 11 MB
% 7.18/1.54 % (4075869)Instructions burned: 36 (million)
% 7.18/1.54 % (4075870)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=4128643694:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/91Mi)
% 7.18/1.54 % (4075873)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=670043147:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2991 on theBenchmark for (2991ds/66Mi)
% 7.18/1.54 % (4075873)Instruction limit reached!
% 7.18/1.54 % (4075873)------------------------------
% 7.18/1.54 % (4075873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.18/1.54 % (4075873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.54 % (4075873)CaDiCaL version: 2.1.3
% 7.18/1.54 % (4075873)Termination reason: Instruction limit
% 7.18/1.54 % (4075873)Termination phase: Preprocessing 3
% 7.18/1.54 % (4075873)Time elapsed: 0.015 s
% 7.18/1.54 % (4075873)Peak memory usage: 12 MB
% 7.18/1.54 % (4075873)Instructions burned: 66 (million)
% 7.18/1.54 % (4075876)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1696118467:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2991 on theBenchmark for (2991ds/22Mi)
% 7.18/1.54 % (4075855)Instruction limit reached!
% 7.18/1.54 % (4075855)------------------------------
% 7.18/1.54 % (4075855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.18/1.54 % (4075855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.54 % (4075855)CaDiCaL version: 2.1.3
% 7.18/1.54 % (4075855)Termination reason: Instruction limit
% 7.18/1.54 % (4075855)Termination phase: Saturation
% 7.18/1.54 % (4075855)Time elapsed: 0.194 s
% 7.18/1.54 % (4075855)Peak memory usage: 19 MB
% 7.18/1.54 % (4075855)Instructions burned: 451 (million)
% 7.18/1.54 % (4075870)Instruction limit reached!
% 7.18/1.54 % (4075870)------------------------------
% 7.18/1.54 % (4075870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.18/1.54 % (4075870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.54 % (4075870)CaDiCaL version: 2.1.3
% 7.18/1.54 % (4075870)Termination reason: Instruction limit
% 7.18/1.54 % (4075870)Termination phase: SInE selection
% 7.18/1.54 % (4075870)Time elapsed: 0.039 s
% 7.18/1.54 % (4075870)Peak memory usage: 12 MB
% 7.18/1.54 % (4075870)Instructions burned: 91 (million)
% 7.18/1.54 % (4075876)Instruction limit reached!
% 7.18/1.54 % (4075876)------------------------------
% 7.18/1.54 % (4075876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.18/1.54 % (4075876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.18/1.54 % (4075876)CaDiCaL version: 2.1.3
% 7.18/1.54 % (4075876)Termination reason: Instruction limit
% 7.18/1.54 % (4075876)Termination phase: shuffling
% 7.18/1.54 % (4075876)Time elapsed: 0.006 s
% 7.18/1.54 % (4075876)Peak memory usage: 11 MB
% 7.18/1.54 % (4075876)Instructions burned: 27 (million)
% 7.18/1.54 % (4075880)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 7.18/1.54 % (4075880)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=708148432:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/137Mi)
% 7.18/1.54 % (4075878)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=2652791308:i=338:bd=all:ins=4:rtra=on_2991 on theBenchmark for (2991ds/338Mi)
% 7.68/1.70 % (4075879)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2814361858:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/28Mi)
% 7.68/1.70 % (4075879)Instruction limit reached!
% 7.68/1.70 % (4075879)------------------------------
% 7.68/1.70 % (4075879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.68/1.70 % (4075879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.68/1.70 % (4075879)CaDiCaL version: 2.1.3
% 7.68/1.70 % (4075879)Termination reason: Instruction limit
% 7.68/1.70 % (4075879)Termination phase: shuffling
% 7.68/1.70 % (4075879)Time elapsed: 0.013 s
% 7.68/1.70 % (4075879)Peak memory usage: 11 MB
% 7.68/1.70 % (4075879)Instructions burned: 29 (million)
% 7.68/1.70 % (4075880)Instruction limit reached!
% 7.68/1.70 % (4075880)------------------------------
% 7.68/1.70 % (4075880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.68/1.70 % (4075880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.68/1.70 % (4075880)CaDiCaL version: 2.1.3
% 7.68/1.70 % (4075880)Termination reason: Instruction limit
% 7.68/1.70 % (4075880)Termination phase: Property scanning
% 7.68/1.70 % (4075880)Time elapsed: 0.030 s
% 7.68/1.70 % (4075880)Peak memory usage: 12 MB
% 7.68/1.70 % (4075880)Instructions burned: 139 (million)
% 7.68/1.70 % (4075885)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=3645439563:i=227:sd=1:bd=all:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/227Mi)
% 7.68/1.70 % (4075884)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=1015087080:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2990 on theBenchmark for (2990ds/340Mi)
% 7.68/1.70 % (4075854)Instruction limit reached!
% 7.68/1.70 % (4075854)------------------------------
% 7.68/1.70 % (4075854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.68/1.70 % (4075854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.68/1.70 % (4075854)CaDiCaL version: 2.1.3
% 7.68/1.70 % (4075854)Termination reason: Instruction limit
% 7.68/1.70 % (4075854)Termination phase: Saturation
% 7.68/1.70 % (4075854)Time elapsed: 0.283 s
% 7.68/1.70 % (4075854)Peak memory usage: 19 MB
% 7.68/1.70 % (4075854)Instructions burned: 571 (million)
% 7.68/1.70 % (4075888)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 7.68/1.70 % (4075888)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2773768277:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/373Mi)
% 7.68/1.70 % (4075864)Instruction limit reached!
% 7.68/1.70 % (4075864)------------------------------
% 7.68/1.70 % (4075864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.68/1.70 % (4075864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.68/1.70 % (4075864)CaDiCaL version: 2.1.3
% 7.68/1.70 % (4075864)Termination reason: Instruction limit
% 7.68/1.70 % (4075864)Termination phase: Saturation
% 7.68/1.70 % (4075864)Time elapsed: 0.172 s
% 7.68/1.70 % (4075864)Peak memory usage: 16 MB
% 7.68/1.70 % (4075864)Instructions burned: 377 (million)
% 7.68/1.70 % (4075885)Instruction limit reached!
% 7.68/1.70 % (4075885)------------------------------
% 7.68/1.70 % (4075885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.68/1.70 % (4075885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.68/1.70 % (4075885)CaDiCaL version: 2.1.3
% 7.68/1.70 % (4075885)Termination reason: Instruction limit
% 7.68/1.70 % (4075885)Termination phase: Saturation
% 7.68/1.70 % (4075885)Time elapsed: 0.051 s
% 7.68/1.70 % (4075885)Peak memory usage: 15 MB
% 7.68/1.70 % (4075885)Instructions burned: 231 (million)
% 7.68/1.70 % (4075891)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1794641719:i=575:rtra=on_2990 on theBenchmark for (2990ds/575Mi)
% 7.68/1.70 % (4075890)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1500229672:i=116:ep=RSTC:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/116Mi)
% 7.68/1.70 % (4075878)Instruction limit reached!
% 7.68/1.70 % (4075878)------------------------------
% 7.68/1.70 % (4075878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.89 % (4075878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.89 % (4075878)CaDiCaL version: 2.1.3
% 8.42/1.89 % (4075878)Termination reason: Instruction limit
% 8.42/1.89 % (4075878)Termination phase: Saturation
% 8.42/1.89 % (4075878)Time elapsed: 0.142 s
% 8.42/1.89 % (4075878)Peak memory usage: 18 MB
% 8.42/1.89 % (4075878)Instructions burned: 340 (million)
% 8.42/1.89 % (4075890)Instruction limit reached!
% 8.42/1.89 % (4075890)------------------------------
% 8.42/1.89 % (4075890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.89 % (4075890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.89 % (4075890)CaDiCaL version: 2.1.3
% 8.42/1.89 % (4075890)Termination reason: Instruction limit
% 8.42/1.89 % (4075890)Termination phase: Property scanning
% 8.42/1.89 % (4075890)Time elapsed: 0.054 s
% 8.42/1.89 % (4075890)Peak memory usage: 14 MB
% 8.42/1.89 % (4075890)Instructions burned: 117 (million)
% 8.42/1.89 % (4075894)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3659617278:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2989 on theBenchmark for (2989ds/270Mi)
% 8.42/1.89 % (4075895)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2580011728:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2989 on theBenchmark for (2989ds/9840Mi)
% 8.42/1.89 % (4075868)Instruction limit reached!
% 8.42/1.89 % (4075868)------------------------------
% 8.42/1.89 % (4075868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.89 % (4075868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.89 % (4075868)CaDiCaL version: 2.1.3
% 8.42/1.89 % (4075868)Termination reason: Instruction limit
% 8.42/1.89 % (4075868)Termination phase: Saturation
% 8.42/1.89 % (4075868)Time elapsed: 0.244 s
% 8.42/1.89 % (4075868)Peak memory usage: 18 MB
% 8.42/1.89 % (4075868)Instructions burned: 497 (million)
% 8.42/1.89 % (4075884)Instruction limit reached!
% 8.42/1.89 % (4075884)------------------------------
% 8.42/1.89 % (4075884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.89 % (4075884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.89 % (4075884)CaDiCaL version: 2.1.3
% 8.42/1.89 % (4075884)Termination reason: Instruction limit
% 8.42/1.89 % (4075884)Termination phase: Saturation
% 8.42/1.89 % (4075884)Time elapsed: 0.146 s
% 8.42/1.89 % (4075884)Peak memory usage: 15 MB
% 8.42/1.89 % (4075884)Instructions burned: 342 (million)
% 8.42/1.89 % (4075899)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.42/1.89 % (4075898)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=4051393749:i=421:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/421Mi)
% 8.42/1.89 % (4075899)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=4142433113:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/270Mi)
% 8.42/1.89 % (4075891)Instruction limit reached!
% 8.42/1.89 % (4075891)------------------------------
% 8.42/1.89 % (4075891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.89 % (4075891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.89 % (4075891)CaDiCaL version: 2.1.3
% 8.42/1.89 % (4075891)Termination reason: Instruction limit
% 8.42/1.89 % (4075891)Termination phase: Saturation
% 8.42/1.89 % (4075891)Time elapsed: 0.134 s
% 8.42/1.89 % (4075891)Peak memory usage: 17 MB
% 8.42/1.89 % (4075891)Instructions burned: 579 (million)
% 8.42/1.89 % (4075888)Instruction limit reached!
% 8.42/1.89 % (4075888)------------------------------
% 8.42/1.89 % (4075888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.89 % (4075888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.89 % (4075888)CaDiCaL version: 2.1.3
% 8.42/1.89 % (4075888)Termination reason: Instruction limit
% 8.42/1.89 % (4075888)Termination phase: Saturation
% 8.42/1.89 % (4075888)Time elapsed: 0.160 s
% 8.42/1.89 % (4075888)Peak memory usage: 14 MB
% 11.23/2.06 % (4075888)Instructions burned: 374 (million)
% 11.23/2.06 % (4075903)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 11.23/2.06 % (4075903)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 11.23/2.06 % (4075903)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=817989822:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2988 on theBenchmark for (2988ds/1440Mi)
% 11.23/2.06 % (4075902)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=145916432:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/31Mi)
% 11.23/2.06 % (4075902)Instruction limit reached!
% 11.23/2.06 % (4075902)------------------------------
% 11.23/2.06 % (4075902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.23/2.06 % (4075902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.23/2.06 % (4075902)CaDiCaL version: 2.1.3
% 11.23/2.06 % (4075902)Termination reason: Instruction limit
% 11.23/2.06 % (4075902)Termination phase: shuffling
% 11.23/2.06 % (4075902)Time elapsed: 0.014 s
% 11.23/2.06 % (4075902)Peak memory usage: 11 MB
% 11.23/2.06 % (4075902)Instructions burned: 32 (million)
% 11.23/2.06 % (4075894)Instruction limit reached!
% 11.23/2.06 % (4075894)------------------------------
% 11.23/2.06 % (4075894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.23/2.06 % (4075894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.23/2.06 % (4075894)CaDiCaL version: 2.1.3
% 11.23/2.06 % (4075894)Termination reason: Instruction limit
% 11.23/2.06 % (4075894)Termination phase: Saturation
% 11.23/2.06 % (4075894)Time elapsed: 0.111 s
% 11.23/2.06 % (4075894)Peak memory usage: 14 MB
% 11.23/2.06 % (4075894)Instructions burned: 271 (million)
% 11.23/2.06 % (4075906)dis+10_2_sil=128000:si=on:random_seed=100391120:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2988 on theBenchmark for (2988ds/339Mi)
% 11.23/2.06 % (4075907)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=3730647036:i=111:add=on:fgj=on:rtra=on:fdi=1024_2988 on theBenchmark for (2988ds/111Mi)
% 11.23/2.06 % (4075899)Instruction limit reached!
% 11.23/2.06 % (4075899)------------------------------
% 11.23/2.06 % (4075899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.23/2.06 % (4075899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.23/2.06 % (4075899)CaDiCaL version: 2.1.3
% 11.23/2.06 % (4075899)Termination reason: Instruction limit
% 11.23/2.06 % (4075899)Termination phase: Saturation
% 11.23/2.06 % (4075899)Time elapsed: 0.115 s
% 11.23/2.06 % (4075899)Peak memory usage: 15 MB
% 11.23/2.06 % (4075899)Instructions burned: 271 (million)
% 11.23/2.06 % (4075910)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3539868549:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2987 on theBenchmark for (2987ds/122Mi)
% 11.23/2.06 % (4075907)Instruction limit reached!
% 11.23/2.06 % (4075907)------------------------------
% 11.23/2.06 % (4075907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.23/2.06 % (4075907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.23/2.06 % (4075907)CaDiCaL version: 2.1.3
% 11.23/2.06 % (4075907)Termination reason: Instruction limit
% 11.23/2.06 % (4075907)Termination phase: Property scanning
% 11.23/2.06 % (4075907)Time elapsed: 0.047 s
% 11.23/2.06 % (4075907)Peak memory usage: 12 MB
% 11.23/2.06 % (4075907)Instructions burned: 111 (million)
% 11.23/2.06 % (4075912)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=847886238:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/136Mi)
% 11.23/2.06 % (4075910)Instruction limit reached!
% 11.23/2.06 % (4075910)------------------------------
% 11.23/2.06 % (4075910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.23/2.06 % (4075910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.23/2.06 % (4075910)CaDiCaL version: 2.1.3
% 11.23/2.06 % (4075910)Termination reason: Instruction limit
% 11.23/2.06 % (4075910)Termination phase: Property scanning
% 12.41/2.25 % (4075910)Time elapsed: 0.052 s
% 12.41/2.25 % (4075910)Peak memory usage: 12 MB
% 12.41/2.25 % (4075910)Instructions burned: 123 (million)
% 12.41/2.25 % (4075898)Instruction limit reached!
% 12.41/2.25 % (4075898)------------------------------
% 12.41/2.25 % (4075898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.41/2.25 % (4075898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.25 % (4075898)CaDiCaL version: 2.1.3
% 12.41/2.25 % (4075898)Termination reason: Instruction limit
% 12.41/2.25 % (4075898)Termination phase: Saturation
% 12.41/2.25 % (4075898)Time elapsed: 0.192 s
% 12.41/2.25 % (4075898)Peak memory usage: 16 MB
% 12.41/2.25 % (4075898)Instructions burned: 422 (million)
% 12.41/2.25 % (4075914)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2201707057:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2987 on theBenchmark for (2987ds/232Mi)
% 12.41/2.25 % (4075915)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=197193863:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2986 on theBenchmark for (2986ds/1254Mi)
% 12.41/2.25 % (4075912)Instruction limit reached!
% 12.41/2.25 % (4075912)------------------------------
% 12.41/2.25 % (4075912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.41/2.25 % (4075912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.25 % (4075912)CaDiCaL version: 2.1.3
% 12.41/2.25 % (4075912)Termination reason: Instruction limit
% 12.41/2.25 % (4075912)Termination phase: Property scanning
% 12.41/2.25 % (4075912)Time elapsed: 0.057 s
% 12.41/2.25 % (4075912)Peak memory usage: 12 MB
% 12.41/2.25 % (4075912)Instructions burned: 138 (million)
% 12.41/2.25 % (4075906)Instruction limit reached!
% 12.41/2.25 % (4075906)------------------------------
% 12.41/2.25 % (4075906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.41/2.25 % (4075906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.25 % (4075906)CaDiCaL version: 2.1.3
% 12.41/2.25 % (4075906)Termination reason: Instruction limit
% 12.41/2.25 % (4075906)Termination phase: Saturation
% 12.41/2.25 % (4075906)Time elapsed: 0.149 s
% 12.41/2.25 % (4075906)Peak memory usage: 15 MB
% 12.41/2.25 % (4075906)Instructions burned: 340 (million)
% 12.41/2.25 % (4075918)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 12.41/2.25 % (4075918)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=816255102:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2986 on theBenchmark for (2986ds/281Mi)
% 12.41/2.25 % (4075919)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=93702822:i=619:add=on:rtra=on_2986 on theBenchmark for (2986ds/619Mi)
% 12.41/2.25 % (4075914)Instruction limit reached!
% 12.41/2.25 % (4075914)------------------------------
% 12.41/2.25 % (4075914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.41/2.25 % (4075914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.25 % (4075914)CaDiCaL version: 2.1.3
% 12.41/2.25 % (4075914)Termination reason: Instruction limit
% 12.41/2.25 % (4075914)Termination phase: Saturation
% 12.41/2.25 % (4075914)Time elapsed: 0.102 s
% 12.41/2.25 % (4075914)Peak memory usage: 15 MB
% 12.41/2.25 % (4075914)Instructions burned: 234 (million)
% 12.41/2.25 % (4075922)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=264376047:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/865Mi)
% 12.41/2.25 % (4075918)Instruction limit reached!
% 12.41/2.25 % (4075918)------------------------------
% 12.41/2.25 % (4075918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.41/2.25 % (4075918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.41/2.25 % (4075918)CaDiCaL version: 2.1.3
% 12.41/2.25 % (4075918)Termination reason: Instruction limit
% 12.41/2.25 % (4075918)Termination phase: Saturation
% 12.41/2.25 % (4075918)Time elapsed: 0.115 s
% 12.41/2.25 % (4075918)Peak memory usage: 13 MB
% 12.41/2.25 % (4075918)Instructions burned: 283 (million)
% 12.41/2.25 % (4075924)lrs+10_1_sil=128000:si=on:urr=on:random_seed=412813087:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/212Mi)
% 13.85/2.45 % (4075903)Instruction limit reached!
% 13.85/2.45 % (4075903)------------------------------
% 13.85/2.45 % (4075903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.45 % (4075903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.45 % (4075903)CaDiCaL version: 2.1.3
% 13.85/2.45 % (4075903)Termination reason: Instruction limit
% 13.85/2.45 % (4075903)Termination phase: Saturation
% 13.85/2.45 % (4075903)Time elapsed: 0.342 s
% 13.85/2.45 % (4075903)Peak memory usage: 27 MB
% 13.85/2.45 % (4075903)Instructions burned: 1441 (million)
% 13.85/2.45 % (4075926)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=3698290781:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/130Mi)
% 13.85/2.45 % (4075926)Instruction limit reached!
% 13.85/2.45 % (4075926)------------------------------
% 13.85/2.45 % (4075926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.45 % (4075926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.45 % (4075926)CaDiCaL version: 2.1.3
% 13.85/2.45 % (4075926)Termination reason: Instruction limit
% 13.85/2.45 % (4075926)Termination phase: Property scanning
% 13.85/2.45 % (4075926)Time elapsed: 0.029 s
% 13.85/2.45 % (4075926)Peak memory usage: 12 MB
% 13.85/2.45 % (4075926)Instructions burned: 133 (million)
% 13.85/2.45 % (4075928)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2850329203:st=1.5:i=346:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/346Mi)
% 13.85/2.45 % (4075924)Instruction limit reached!
% 13.85/2.45 % (4075924)------------------------------
% 13.85/2.45 % (4075924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.45 % (4075924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.45 % (4075924)CaDiCaL version: 2.1.3
% 13.85/2.45 % (4075924)Termination reason: Instruction limit
% 13.85/2.45 % (4075924)Termination phase: Saturation
% 13.85/2.45 % (4075924)Time elapsed: 0.090 s
% 13.85/2.45 % (4075924)Peak memory usage: 14 MB
% 13.85/2.45 % (4075924)Instructions burned: 213 (million)
% 13.85/2.45 % (4075930)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=1247636198:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2984 on theBenchmark for (2984ds/152Mi)
% 13.85/2.45 % (4075928)Instruction limit reached!
% 13.85/2.45 % (4075928)------------------------------
% 13.85/2.45 % (4075928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.45 % (4075928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.45 % (4075928)CaDiCaL version: 2.1.3
% 13.85/2.45 % (4075928)Termination reason: Instruction limit
% 13.85/2.45 % (4075928)Termination phase: Saturation
% 13.85/2.45 % (4075928)Time elapsed: 0.077 s
% 13.85/2.45 % (4075928)Peak memory usage: 16 MB
% 13.85/2.45 % (4075928)Instructions burned: 349 (million)
% 13.85/2.45 % (4075919)Instruction limit reached!
% 13.85/2.45 % (4075919)------------------------------
% 13.85/2.45 % (4075919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.45 % (4075919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.45 % (4075919)CaDiCaL version: 2.1.3
% 13.85/2.45 % (4075919)Termination reason: Instruction limit
% 13.85/2.45 % (4075919)Termination phase: Saturation
% 13.85/2.45 % (4075919)Time elapsed: 0.265 s
% 13.85/2.45 % (4075919)Peak memory usage: 16 MB
% 13.85/2.45 % (4075919)Instructions burned: 621 (million)
% 13.85/2.45 % (4075932)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3550903574:i=75:ep=R:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/75Mi)
% 13.85/2.45 % (4075933)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=744977931:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2983 on theBenchmark for (2983ds/387Mi)
% 13.85/2.45 % (4075932)Instruction limit reached!
% 13.85/2.45 % (4075932)------------------------------
% 13.85/2.45 % (4075932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.45 % (4075932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.45 % (4075932)CaDiCaL version: 2.1.3
% 13.85/2.45 % (4075932)Termination reason: Instruction limit
% 13.85/2.45 % (4075932)Termination phase: Property scanning
% 13.85/2.45 % (4075932)Time elapsed: 0.017 s
% 13.85/2.45 % (4075932)Peak memory usage: 11 MB
% 13.85/2.45 % (4075932)Instructions burned: 76 (million)
% 13.85/2.45 % (4075930)Instruction limit reached!
% 13.85/2.45 % (4075930)------------------------------
% 13.85/2.45 % (4075930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075930)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075930)Termination reason: Instruction limit
% 13.85/2.46 % (4075930)Termination phase: Property scanning
% 13.85/2.46 % (4075930)Time elapsed: 0.065 s
% 13.85/2.46 % (4075930)Peak memory usage: 12 MB
% 13.85/2.46 % (4075930)Instructions burned: 153 (million)
% 13.85/2.46 % (4075936)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3375635948:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2983 on theBenchmark for (2983ds/148Mi)
% 13.85/2.46 % (4075937)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=1999427469:i=161:piset=and:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/161Mi)
% 13.85/2.46 % (4075936)Instruction limit reached!
% 13.85/2.46 % (4075936)------------------------------
% 13.85/2.46 % (4075936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075936)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075936)Termination reason: Instruction limit
% 13.85/2.46 % (4075936)Termination phase: Saturation
% 13.85/2.46 % (4075936)Time elapsed: 0.032 s
% 13.85/2.46 % (4075936)Peak memory usage: 13 MB
% 13.85/2.46 % (4075936)Instructions burned: 151 (million)
% 13.85/2.46 % (4075940)lrs+10_1_sil=128000:si=on:random_seed=359126834:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2983 on theBenchmark for (2983ds/888Mi)
% 13.85/2.46 % (4075937)Instruction limit reached!
% 13.85/2.46 % (4075937)------------------------------
% 13.85/2.46 % (4075937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075937)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075937)Termination reason: Instruction limit
% 13.85/2.46 % (4075937)Termination phase: Saturation
% 13.85/2.46 % (4075937)Time elapsed: 0.067 s
% 13.85/2.46 % (4075937)Peak memory usage: 13 MB
% 13.85/2.46 % (4075937)Instructions burned: 163 (million)
% 13.85/2.46 % (4075942)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=3878567450:i=136:add=on:ins=4:rtra=on:sup=off_2982 on theBenchmark for (2982ds/136Mi)
% 13.85/2.46 % (4075933)Instruction limit reached!
% 13.85/2.46 % (4075933)------------------------------
% 13.85/2.46 % (4075933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075933)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075933)Termination reason: Instruction limit
% 13.85/2.46 % (4075933)Termination phase: Saturation
% 13.85/2.46 % (4075933)Time elapsed: 0.158 s
% 13.85/2.46 % (4075933)Peak memory usage: 16 MB
% 13.85/2.46 % (4075933)Instructions burned: 388 (million)
% 13.85/2.46 % (4075942)Instruction limit reached!
% 13.85/2.46 % (4075942)------------------------------
% 13.85/2.46 % (4075942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075942)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075942)Termination reason: Instruction limit
% 13.85/2.46 % (4075942)Termination phase: Property scanning
% 13.85/2.46 % (4075942)Time elapsed: 0.057 s
% 13.85/2.46 % (4075942)Peak memory usage: 12 MB
% 13.85/2.46 % (4075942)Instructions burned: 136 (million)
% 13.85/2.46 % (4075944)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1181818076:i=88:s2at=3:nm=2:rtra=on:rawr=on_2981 on theBenchmark for (2981ds/88Mi)
% 13.85/2.46 % (4075946)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2051153919:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2981 on theBenchmark for (2981ds/93Mi)
% 13.85/2.46 % (4075922)Instruction limit reached!
% 13.85/2.46 % (4075922)------------------------------
% 13.85/2.46 % (4075922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075922)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075922)Termination reason: Instruction limit
% 13.85/2.46 % (4075922)Termination phase: Saturation
% 13.85/2.46 % (4075922)Time elapsed: 0.410 s
% 13.85/2.46 % (4075922)Peak memory usage: 23 MB
% 13.85/2.46 % (4075922)Instructions burned: 866 (million)
% 13.85/2.46 % (4075944)Instruction limit reached!
% 13.85/2.46 % (4075944)------------------------------
% 13.85/2.46 % (4075944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075944)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075944)Termination reason: Instruction limit
% 13.85/2.46 % (4075944)Termination phase: SInE selection
% 13.85/2.46 % (4075944)Time elapsed: 0.038 s
% 13.85/2.46 % (4075944)Peak memory usage: 12 MB
% 13.85/2.46 % (4075944)Instructions burned: 90 (million)
% 13.85/2.46 % (4075948)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=110657987:i=2186:rtra=on:ixr=off_2981 on theBenchmark for (2981ds/2186Mi)
% 13.85/2.46 % (4075949)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=164653397:s2a=on:i=240:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/240Mi)
% 13.85/2.46 % (4075946)Instruction limit reached!
% 13.85/2.46 % (4075946)------------------------------
% 13.85/2.46 % (4075946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075946)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075946)Termination reason: Instruction limit
% 13.85/2.46 % (4075946)Termination phase: SInE selection
% 13.85/2.46 % (4075946)Time elapsed: 0.039 s
% 13.85/2.46 % (4075946)Peak memory usage: 12 MB
% 13.85/2.46 % (4075946)Instructions burned: 93 (million)
% 13.85/2.46 % (4075952)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=3931940744:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2981 on theBenchmark for (2981ds/805Mi)
% 13.85/2.46 % (4075940)Instruction limit reached!
% 13.85/2.46 % (4075940)------------------------------
% 13.85/2.46 % (4075940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075940)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075940)Termination reason: Instruction limit
% 13.85/2.46 % (4075940)Termination phase: Saturation
% 13.85/2.46 % (4075940)Time elapsed: 0.231 s
% 13.85/2.46 % (4075940)Peak memory usage: 19 MB
% 13.85/2.46 % (4075940)Instructions burned: 888 (million)
% 13.85/2.46 % (4075954)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 13.85/2.46 % (4075954)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=38746017:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2980 on theBenchmark for (2980ds/391Mi)
% 13.85/2.46 % (4075915) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4075570-4075915"...
% 13.85/2.46 % (4075949)Instruction limit reached!
% 13.85/2.46 % (4075949)------------------------------
% 13.85/2.46 % (4075949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075949)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075949)Termination reason: Instruction limit
% 13.85/2.46 % (4075949)Termination phase: Saturation
% 13.85/2.46 % (4075949)Time elapsed: 0.106 s
% 13.85/2.46 % (4075949)Peak memory usage: 16 MB
% 13.85/2.46 % (4075949)Instructions burned: 242 (million)
% 13.85/2.46 % (4075956)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=1097829606:i=355:av=off:fsr=off:rtra=on:ixr=off_2980 on theBenchmark for (2980ds/355Mi)
% 13.85/2.46 % (4075954)Instruction limit reached!
% 13.85/2.46 % (4075954)------------------------------
% 13.85/2.46 % (4075954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.46 % (4075954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.46 % (4075954)CaDiCaL version: 2.1.3
% 13.85/2.46 % (4075954)Termination reason: Instruction limit
% 13.85/2.46 % (4075954)Termination phase: Saturation
% 13.85/2.46 % (4075954)Time elapsed: 0.087 s
% 13.85/2.46 % (4075954)Peak memory usage: 15 MB
% 13.85/2.46 % (4075954)Instructions burned: 393 (million)
% 13.85/2.46 % (4075958)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=3413541948:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2979 on theBenchmark for (2979ds/314Mi)
% 13.85/2.46 % (4075915)...printing done.
% 13.85/2.46 % (4075915)Refutation found. Thanks to Tanya!
% 13.85/2.46 % SZS status Theorem for theBenchmark
% 13.85/2.46 % SZS output start Proof for theBenchmark
% 13.85/2.46 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 13.85/2.46 thf(func_def_0, type, in: ($i > $i > $o)).
% 13.85/2.46 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 13.85/2.46 thf(func_def_3, type, setextAx: $o).
% 13.85/2.46 thf(func_def_5, type, emptysetAx: $o).
% 13.85/2.46 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 13.85/2.46 thf(func_def_7, type, setadjoinAx: $o).
% 13.85/2.46 thf(func_def_8, type, powerset: ($i > $i)).
% 13.85/2.46 thf(func_def_9, type, powersetAx: $o).
% 13.85/2.46 thf(func_def_10, type, setunion: ($i > $i)).
% 13.85/2.46 thf(func_def_11, type, setunionAx: $o).
% 13.85/2.46 thf(func_def_13, type, omega0Ax: $o).
% 13.85/2.46 thf(func_def_14, type, omegaSAx: $o).
% 13.85/2.46 thf(func_def_15, type, omegaIndAx: $o).
% 13.85/2.46 thf(func_def_16, type, replAx: $o).
% 13.85/2.46 thf(func_def_17, type, foundationAx: $o).
% 13.85/2.46 thf(func_def_18, type, wellorderingAx: $o).
% 13.85/2.46 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 13.85/2.46 thf(func_def_20, type, descrp: $o).
% 13.85/2.46 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 13.85/2.46 thf(func_def_22, type, dsetconstrI: $o).
% 13.85/2.46 thf(func_def_23, type, dsetconstrEL: $o).
% 13.85/2.46 thf(func_def_24, type, dsetconstrER: $o).
% 13.85/2.46 thf(func_def_25, type, exuE1: $o).
% 13.85/2.46 thf(func_def_26, type, prop2set: ($o > $i)).
% 13.85/2.46 thf(func_def_27, type, prop2setE: $o).
% 13.85/2.46 thf(func_def_28, type, emptysetE: $o).
% 13.85/2.46 thf(func_def_29, type, emptysetimpfalse: $o).
% 13.85/2.46 thf(func_def_30, type, notinemptyset: $o).
% 13.85/2.46 thf(func_def_31, type, exuE3e: $o).
% 13.85/2.46 thf(func_def_32, type, setext: $o).
% 13.85/2.46 thf(func_def_33, type, emptyI: $o).
% 13.85/2.46 thf(func_def_34, type, noeltsimpempty: $o).
% 13.85/2.46 thf(func_def_35, type, setbeta: $o).
% 13.85/2.46 thf(func_def_36, type, nonempty: ($i > $o)).
% 13.85/2.46 thf(func_def_37, type, nonemptyE1: $o).
% 13.85/2.46 thf(func_def_38, type, nonemptyI: $o).
% 13.85/2.46 thf(func_def_39, type, nonemptyI1: $o).
% 13.85/2.46 thf(func_def_40, type, setadjoinIL: $o).
% 13.85/2.46 thf(func_def_41, type, emptyinunitempty: $o).
% 13.85/2.46 thf(func_def_42, type, setadjoinIR: $o).
% 13.85/2.46 thf(func_def_43, type, setadjoinE: $o).
% 13.85/2.46 thf(func_def_44, type, setadjoinOr: $o).
% 13.85/2.46 thf(func_def_45, type, setoftrueEq: $o).
% 13.85/2.46 thf(func_def_46, type, powersetI: $o).
% 13.85/2.46 thf(func_def_47, type, emptyinPowerset: $o).
% 13.85/2.46 thf(func_def_48, type, emptyInPowerset: $o).
% 13.85/2.46 thf(func_def_49, type, powersetE: $o).
% 13.85/2.46 thf(func_def_50, type, setunionI: $o).
% 13.85/2.46 thf(func_def_51, type, setunionE: $o).
% 13.85/2.46 thf(func_def_52, type, subPowSU: $o).
% 13.85/2.46 thf(func_def_53, type, exuE2: $o).
% 13.85/2.46 thf(func_def_54, type, nonemptyImpWitness: $o).
% 13.85/2.46 thf(func_def_55, type, uniqinunit: $o).
% 13.85/2.46 thf(func_def_56, type, notinsingleton: $o).
% 13.85/2.46 thf(func_def_57, type, eqinunit: $o).
% 13.85/2.46 thf(func_def_58, type, singletonsswitch: $o).
% 13.85/2.46 thf(func_def_59, type, upairsetE: $o).
% 13.85/2.46 thf(func_def_60, type, upairsetIL: $o).
% 13.85/2.46 thf(func_def_61, type, upairsetIR: $o).
% 13.85/2.46 thf(func_def_62, type, emptyE1: $o).
% 13.85/2.46 thf(func_def_63, type, vacuousDall: $o).
% 13.85/2.46 thf(func_def_64, type, quantDeMorgan1: $o).
% 13.85/2.46 thf(func_def_65, type, quantDeMorgan2: $o).
% 13.85/2.46 thf(func_def_66, type, quantDeMorgan3: $o).
% 13.85/2.46 thf(func_def_67, type, quantDeMorgan4: $o).
% 13.85/2.46 thf(func_def_68, type, prop2setI: $o).
% 13.85/2.46 thf(func_def_69, type, set2prop: ($i > $o)).
% 13.85/2.46 thf(func_def_70, type, prop2set2propI: $o).
% 13.85/2.46 thf(func_def_71, type, notdexE: $o).
% 13.85/2.46 thf(func_def_72, type, notdallE: $o).
% 13.85/2.46 thf(func_def_73, type, exuI1: $o).
% 13.85/2.46 thf(func_def_74, type, exuI3: $o).
% 13.85/2.46 thf(func_def_75, type, exuI2: $o).
% 13.85/2.46 thf(func_def_76, type, inCongP: $o).
% 13.85/2.46 thf(func_def_77, type, in__Cong: $o).
% 13.85/2.46 thf(func_def_78, type, exuE3u: $o).
% 13.85/2.46 thf(func_def_79, type, exu__Cong: $o).
% 13.85/2.46 thf(func_def_80, type, emptyset__Cong: $o).
% 13.85/2.46 thf(func_def_81, type, setadjoin__Cong: $o).
% 13.85/2.46 thf(func_def_82, type, powerset__Cong: $o).
% 13.85/2.46 thf(func_def_83, type, setunion__Cong: $o).
% 13.85/2.46 thf(func_def_84, type, omega__Cong: $o).
% 13.85/2.46 thf(func_def_85, type, exuEu: $o).
% 13.85/2.46 thf(func_def_86, type, descr__Cong: $o).
% 13.85/2.46 thf(func_def_87, type, dsetconstr__Cong: $o).
% 13.85/2.46 thf(func_def_88, type, subset: ($i > $i > $o)).
% 13.85/2.46 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 13.85/2.46 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 13.85/2.46 thf(func_def_91, type, subsetI1: $o).
% 13.85/2.46 thf(func_def_92, type, eqimpsubset2: $o).
% 13.85/2.46 thf(func_def_93, type, eqimpsubset1: $o).
% 13.85/2.46 thf(func_def_94, type, subsetI2: $o).
% 13.85/2.46 thf(func_def_95, type, emptysetsubset: $o).
% 13.85/2.46 thf(func_def_96, type, subsetE: $o).
% 13.85/2.46 thf(func_def_97, type, subsetE2: $o).
% 13.85/2.46 thf(func_def_98, type, notsubsetI: $o).
% 13.85/2.46 thf(func_def_99, type, notequalI1: $o).
% 13.85/2.46 thf(func_def_100, type, notequalI2: $o).
% 13.85/2.46 thf(func_def_101, type, subsetRefl: $o).
% 13.85/2.46 thf(func_def_102, type, subsetTrans: $o).
% 13.85/2.46 thf(func_def_103, type, setadjoinSub: $o).
% 13.85/2.46 thf(func_def_104, type, setadjoinSub2: $o).
% 13.85/2.46 thf(func_def_105, type, subset2powerset: $o).
% 13.85/2.46 thf(func_def_106, type, setextsub: $o).
% 13.85/2.46 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 13.85/2.46 thf(func_def_108, type, powersetI1: $o).
% 13.85/2.46 thf(func_def_109, type, powersetE1: $o).
% 13.85/2.46 thf(func_def_110, type, inPowerset: $o).
% 13.85/2.46 thf(func_def_111, type, powersetsubset: $o).
% 13.85/2.46 thf(func_def_112, type, sepInPowerset: $o).
% 13.85/2.46 thf(func_def_113, type, sepSubset: $o).
% 13.85/2.46 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 13.85/2.46 thf(func_def_115, type, binunionIL: $o).
% 13.85/2.46 thf(func_def_116, type, upairset2IR: $o).
% 13.85/2.46 thf(func_def_117, type, binunionIR: $o).
% 13.85/2.46 thf(func_def_118, type, binunionEcases: $o).
% 13.85/2.46 thf(func_def_119, type, binunionE: $o).
% 13.85/2.46 thf(func_def_120, type, binunionLsub: $o).
% 13.85/2.46 thf(func_def_121, type, binunionRsub: $o).
% 13.85/2.46 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 13.85/2.46 thf(func_def_123, type, binintersectI: $o).
% 13.85/2.46 thf(func_def_124, type, binintersectSubset5: $o).
% 13.85/2.46 thf(func_def_125, type, binintersectEL: $o).
% 13.85/2.46 thf(func_def_126, type, binintersectLsub: $o).
% 13.85/2.46 thf(func_def_127, type, binintersectSubset2: $o).
% 13.85/2.46 thf(func_def_128, type, binintersectSubset3: $o).
% 13.85/2.46 thf(func_def_129, type, binintersectER: $o).
% 13.85/2.46 thf(func_def_130, type, disjointsetsI1: $o).
% 13.85/2.46 thf(func_def_131, type, binintersectRsub: $o).
% 13.85/2.46 thf(func_def_132, type, binintersectSubset4: $o).
% 13.85/2.46 thf(func_def_133, type, binintersectSubset1: $o).
% 13.85/2.46 thf(func_def_134, type, bs114d: $o).
% 13.85/2.46 thf(func_def_135, type, regular: ($i > $o)).
% 13.85/2.46 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 13.85/2.46 thf(func_def_137, type, setminusI: $o).
% 13.85/2.46 thf(func_def_138, type, setminusEL: $o).
% 13.85/2.46 thf(func_def_139, type, setminusER: $o).
% 13.85/2.46 thf(func_def_140, type, setminusSubset2: $o).
% 13.85/2.46 thf(func_def_141, type, setminusERneg: $o).
% 13.85/2.46 thf(func_def_142, type, setminusELneg: $o).
% 13.85/2.46 thf(func_def_143, type, setminusILneg: $o).
% 13.85/2.46 thf(func_def_144, type, setminusIRneg: $o).
% 13.85/2.46 thf(func_def_145, type, setminusLsub: $o).
% 13.85/2.46 thf(func_def_146, type, setminusSubset1: $o).
% 13.85/2.46 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 13.85/2.46 thf(func_def_148, type, symdiffE: $o).
% 13.85/2.46 thf(func_def_149, type, symdiffI1: $o).
% 13.85/2.46 thf(func_def_150, type, symdiffI2: $o).
% 13.85/2.46 thf(func_def_151, type, symdiffIneg1: $o).
% 13.85/2.46 thf(func_def_152, type, symdiffIneg2: $o).
% 13.85/2.46 thf(func_def_153, type, iskpair: ($i > $o)).
% 13.85/2.46 thf(func_def_154, type, secondinupair: $o).
% 13.85/2.46 thf(func_def_155, type, setukpairIL: $o).
% 13.85/2.46 thf(func_def_156, type, setukpairIR: $o).
% 13.85/2.46 thf(func_def_157, type, kpairiskpair: $o).
% 13.85/2.46 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 13.85/2.46 thf(func_def_159, type, kpairp: $o).
% 13.85/2.46 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 13.85/2.46 thf(func_def_161, type, singletonsubset: $o).
% 13.85/2.46 thf(func_def_162, type, singletoninpowerset: $o).
% 13.85/2.46 thf(func_def_163, type, singletoninpowunion: $o).
% 13.85/2.46 thf(func_def_164, type, upairset2E: $o).
% 13.85/2.46 thf(func_def_165, type, upairsubunion: $o).
% 13.85/2.46 thf(func_def_166, type, upairinpowunion: $o).
% 13.85/2.46 thf(func_def_167, type, ubforcartprodlem1: $o).
% 13.85/2.46 thf(func_def_168, type, ubforcartprodlem2: $o).
% 13.85/2.46 thf(func_def_169, type, ubforcartprodlem3: $o).
% 13.85/2.46 thf(func_def_170, type, cartprodpairin: $o).
% 13.85/2.46 thf(func_def_171, type, cartprodmempair1: $o).
% 13.85/2.46 thf(func_def_172, type, cartprodmempair: $o).
% 13.85/2.46 thf(func_def_173, type, setunionE2: $o).
% 13.85/2.46 thf(func_def_174, type, setunionsingleton1: $o).
% 13.85/2.46 thf(func_def_175, type, setunionsingleton2: $o).
% 13.85/2.46 thf(func_def_176, type, setunionsingleton: $o).
% 13.85/2.46 thf(func_def_177, type, singleton: ($i > $o)).
% 13.85/2.46 thf(func_def_178, type, singletonprop: $o).
% 13.85/2.46 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 13.85/2.46 thf(func_def_180, type, ex1E1: $o).
% 13.85/2.46 thf(func_def_181, type, ex1I: $o).
% 13.85/2.46 thf(func_def_182, type, ex1I2: $o).
% 13.85/2.46 thf(func_def_183, type, singletonsuniq: $o).
% 13.85/2.46 thf(func_def_184, type, atmost1p: ($i > $o)).
% 13.85/2.46 thf(func_def_185, type, atleast2p: ($i > $o)).
% 13.85/2.46 thf(func_def_186, type, atmost2p: ($i > $o)).
% 13.85/2.46 thf(func_def_187, type, upairsetp: ($i > $o)).
% 13.85/2.46 thf(func_def_188, type, setukpairinjL1: $o).
% 13.85/2.46 thf(func_def_189, type, kfstsingleton: $o).
% 13.85/2.46 thf(func_def_190, type, theprop: $o).
% 13.85/2.46 thf(func_def_191, type, kfst: ($i > $i)).
% 13.85/2.46 thf(func_def_192, type, kfstpairEq: $o).
% 13.85/2.46 thf(func_def_193, type, cartprodfstin: $o).
% 13.85/2.46 thf(func_def_194, type, setukpairinjL2: $o).
% 13.85/2.46 thf(func_def_195, type, setukpairinjL: $o).
% 13.85/2.46 thf(func_def_196, type, setukpairinjR11: $o).
% 13.85/2.46 thf(func_def_197, type, setukpairinjR12: $o).
% 13.85/2.46 thf(func_def_198, type, setukpairinjR1: $o).
% 13.85/2.46 thf(func_def_199, type, upairequniteq: $o).
% 13.85/2.46 thf(func_def_200, type, setukpairinjR2: $o).
% 13.85/2.46 thf(func_def_201, type, setukpairinjR: $o).
% 13.85/2.46 thf(func_def_202, type, ksndsingleton: $o).
% 13.85/2.46 thf(func_def_203, type, ksnd: ($i > $i)).
% 13.85/2.46 thf(func_def_204, type, ksndpairEq: $o).
% 13.85/2.46 thf(func_def_205, type, kpairsurjEq: $o).
% 13.85/2.46 thf(func_def_206, type, cartprodsndin: $o).
% 13.85/2.46 thf(func_def_207, type, cartprodpairmemEL: $o).
% 13.85/2.46 thf(func_def_208, type, cartprodpairmemER: $o).
% 13.85/2.46 thf(func_def_209, type, cartprodmempaircEq: $o).
% 13.85/2.46 thf(func_def_210, type, cartprodfstpairEq: $o).
% 13.85/2.46 thf(func_def_211, type, cartprodsndpairEq: $o).
% 13.85/2.46 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 13.85/2.46 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 13.85/2.46 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 13.85/2.46 thf(func_def_215, type, dpsetconstrI: $o).
% 13.85/2.46 thf(func_def_216, type, dpsetconstrSub: $o).
% 13.85/2.46 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 13.85/2.46 thf(func_def_218, type, dpsetconstrERa: $o).
% 13.85/2.46 thf(func_def_219, type, dpsetconstrEL1: $o).
% 13.85/2.46 thf(func_def_220, type, dpsetconstrEL2: $o).
% 13.85/2.46 thf(func_def_221, type, dpsetconstrER: $o).
% 13.85/2.46 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 13.85/2.46 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 13.85/2.46 thf(func_def_224, type, funcImageSingleton: $o).
% 13.85/2.46 thf(func_def_225, type, apProp: $o).
% 13.85/2.46 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 13.85/2.46 thf(func_def_227, type, app: $o).
% 13.85/2.46 thf(func_def_228, type, infuncsetfunc: $o).
% 13.85/2.46 thf(func_def_229, type, ap2p: $o).
% 13.85/2.46 thf(func_def_230, type, funcinfuncset: $o).
% 13.85/2.46 thf(func_def_231, type, lamProp: $o).
% 13.85/2.46 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 13.85/2.46 thf(func_def_233, type, lamp: $o).
% 13.85/2.46 thf(func_def_234, type, lam2p: $o).
% 13.85/2.46 thf(func_def_235, type, brelnall1: $o).
% 13.85/2.46 thf(func_def_236, type, brelnall2: $o).
% 13.85/2.46 thf(func_def_237, type, ex1E2: $o).
% 13.85/2.46 thf(func_def_238, type, funcGraphProp1: $o).
% 13.85/2.46 thf(func_def_239, type, funcGraphProp3: $o).
% 13.85/2.46 thf(func_def_240, type, funcGraphProp2: $o).
% 13.85/2.46 thf(func_def_241, type, funcextLem: $o).
% 13.85/2.46 thf(func_def_242, type, funcGraphProp4: $o).
% 13.85/2.46 thf(func_def_243, type, subbreln: $o).
% 13.85/2.46 thf(func_def_244, type, eqbreln: $o).
% 13.85/2.46 thf(func_def_245, type, funcext: $o).
% 13.85/2.46 thf(func_def_246, type, funcext2: $o).
% 13.85/2.46 thf(func_def_247, type, ap2apEq1: $o).
% 13.85/2.46 thf(func_def_248, type, ap2apEq2: $o).
% 13.85/2.46 thf(func_def_249, type, beta1: $o).
% 13.85/2.46 thf(func_def_250, type, eta1: $o).
% 13.85/2.46 thf(func_def_251, type, lam2lamEq: $o).
% 13.85/2.46 thf(func_def_252, type, beta2: $o).
% 13.85/2.46 thf(func_def_253, type, eta2: $o).
% 13.85/2.46 thf(func_def_254, type, iffalseProp1: $o).
% 13.85/2.46 thf(func_def_255, type, iffalseProp2: $o).
% 13.85/2.46 thf(func_def_256, type, iftrueProp1: $o).
% 13.85/2.46 thf(func_def_257, type, iftrueProp2: $o).
% 13.85/2.46 thf(func_def_258, type, ifSingleton: $o).
% 13.85/2.46 thf(func_def_259, type, if: ($i > $o > $i > $i > $i)).
% 13.85/2.46 thf(func_def_260, type, ifp: $o).
% 13.85/2.46 thf(func_def_261, type, theeq: $o).
% 13.85/2.46 thf(func_def_262, type, iftrue: $o).
% 13.85/2.46 thf(func_def_263, type, iffalse: $o).
% 13.85/2.46 thf(func_def_264, type, iftrueorfalse: $o).
% 13.85/2.46 thf(func_def_265, type, binintersectT_lem: $o).
% 13.85/2.46 thf(func_def_266, type, binunionT_lem: $o).
% 13.85/2.46 thf(func_def_267, type, powersetT_lem: $o).
% 13.85/2.46 thf(func_def_268, type, setminusT_lem: $o).
% 13.85/2.46 thf(func_def_269, type, complementT_lem: $o).
% 13.85/2.46 thf(func_def_270, type, setextT: $o).
% 13.85/2.46 thf(func_def_271, type, subsetTI: $o).
% 13.85/2.46 thf(func_def_272, type, powersetTI1: $o).
% 13.85/2.46 thf(func_def_273, type, powersetTE1: $o).
% 13.85/2.46 thf(func_def_274, type, complementTI1: $o).
% 13.85/2.46 thf(func_def_275, type, complementTE1: $o).
% 13.85/2.46 thf(func_def_276, type, binintersectTELcontra: $o).
% 13.85/2.46 thf(func_def_277, type, binintersectTERcontra: $o).
% 13.85/2.46 thf(func_def_278, type, contrasubsetT: $o).
% 13.85/2.46 thf(func_def_279, type, contrasubsetT1: $o).
% 13.85/2.46 thf(func_def_280, type, contrasubsetT2: $o).
% 13.85/2.46 thf(func_def_281, type, contrasubsetT3: $o).
% 13.85/2.46 thf(func_def_282, type, doubleComplementI1: $o).
% 13.85/2.47 thf(func_def_283, type, doubleComplementE1: $o).
% 13.85/2.47 thf(func_def_284, type, doubleComplementSub1: $o).
% 13.85/2.47 thf(func_def_285, type, doubleComplementSub2: $o).
% 13.85/2.47 thf(func_def_286, type, doubleComplementEq: $o).
% 13.85/2.47 thf(func_def_287, type, complementTnotintersectT: $o).
% 13.85/2.47 thf(func_def_288, type, complementImpComplementIntersect: $o).
% 13.85/2.47 thf(func_def_289, type, complementSubsetComplementIntersect: $o).
% 13.85/2.47 thf(func_def_290, type, complementInPowersetComplementIntersect: $o).
% 13.85/2.47 thf(func_def_291, type, contraSubsetComplement: $o).
% 13.85/2.47 thf(func_def_292, type, complementTcontraSubset: $o).
% 13.85/2.47 thf(func_def_293, type, binunionTILcontra: $o).
% 13.85/2.47 thf(func_def_294, type, binunionTIRcontra: $o).
% 13.85/2.47 thf(func_def_295, type, inIntersectImpInUnion: $o).
% 13.85/2.47 thf(func_def_296, type, inIntersectImpInUnion2: $o).
% 13.85/2.47 thf(func_def_297, type, inIntersectImpInIntersectUnions: $o).
% 13.85/2.47 thf(func_def_298, type, intersectInPowersetIntersectUnions: $o).
% 13.85/2.47 thf(func_def_299, type, inComplementUnionImpNotIn1: $o).
% 13.85/2.47 thf(func_def_300, type, inComplementUnionImpInComplement1: $o).
% 13.85/2.47 thf(func_def_301, type, binunionTE: $o).
% 13.85/2.47 thf(func_def_302, type, binunionTEcontra: $o).
% 13.85/2.47 thf(func_def_303, type, demorgan2a1: $o).
% 13.85/2.47 thf(func_def_304, type, complementUnionInPowersetComplement: $o).
% 13.85/2.47 thf(func_def_305, type, demorgan2a2: $o).
% 13.85/2.47 thf(func_def_306, type, demorgan1a: $o).
% 13.85/2.47 thf(func_def_307, type, demorgan1b: $o).
% 13.85/2.47 thf(func_def_308, type, demorgan1: $o).
% 13.85/2.47 thf(func_def_309, type, demorgan2a: $o).
% 13.85/2.47 thf(func_def_310, type, demorgan2b2: $o).
% 13.85/2.47 thf(func_def_311, type, demorgan2b: $o).
% 13.85/2.47 thf(func_def_312, type, demorgan2: $o).
% 13.85/2.47 thf(func_def_313, type, woz13rule0: $o).
% 13.85/2.47 thf(func_def_314, type, woz13rule1: $o).
% 13.85/2.47 thf(func_def_315, type, woz13rule2: $o).
% 13.85/2.47 thf(func_def_316, type, woz13rule3: $o).
% 13.85/2.47 thf(func_def_317, type, woz13rule4: $o).
% 13.85/2.47 thf(func_def_318, type, woz1_1: $o).
% 13.85/2.47 thf(func_def_319, type, woz1_2: $o).
% 13.85/2.47 thf(func_def_320, type, woz1_3: $o).
% 13.85/2.47 thf(func_def_321, type, woz1_4: $o).
% 13.85/2.47 thf(func_def_322, type, woz1_5: $o).
% 13.85/2.47 thf(func_def_323, type, breln1: ($i > $i > $o)).
% 13.85/2.47 thf(func_def_324, type, breln1all2: $o).
% 13.85/2.47 thf(func_def_325, type, breln1Set: ($i > $i)).
% 13.85/2.47 thf(func_def_326, type, breln1SetBreln1: $o).
% 13.85/2.47 thf(func_def_327, type, transitive: ($i > $i > $o)).
% 13.85/2.47 thf(func_def_328, type, antisymmetric: ($i > $i > $o)).
% 13.85/2.47 thf(func_def_329, type, reflexive: ($i > $i > $o)).
% 13.85/2.47 thf(func_def_330, type, refltransitive: ($i > $i > $o)).
% 13.85/2.47 thf(func_def_331, type, refllinearorder: ($i > $i > $o)).
% 13.85/2.47 thf(func_def_332, type, reflwellordering: ($i > $i > $o)).
% 13.85/2.47 thf(func_def_333, type, choice2fnsingleton: $o).
% 13.85/2.47 thf(func_def_334, type, setOfPairsIsBReln1: $o).
% 13.85/2.47 thf(func_def_335, type, breln1all1: $o).
% 13.85/2.47 thf(func_def_336, type, subbreln1: $o).
% 13.85/2.47 thf(func_def_337, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 13.85/2.47 thf(func_def_338, type, vIMP: ($o > $o > $o)).
% 13.85/2.47 thf(func_def_339, type, db0: !>[X0: $tType]:(X0)).
% 13.85/2.47 thf(func_def_340, type, db2: !>[X0: $tType]:(X0)).
% 13.85/2.47 thf(func_def_341, type, db1: !>[X0: $tType]:(X0)).
% 13.85/2.47 thf(func_def_342, type, db3: !>[X0: $tType]:(X0)).
% 13.85/2.47 thf(func_def_343, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 13.85/2.47 thf(func_def_344, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 13.85/2.47 thf(func_def_347, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 13.85/2.47 thf(func_def_348, type, vAND: ($o > $o > $o)).
% 13.85/2.47 thf(func_def_349, type, vNOT: ($o > $o)).
% 13.85/2.47 thf(func_def_350, type, db6: !>[X0: $tType]:(X0)).
% 13.85/2.47 thf(func_def_351, type, vIFF: ($o > $o > $o)).
% 13.85/2.47 thf(func_def_352, type, vOR: ($o > $o > $o)).
% 13.85/2.47 thf(func_def_353, type, db4: !>[X0: $tType]:(X0)).
% 13.85/2.47 thf(func_def_354, type, db5: !>[X0: $tType]:(X0)).
% 13.85/2.47 thf(func_def_355, type, sF0: $o).
% 13.85/2.47 thf(func_def_356, type, sF1: $o).
% 13.85/2.47 thf(func_def_357, type, sF2: $o).
% 13.85/2.47 thf(func_def_358, type, sF3: $o).
% 13.85/2.47 thf(func_def_359, type, sF4: $o).
% 13.85/2.47 thf(func_def_360, type, sF5: $o).
% 13.85/2.47 thf(func_def_361, type, sF6: $o).
% 13.85/2.47 thf(func_def_362, type, sF7: $o).
% 13.85/2.47 thf(func_def_363, type, sF8: $o).
% 13.85/2.47 thf(func_def_364, type, sF9: $o).
% 13.85/2.47 thf(func_def_365, type, sF10: $o).
% 13.85/2.47 thf(func_def_366, type, sF11: $o).
% 13.85/2.47 thf(func_def_367, type, sF12: $o).
% 13.85/2.47 thf(func_def_368, type, sF13: $o).
% 13.85/2.47 thf(func_def_369, type, sF14: $o).
% 13.85/2.47 thf(func_def_370, type, sF15: $o).
% 13.85/2.47 thf(func_def_371, type, sF16: $o).
% 13.85/2.47 thf(func_def_372, type, sF17: $o).
% 13.85/2.47 thf(func_def_373, type, sF18: $o).
% 13.85/2.47 thf(func_def_374, type, sF19: $o).
% 13.85/2.47 thf(func_def_375, type, sF20: $o).
% 13.85/2.47 thf(func_def_376, type, sF21: $o).
% 13.85/2.47 thf(func_def_377, type, sF22: $o).
% 13.85/2.47 thf(func_def_378, type, sF23: $o).
% 13.85/2.47 thf(func_def_379, type, sF24: $o).
% 13.85/2.47 thf(func_def_380, type, sF25: $o).
% 13.85/2.47 thf(func_def_381, type, sF26: $o).
% 13.85/2.47 thf(func_def_382, type, sF27: $o).
% 13.85/2.47 thf(func_def_383, type, sF28: $o).
% 13.85/2.47 thf(func_def_384, type, sF29: $o).
% 13.85/2.47 thf(func_def_385, type, sF30: $o).
% 13.85/2.47 thf(func_def_386, type, sF31: $o).
% 13.85/2.47 thf(func_def_387, type, sF32: $o).
% 13.85/2.47 thf(func_def_388, type, sF33: $o).
% 13.85/2.47 thf(func_def_389, type, sF34: $o).
% 13.85/2.47 thf(func_def_390, type, sF35: $o).
% 13.85/2.47 thf(func_def_391, type, sF36: $o).
% 13.85/2.47 thf(func_def_392, type, sF37: $o).
% 13.85/2.47 thf(func_def_393, type, sF38: $o).
% 13.85/2.47 thf(func_def_394, type, sF39: $o).
% 13.85/2.47 thf(func_def_395, type, sF40: $o).
% 13.85/2.47 thf(func_def_396, type, sF41: $o).
% 13.85/2.47 thf(func_def_397, type, sF42: $o).
% 13.85/2.47 thf(func_def_398, type, sF43: $o).
% 13.85/2.47 thf(func_def_399, type, sF44: $o).
% 13.85/2.47 thf(func_def_400, type, sF45: $o).
% 13.85/2.47 thf(func_def_401, type, sF46: $o).
% 13.85/2.47 thf(func_def_402, type, sF47: $o).
% 13.85/2.47 thf(func_def_403, type, sF48: $o).
% 13.85/2.47 thf(func_def_404, type, sF49: $o).
% 13.85/2.47 thf(func_def_405, type, sF50: $o).
% 13.85/2.47 thf(func_def_406, type, sF51: $o).
% 13.85/2.47 thf(func_def_407, type, sF52: $o).
% 13.85/2.47 thf(func_def_408, type, sF53: $o).
% 13.85/2.47 thf(func_def_409, type, sF54: $o).
% 13.85/2.47 thf(func_def_410, type, sF55: $o).
% 13.85/2.47 thf(func_def_411, type, sF56: $o).
% 13.85/2.47 thf(func_def_412, type, sF57: $o).
% 13.85/2.47 thf(func_def_413, type, sF58: $o).
% 13.85/2.47 thf(func_def_414, type, sF59: $o).
% 13.85/2.47 thf(func_def_415, type, sF60: $o).
% 13.85/2.47 thf(func_def_416, type, sF61: $o).
% 13.85/2.47 thf(func_def_417, type, sF62: $o).
% 13.85/2.47 thf(func_def_418, type, sF63: $o).
% 13.85/2.47 thf(func_def_419, type, sF64: $o).
% 13.85/2.47 thf(func_def_420, type, sF65: $o).
% 13.85/2.47 thf(func_def_421, type, sF66: $o).
% 13.85/2.47 thf(func_def_422, type, sF67: $o).
% 13.85/2.47 thf(func_def_423, type, sF68: $o).
% 13.85/2.47 thf(func_def_424, type, sF69: $o).
% 13.85/2.47 thf(func_def_425, type, sF70: $o).
% 13.85/2.47 thf(func_def_426, type, sF71: $o).
% 13.85/2.47 thf(func_def_427, type, sF72: $o).
% 13.85/2.47 thf(func_def_428, type, sF73: $o).
% 13.85/2.47 thf(func_def_429, type, sF74: $o).
% 13.85/2.47 thf(func_def_430, type, sF75: $o).
% 13.85/2.47 thf(func_def_431, type, sF76: $o).
% 13.85/2.47 thf(func_def_432, type, sF77: $o).
% 13.85/2.47 thf(func_def_433, type, sF78: $o).
% 13.85/2.47 thf(func_def_434, type, sF79: $o).
% 13.85/2.47 thf(func_def_435, type, sF80: $o).
% 13.85/2.47 thf(func_def_436, type, sF81: $o).
% 13.85/2.47 thf(func_def_437, type, sF82: $o).
% 13.85/2.47 thf(func_def_438, type, sF83: $o).
% 13.85/2.47 thf(func_def_439, type, sF84: $o).
% 13.85/2.47 thf(func_def_440, type, sF85: $o).
% 13.85/2.47 thf(func_def_441, type, sF86: $o).
% 13.85/2.47 thf(func_def_442, type, sF87: $o).
% 13.85/2.47 thf(func_def_443, type, sF88: $o).
% 13.85/2.47 thf(func_def_444, type, sF89: $o).
% 13.85/2.47 thf(func_def_445, type, sF90: $o).
% 13.85/2.47 thf(func_def_446, type, sF91: $o).
% 13.85/2.47 thf(func_def_447, type, sF92: $o).
% 13.85/2.47 thf(func_def_448, type, sF93: $o).
% 13.85/2.47 thf(func_def_449, type, sF94: $o).
% 13.85/2.47 thf(func_def_450, type, sF95: $o).
% 13.85/2.47 thf(func_def_451, type, sF96: $o).
% 13.85/2.47 thf(func_def_452, type, sF97: $o).
% 13.85/2.47 thf(func_def_453, type, sF98: $o).
% 13.85/2.47 thf(func_def_454, type, sF99: $o).
% 13.85/2.47 thf(func_def_455, type, sF100: $o).
% 13.85/2.47 thf(func_def_456, type, sF101: $o).
% 13.85/2.47 thf(func_def_457, type, sF102: $o).
% 13.85/2.47 thf(func_def_458, type, sF103: $o).
% 13.85/2.47 thf(func_def_459, type, sF104: $o).
% 13.85/2.47 thf(func_def_460, type, sF105: $o).
% 13.85/2.47 thf(func_def_461, type, sF106: $o).
% 13.85/2.47 thf(func_def_462, type, sF107: $o).
% 13.85/2.47 thf(func_def_463, type, sF108: $o).
% 13.85/2.47 thf(func_def_464, type, sF109: $o).
% 13.85/2.47 thf(func_def_465, type, sF110: $o).
% 13.85/2.47 thf(func_def_466, type, sF111: $o).
% 13.85/2.47 thf(func_def_467, type, sF112: $o).
% 13.85/2.47 thf(func_def_468, type, sF113: $o).
% 13.85/2.47 thf(func_def_469, type, sF114: $o).
% 13.85/2.47 thf(func_def_470, type, sF115: $o).
% 13.85/2.47 thf(func_def_471, type, sF116: $o).
% 13.85/2.47 thf(func_def_472, type, sF117: $o).
% 13.85/2.47 thf(func_def_473, type, sF118: $o).
% 13.85/2.47 thf(func_def_474, type, sF119: $o).
% 13.85/2.47 thf(func_def_475, type, sF120: $o).
% 13.85/2.47 thf(func_def_476, type, sF121: $o).
% 13.85/2.47 thf(func_def_477, type, sF122: $o).
% 13.85/2.47 thf(func_def_478, type, sF123: $o).
% 13.85/2.47 thf(func_def_479, type, sF124: $o).
% 13.85/2.47 thf(func_def_480, type, sF125: $o).
% 13.85/2.47 thf(func_def_481, type, sF126: $o).
% 13.85/2.47 thf(func_def_482, type, sF127: $o).
% 13.85/2.47 thf(func_def_483, type, sF128: $o).
% 13.85/2.47 thf(func_def_484, type, sF129: $o).
% 13.85/2.47 thf(func_def_485, type, sF130: $o).
% 13.85/2.47 thf(func_def_486, type, sF131: $o).
% 13.85/2.47 thf(func_def_487, type, sF132: $o).
% 13.85/2.47 thf(func_def_488, type, sF133: $o).
% 13.85/2.47 thf(func_def_489, type, sF134: $o).
% 13.85/2.47 thf(func_def_490, type, sF135: $o).
% 13.85/2.47 thf(func_def_491, type, sF136: $o).
% 13.85/2.47 thf(func_def_492, type, sF137: $o).
% 13.85/2.47 thf(func_def_493, type, sF138: $o).
% 13.85/2.47 thf(func_def_494, type, sF139: $o).
% 13.85/2.47 thf(func_def_495, type, sF140: $o).
% 13.85/2.47 thf(func_def_496, type, sF141: $o).
% 13.85/2.47 thf(func_def_497, type, sF142: $o).
% 13.85/2.47 thf(func_def_498, type, sF143: $o).
% 13.85/2.47 thf(func_def_499, type, sF144: $o).
% 13.85/2.47 thf(func_def_500, type, sF145: $o).
% 13.85/2.47 thf(func_def_501, type, sF146: $o).
% 13.85/2.47 thf(func_def_502, type, sF147: $o).
% 13.85/2.47 thf(func_def_503, type, sF148: $o).
% 13.85/2.47 thf(func_def_504, type, sF149: $o).
% 13.85/2.47 thf(func_def_505, type, sF150: $o).
% 13.85/2.47 thf(func_def_506, type, sF151: $o).
% 13.85/2.47 thf(func_def_507, type, sF152: $o).
% 13.85/2.47 thf(func_def_508, type, sF153: $o).
% 13.85/2.47 thf(func_def_509, type, sF154: $o).
% 13.85/2.47 thf(func_def_510, type, sF155: $o).
% 13.85/2.47 thf(func_def_511, type, sF156: $o).
% 13.85/2.47 thf(func_def_512, type, sF157: $o).
% 13.85/2.47 thf(func_def_513, type, sF158: $o).
% 13.85/2.47 thf(func_def_514, type, sF159: $o).
% 13.85/2.47 thf(func_def_515, type, sF160: $o).
% 13.85/2.47 thf(func_def_516, type, sF161: $o).
% 13.85/2.47 thf(func_def_517, type, sF162: $o).
% 13.85/2.47 thf(func_def_518, type, sF163: $o).
% 13.85/2.47 thf(func_def_519, type, sF164: $o).
% 13.85/2.47 thf(func_def_520, type, sF165: $o).
% 13.85/2.47 thf(func_def_521, type, sF166: $o).
% 13.85/2.47 thf(func_def_522, type, sF167: $o).
% 13.85/2.47 thf(func_def_523, type, sF168: $o).
% 13.85/2.47 thf(func_def_524, type, sF169: $o).
% 13.85/2.47 thf(func_def_525, type, sF170: $o).
% 13.85/2.47 thf(func_def_526, type, sF171: $o).
% 13.85/2.47 thf(func_def_527, type, sF172: $o).
% 13.85/2.47 thf(func_def_528, type, sF173: $o).
% 13.85/2.47 thf(func_def_529, type, sF174: $o).
% 13.85/2.47 thf(func_def_530, type, sF175: $o).
% 13.85/2.47 thf(func_def_531, type, sF176: $o).
% 13.85/2.47 thf(func_def_532, type, sF177: $o).
% 13.85/2.47 thf(func_def_533, type, sF178: $o).
% 13.85/2.47 thf(func_def_534, type, sF179: $o).
% 13.85/2.47 thf(func_def_535, type, sF180: $o).
% 13.85/2.47 thf(func_def_536, type, sF181: $o).
% 13.85/2.47 thf(func_def_537, type, sF182: $o).
% 13.85/2.47 thf(func_def_538, type, sF183: $o).
% 13.85/2.47 thf(func_def_539, type, sF184: $o).
% 13.85/2.47 thf(func_def_540, type, sF185: $o).
% 13.85/2.47 thf(func_def_541, type, sF186: $o).
% 13.85/2.47 thf(func_def_542, type, sF187: $o).
% 13.85/2.47 thf(func_def_543, type, sF188: $o).
% 13.85/2.47 thf(func_def_544, type, sF189: $o).
% 13.85/2.47 thf(func_def_545, type, sF190: $o).
% 13.85/2.47 thf(func_def_546, type, sF191: $o).
% 13.85/2.47 thf(func_def_547, type, sF192: $o).
% 13.85/2.47 thf(func_def_548, type, sF193: $o).
% 13.85/2.47 thf(func_def_549, type, sF194: $o).
% 13.85/2.47 thf(func_def_550, type, sF195: $o).
% 13.85/2.47 thf(func_def_551, type, sF196: $o).
% 13.85/2.47 thf(func_def_552, type, sF197: $o).
% 13.85/2.47 thf(func_def_553, type, sF198: $o).
% 13.85/2.47 thf(func_def_554, type, sF199: $o).
% 13.85/2.47 thf(func_def_555, type, sF200: $o).
% 13.85/2.47 thf(func_def_556, type, sF201: $o).
% 13.85/2.47 thf(func_def_557, type, sF202: $o).
% 13.85/2.47 thf(func_def_558, type, sF203: $o).
% 13.85/2.47 thf(func_def_559, type, sF204: $o).
% 13.85/2.47 thf(func_def_560, type, sF205: $o).
% 13.85/2.47 thf(func_def_561, type, sF206: $o).
% 13.85/2.47 thf(func_def_562, type, sF207: $o).
% 13.85/2.47 thf(func_def_563, type, sF208: $o).
% 13.85/2.47 thf(func_def_564, type, sF209: $o).
% 13.85/2.47 thf(func_def_565, type, sF210: $o).
% 13.85/2.47 thf(func_def_566, type, sF211: $o).
% 13.85/2.47 thf(func_def_567, type, sF212: $o).
% 13.85/2.47 thf(func_def_568, type, sF213: $o).
% 13.85/2.47 thf(func_def_569, type, sF214: $o).
% 13.85/2.47 thf(func_def_570, type, sF215: $o).
% 13.85/2.47 thf(func_def_571, type, sF216: $o).
% 13.85/2.47 thf(func_def_572, type, sF217: $o).
% 13.85/2.47 thf(func_def_573, type, sF218: $o).
% 13.85/2.47 thf(func_def_574, type, sF219: $o).
% 13.85/2.47 thf(func_def_575, type, sF220: $o).
% 13.85/2.47 thf(func_def_576, type, sF221: $o).
% 13.85/2.47 thf(func_def_577, type, sF222: $o).
% 13.85/2.47 thf(func_def_578, type, sF223: $o).
% 13.85/2.47 thf(func_def_579, type, sF224: $o).
% 13.85/2.47 thf(func_def_580, type, sF225: $o).
% 13.85/2.47 thf(func_def_581, type, sF226: $o).
% 13.85/2.47 thf(func_def_582, type, sF227: $o).
% 13.85/2.47 thf(func_def_583, type, sF228: $o).
% 13.85/2.47 thf(func_def_584, type, sF229: $o).
% 13.85/2.47 thf(func_def_585, type, sF230: $o).
% 13.85/2.47 thf(func_def_586, type, sF231: $o).
% 13.85/2.47 thf(func_def_587, type, sF232: $o).
% 13.85/2.47 thf(func_def_588, type, sF233: $o).
% 13.85/2.47 thf(func_def_589, type, sF234: $o).
% 13.85/2.47 thf(func_def_590, type, sF235: $o).
% 13.85/2.47 thf(func_def_591, type, sF236: $o).
% 13.85/2.47 thf(func_def_592, type, sF237: $o).
% 13.85/2.47 thf(func_def_593, type, sF238: $o).
% 13.85/2.47 thf(func_def_594, type, sF239: $o).
% 13.85/2.47 thf(func_def_595, type, sF240: $o).
% 13.85/2.47 thf(func_def_596, type, sF241: $o).
% 13.85/2.47 thf(func_def_597, type, sF242: $o).
% 13.85/2.47 thf(func_def_598, type, sF243: $o).
% 13.85/2.47 thf(func_def_599, type, sF244: $o).
% 13.85/2.47 thf(func_def_600, type, sF245: $o).
% 13.85/2.47 thf(func_def_601, type, sF246: $o).
% 13.85/2.47 thf(func_def_602, type, sF247: $o).
% 13.85/2.47 thf(func_def_603, type, sF248: $o).
% 13.85/2.47 thf(func_def_604, type, sF249: $o).
% 13.85/2.47 thf(func_def_605, type, sF250: $o).
% 13.85/2.47 thf(func_def_606, type, sF251: $o).
% 13.85/2.47 thf(func_def_607, type, sF252: $o).
% 13.85/2.47 thf(func_def_608, type, sF253: $o).
% 13.85/2.47 thf(func_def_609, type, sF254: $o).
% 13.85/2.47 thf(func_def_610, type, sF255: $o).
% 13.85/2.47 thf(func_def_611, type, sF256: $o).
% 13.85/2.47 thf(func_def_612, type, sF257: $o).
% 13.85/2.47 thf(func_def_613, type, sF258: $o).
% 13.85/2.47 thf(func_def_614, type, sF259: $o).
% 13.85/2.47 thf(func_def_615, type, sF260: $o).
% 13.85/2.47 thf(func_def_616, type, sF261: $o).
% 13.85/2.47 thf(func_def_617, type, sF262: $o).
% 13.85/2.47 thf(func_def_618, type, sF263: $o).
% 13.85/2.47 thf(func_def_619, type, sF264: $o).
% 13.85/2.47 thf(func_def_620, type, sF265: $o).
% 13.85/2.47 thf(func_def_621, type, sF266: $o).
% 13.85/2.47 thf(func_def_622, type, sF267: $o).
% 13.85/2.47 thf(func_def_623, type, sF268: $o).
% 13.85/2.47 thf(func_def_624, type, sF269: $o).
% 13.85/2.47 thf(func_def_625, type, sF270: $o).
% 13.85/2.47 thf(func_def_626, type, sF271: $o).
% 13.85/2.47 thf(func_def_627, type, sF272: $o).
% 13.85/2.47 thf(func_def_628, type, sF273: $o).
% 13.85/2.47 thf(func_def_629, type, sF274: $o).
% 13.85/2.47 thf(func_def_630, type, sF275: $o).
% 13.85/2.47 thf(func_def_631, type, sF276: $o).
% 13.85/2.47 thf(func_def_632, type, sF277: $o).
% 13.85/2.47 thf(func_def_633, type, sF278: $o).
% 13.85/2.47 thf(func_def_634, type, sF279: $o).
% 13.85/2.47 thf(func_def_635, type, sF280: $o).
% 13.85/2.47 thf(func_def_636, type, sF281: $o).
% 13.85/2.47 thf(func_def_637, type, sF282: $o).
% 13.85/2.47 thf(func_def_638, type, sF283: $o).
% 13.85/2.47 thf(func_def_639, type, sF284: $o).
% 13.85/2.47 thf(func_def_640, type, sF285: $o).
% 13.85/2.47 thf(func_def_641, type, sF286: $o).
% 13.85/2.47 thf(func_def_642, type, sF287: $o).
% 13.85/2.47 thf(func_def_643, type, sF288: $o).
% 13.85/2.47 thf(func_def_644, type, sF289: $o).
% 13.85/2.47 thf(func_def_645, type, sF290: $o).
% 13.85/2.47 thf(func_def_646, type, sF291: $o).
% 13.85/2.47 thf(func_def_649, type, sK294: ($i > $i)).
% 13.85/2.47 thf(f1,axiom,(
% 13.85/2.47 ((^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu)).
% 13.85/2.47 thf(f2,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) <=> (in @ X2 @ X1)) => (X0 = X1)) = setextAx)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx)).
% 13.85/2.47 thf(f3,axiom,(
% 13.85/2.47 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx)).
% 13.85/2.47 thf(f4,axiom,(
% 13.85/2.47 (! [X2 : $i,X1 : $i,X0 : $i] : (((X2 = X0) | (in @ X2 @ X1)) <=> (in @ X2 @ (setadjoin @ X0 @ X1))) = setadjoinAx)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx)).
% 13.85/2.47 thf(f5,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))) = powersetAx)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx)).
% 13.85/2.47 thf(f7,axiom,(
% 13.85/2.47 (omega0Ax = ((in @ emptyset @ omega)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax)).
% 13.85/2.47 thf(f8,axiom,(
% 13.85/2.47 (! [X0 : $i] : ((in @ X0 @ omega) => (in @ (setadjoin @ X0 @ X0) @ omega)) = omegaSAx)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx)).
% 13.85/2.47 thf(f17,axiom,(
% 13.85/2.47 (exuE1 = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1)).
% 13.85/2.47 thf(f18,axiom,(
% 13.85/2.47 (prop2setE = ! [X1 : $i,X0 : $o] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE)).
% 13.85/2.47 thf(f19,axiom,(
% 13.85/2.47 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 13.85/2.47 thf(f20,axiom,(
% 13.85/2.47 (! [X0 : $i] : ((in @ X0 @ emptyset) => $false) = emptysetimpfalse)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse)).
% 13.85/2.47 thf(f21,axiom,(
% 13.85/2.47 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset)).
% 13.85/2.47 thf(f23,axiom,(
% 13.85/2.47 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext)).
% 13.85/2.47 thf(f24,axiom,(
% 13.85/2.47 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = emptyI)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI)).
% 13.85/2.47 thf(f25,axiom,(
% 13.85/2.47 (noeltsimpempty = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty)).
% 13.85/2.47 thf(f26,axiom,(
% 13.85/2.47 (setbeta = ! [X0 : $i,X2 : $i,X1 : ($i > $o)] : ((in @ X2 @ X0) => ((X1 @ X2) <=> (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta)).
% 13.85/2.47 thf(f27,axiom,(
% 13.85/2.47 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)).
% 13.85/2.47 thf(f28,axiom,(
% 13.85/2.47 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1)).
% 13.85/2.47 thf(f29,axiom,(
% 13.85/2.47 (nonemptyI = ! [X0 : $i,X2 : $i,X1 : ($i > $o)] : ((in @ X2 @ X0) => ((X1 @ X2) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI)).
% 13.85/2.47 thf(f30,axiom,(
% 13.85/2.47 (nonemptyI1 = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1)).
% 13.85/2.47 thf(f31,axiom,(
% 13.85/2.47 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL)).
% 13.85/2.47 thf(f32,axiom,(
% 13.85/2.47 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty)).
% 13.85/2.47 thf(f33,axiom,(
% 13.85/2.47 (setadjoinIR = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR)).
% 13.85/2.47 thf(f35,axiom,(
% 13.85/2.47 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ((in @ X2 @ X1) | (X2 = X0))) = setadjoinOr)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr)).
% 13.85/2.47 thf(f36,axiom,(
% 13.85/2.47 (setoftrueEq = ! [X0 : $i] : (X0 = ((dsetconstr @ X0 @ (^[X1 : $i] : ($true))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq)).
% 13.85/2.47 thf(f37,axiom,(
% 13.85/2.47 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)).
% 13.85/2.47 thf(f38,axiom,(
% 13.85/2.47 (! [X0 : $i] : (in @ emptyset @ (powerset @ X0)) = emptyinPowerset)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset)).
% 13.85/2.47 thf(f39,axiom,(
% 13.85/2.47 (emptyInPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset)).
% 13.85/2.47 thf(f40,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE)).
% 13.85/2.47 thf(f41,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))) = setunionI)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI)).
% 13.85/2.47 thf(f42,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)) = setunionE)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE)).
% 13.85/2.47 thf(f43,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0)))) = subPowSU)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU)).
% 13.85/2.47 thf(f45,axiom,(
% 13.85/2.47 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))) = nonemptyImpWitness)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 13.85/2.47 thf(f46,axiom,(
% 13.85/2.47 (uniqinunit = ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)).
% 13.85/2.47 thf(f47,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))) = notinsingleton)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton)).
% 13.85/2.47 thf(f48,axiom,(
% 13.85/2.47 (eqinunit = ! [X1 : $i,X0 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit)).
% 13.85/2.47 thf(f49,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = singletonsswitch)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch)).
% 13.85/2.47 thf(f51,axiom,(
% 13.85/2.47 (upairsetIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL)).
% 13.85/2.47 thf(f52,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = upairsetIR)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR)).
% 13.85/2.47 thf(f54,axiom,(
% 13.85/2.47 (! [X0 : ($i > $o),X1 : $i] : ((in @ X1 @ emptyset) => (X0 @ X1)) = vacuousDall)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall)).
% 13.85/2.47 thf(f57,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : ($i > $o)] : (~ ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2))) = quantDeMorgan3)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3)).
% 13.85/2.47 thf(f58,axiom,(
% 13.85/2.47 (quantDeMorgan4 = ! [X1 : ($i > $o),X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & ~(X1 @ X2)) => ~ ! [X2 : $i] : ((in @ X2 @ X0) => (X1 @ X2))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4)).
% 13.85/2.47 thf(f59,axiom,(
% 13.85/2.47 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI)).
% 13.85/2.47 thf(f61,axiom,(
% 13.85/2.47 (notdexE = ! [X0 : $i,X1 : ($i > $o)] : (~ ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE)).
% 13.85/2.47 thf(f63,axiom,(
% 13.85/2.47 (! [X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X1 : $i] : ((X0 @ X1))))) = exuI1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1)).
% 13.85/2.47 thf(f64,axiom,(
% 13.85/2.47 (! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1)))))) = exuI3)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3)).
% 13.85/2.47 thf(f65,axiom,(
% 13.85/2.47 (exuI2 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2)) => (exu @ (^[X1 : $i] : ((X0 @ X1))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2)).
% 13.85/2.47 thf(f66,axiom,(
% 13.85/2.47 (inCongP = ! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP)).
% 13.85/2.47 thf(f68,axiom,(
% 13.85/2.47 (exuE3u = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u)).
% 13.85/2.47 thf(f69,axiom,(
% 13.85/2.47 (! [X0 : ($i > $o),X1 : ($i > $o)] : (! [X3 : $i,X2 : $i] : ((X2 = X3) => ((X0 @ X2) <=> (X1 @ X3))) => ((exu @ (^[X2 : $i] : ((X0 @ X2)))) <=> (exu @ (^[X2 : $i] : ((X1 @ X2)))))) = exu__Cong)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong)).
% 13.85/2.47 thf(f70,axiom,(
% 13.85/2.47 ((emptyset = emptyset) = emptyset__Cong)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong)).
% 13.85/2.47 thf(f71,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => (((setadjoin @ X0 @ X2)) = ((setadjoin @ X1 @ X3))))) = setadjoin__Cong)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong)).
% 13.85/2.47 thf(f72,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (((powerset @ X0)) = ((powerset @ X1)))) = powerset__Cong)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong)).
% 13.85/2.47 thf(f74,axiom,(
% 13.85/2.47 ((omega = omega) = omega__Cong)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong)).
% 13.85/2.47 thf(f75,axiom,(
% 13.85/2.47 (exuEu = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu)).
% 13.85/2.47 thf(f77,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : ($i > $o),X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((X4 = X5) => ((X2 @ X4) <=> (X3 @ X5))))) => (((dsetconstr @ X0 @ (^[X4 : $i] : ((X2 @ X4))))) = ((dsetconstr @ X1 @ (^[X4 : $i] : ((X3 @ X4)))))))) = dsetconstr__Cong)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong)).
% 13.85/2.47 thf(f78,axiom,(
% 13.85/2.47 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 13.85/2.47 thf(f79,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset2)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2)).
% 13.85/2.47 thf(f80,axiom,(
% 13.85/2.47 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1)).
% 13.85/2.47 thf(f81,axiom,(
% 13.85/2.47 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 13.85/2.47 thf(f82,axiom,(
% 13.85/2.47 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset)).
% 13.85/2.47 thf(f83,axiom,(
% 13.85/2.47 (! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 13.85/2.47 thf(f86,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)) = notequalI1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1)).
% 13.85/2.47 thf(f87,axiom,(
% 13.85/2.47 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (X0 != X1))) = notequalI2)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2)).
% 13.85/2.47 thf(f88,axiom,(
% 13.85/2.47 (subsetRefl = ! [X0 : $i] : (subset @ X0 @ X0))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl)).
% 13.85/2.47 thf(f89,axiom,(
% 13.85/2.47 (subsetTrans = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans)).
% 13.85/2.47 thf(f90,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)) = setadjoinSub)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub)).
% 13.85/2.47 thf(f91,axiom,(
% 13.85/2.47 (setadjoinSub2 = ! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X2) => (subset @ X0 @ (setadjoin @ X1 @ X2))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2)).
% 13.85/2.47 thf(f92,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))) = subset2powerset)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset)).
% 13.85/2.47 thf(f93,axiom,(
% 13.85/2.47 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub)).
% 13.85/2.47 thf(f94,axiom,(
% 13.85/2.47 (! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)) = subsetemptysetimpeq)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq)).
% 13.85/2.47 thf(f95,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1)).
% 13.85/2.47 thf(f96,axiom,(
% 13.85/2.47 (powersetE1 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1)).
% 13.85/2.47 thf(f97,axiom,(
% 13.85/2.47 (inPowerset = ! [X0 : $i] : (in @ X0 @ (powerset @ X0)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset)).
% 13.85/2.47 thf(f98,axiom,(
% 13.85/2.47 (powersetsubset = ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset)).
% 13.85/2.47 thf(f99,axiom,(
% 13.85/2.47 (sepInPowerset = ! [X1 : ($i > $o),X0 : $i] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ (powerset @ X0)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset)).
% 13.85/2.47 thf(f100,axiom,(
% 13.85/2.47 (sepSubset = ! [X1 : ($i > $o),X0 : $i] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ X0))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset)).
% 13.85/2.47 thf(f102,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = upairset2IR)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR)).
% 13.85/2.47 thf(f103,axiom,(
% 13.85/2.47 (binunionIR = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR)).
% 13.85/2.47 thf(f106,axiom,(
% 13.85/2.47 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub)).
% 13.85/2.47 thf(f107,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)) = binunionRsub)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub)).
% 13.85/2.47 thf(f108,axiom,(
% 13.85/2.47 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI)).
% 13.85/2.47 thf(f109,axiom,(
% 13.85/2.47 (binintersectSubset5 = ! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X2 @ X0) => ((subset @ X2 @ X1) => (subset @ X2 @ (binintersect @ X0 @ X1)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5)).
% 13.85/2.47 thf(f111,axiom,(
% 13.85/2.47 (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub)).
% 13.85/2.47 thf(f112,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0)) = binintersectSubset2)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2)).
% 13.85/2.47 thf(f113,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0)) = binintersectSubset3)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3)).
% 13.85/2.47 thf(f114,axiom,(
% 13.85/2.47 (binintersectER = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER)).
% 13.85/2.47 thf(f115,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (((binintersect @ X0 @ X1)) = emptyset)) = disjointsetsI1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1)).
% 13.85/2.47 thf(f116,axiom,(
% 13.85/2.47 (binintersectRsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub)).
% 13.85/2.47 thf(f117,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X0 @ X1)) = X1)) = binintersectSubset4)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4)).
% 13.85/2.47 thf(f118,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)) = binintersectSubset1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1)).
% 13.85/2.47 thf(f119,axiom,(
% 13.85/2.47 (! [X0 : $i,X2 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X2))) = ((binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2)))) = bs114d)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d)).
% 13.85/2.47 thf(f120,axiom,(
% 13.85/2.47 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI)).
% 13.85/2.47 thf(f121,axiom,(
% 13.85/2.47 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)) = setminusEL)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL)).
% 13.85/2.47 thf(f122,axiom,(
% 13.85/2.47 (setminusER = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER)).
% 13.85/2.47 thf(f124,axiom,(
% 13.85/2.47 (setminusERneg = ! [X2 : $i,X0 : $i,X1 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg)).
% 13.85/2.47 thf(f125,axiom,(
% 13.85/2.47 (setminusELneg = ! [X0 : $i,X2 : $i,X1 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg)).
% 13.85/2.47 thf(f126,axiom,(
% 13.85/2.47 (setminusILneg = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X0 @ X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg)).
% 13.85/2.47 thf(f128,axiom,(
% 13.85/2.47 (setminusLsub = ! [X1 : $i,X0 : $i] : (subset @ (setminus @ X0 @ X1) @ X0))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub)).
% 13.85/2.47 thf(f129,axiom,(
% 13.85/2.47 (setminusSubset1 = ! [X1 : $i,X0 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1)).
% 13.85/2.47 thf(f134,axiom,(
% 13.85/2.47 (symdiffIneg2 = ! [X0 : $i,X2 : $i,X1 : $i] : (~(in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(in @ X2 @ (symdiff @ X0 @ X1)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2)).
% 13.85/2.47 thf(f135,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair)).
% 13.85/2.47 thf(f136,axiom,(
% 13.85/2.47 (setukpairIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL)).
% 13.85/2.47 thf(f139,axiom,(
% 13.85/2.47 (kpairp = ! [X1 : $i,X0 : $i] : (iskpair @ (kpair @ X0 @ X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp)).
% 13.85/2.47 thf(f140,axiom,(
% 13.85/2.47 (singletonsubset = ! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (subset @ (setadjoin @ X1 @ emptyset) @ X0)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset)).
% 13.85/2.47 thf(f142,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))) = singletoninpowunion)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion)).
% 13.85/2.47 thf(f145,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))) = upairinpowunion)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion)).
% 13.85/2.47 thf(f147,axiom,(
% 13.85/2.47 (ubforcartprodlem2 = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2)).
% 13.85/2.47 thf(f148,axiom,(
% 13.85/2.47 (ubforcartprodlem3 = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3)).
% 13.85/2.47 thf(f152,axiom,(
% 13.85/2.47 (setunionE2 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2)).
% 13.85/2.47 thf(f153,axiom,(
% 13.85/2.47 (setunionsingleton1 = ! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1)).
% 13.85/2.47 thf(f154,axiom,(
% 13.85/2.47 (! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))) = setunionsingleton2)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2)).
% 13.85/2.47 thf(f155,axiom,(
% 13.85/2.47 (setunionsingleton = ! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset))) = X0))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton)).
% 13.85/2.47 thf(f156,axiom,(
% 13.85/2.47 (singletonprop = ! [X1 : ($i > $o),X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop)).
% 13.85/2.47 thf(f157,axiom,(
% 13.85/2.47 (ex1E1 = ! [X0 : $i,X1 : ($i > $o)] : ((ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) => ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1)).
% 13.85/2.47 thf(f160,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X1 @ emptyset))) => (X0 = X1)) = singletonsuniq)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq)).
% 13.85/2.47 thf(f161,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)) = setukpairinjL1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1)).
% 13.85/2.47 thf(f163,axiom,(
% 13.85/2.47 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop)).
% 13.85/2.47 thf(f164,axiom,(
% 13.85/2.47 (kfstpairEq = ! [X0 : $i,X1 : $i] : (((kfst @ (kpair @ X0 @ X1))) = X0))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq)).
% 13.85/2.47 thf(f165,axiom,(
% 13.85/2.47 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (kfst @ X2) @ X0)) = cartprodfstin)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin)).
% 13.85/2.47 thf(f167,axiom,(
% 13.85/2.47 (! [X2 : $i,X0 : $i,X3 : $i,X1 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X0 = X2)) = setukpairinjL)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL)).
% 13.85/2.47 thf(f168,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((X0 = X1) => (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset)))) = setukpairinjR11)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11)).
% 13.85/2.47 thf(f171,axiom,(
% 13.85/2.47 (upairequniteq = ! [X2 : $i,X1 : $i,X0 : $i] : ((((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) => (X0 = X1)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq)).
% 13.85/2.47 thf(f172,axiom,(
% 13.85/2.47 (setukpairinjR2 = ! [X0 : $i,X1 : $i,X3 : $i,X2 : $i] : ((((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = ((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) => (X1 = X3)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2)).
% 13.85/2.47 thf(f173,axiom,(
% 13.85/2.47 (! [X3 : $i,X2 : $i,X1 : $i,X0 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X1 = X3)) = setukpairinjR)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR)).
% 13.85/2.47 thf(f174,axiom,(
% 13.85/2.47 (ksndsingleton = ! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : ((X0 = ((kpair @ (kfst @ X0) @ X1)))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton)).
% 13.85/2.47 thf(f175,axiom,(
% 13.85/2.47 (ksndpairEq = ! [X1 : $i,X0 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq)).
% 13.85/2.47 thf(f176,axiom,(
% 13.85/2.47 (! [X0 : $i] : ((iskpair @ X0) => (((kpair @ (kfst @ X0) @ (ksnd @ X0))) = X0)) = kpairsurjEq)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq)).
% 13.85/2.47 thf(f177,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (ksnd @ X2) @ X1)) = cartprodsndin)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin)).
% 13.85/2.47 thf(f178,axiom,(
% 13.85/2.47 (cartprodpairmemEL = ! [X3 : $i,X2 : $i,X1 : $i,X0 : $i] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) => (in @ X2 @ X0)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL)).
% 13.85/2.47 thf(f180,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kpair @ X2 @ X3)) = ((kpair @ X2 @ X3))))) = cartprodmempaircEq)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq)).
% 13.85/2.47 thf(f181,axiom,(
% 13.85/2.47 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kfst @ (kpair @ X2 @ X3))) = X2))) = cartprodfstpairEq)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq)).
% 13.85/2.47 thf(f182,axiom,(
% 13.85/2.47 (cartprodsndpairEq = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((ksnd @ (kpair @ X2 @ X3))) = X3))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq)).
% 13.85/2.47 thf(f183,axiom,(
% 13.85/2.47 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (((kpair @ (kfst @ X2) @ (ksnd @ X2))) = X2)) = cartprodpairsurjEq)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq)).
% 13.85/2.47 thf(f184,axiom,(
% 13.85/2.47 ((^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))) = breln)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 13.85/2.47 thf(f185,axiom,(
% 13.85/2.47 (! [X2 : ($i > $i > $o),X1 : $i,X0 : $i,X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X2 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6)))))))) = dpsetconstrI)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI)).
% 13.85/2.47 thf(f187,axiom,(
% 13.85/2.47 (setOfPairsIsBReln = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : (breln @ X0 @ X1 @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((X2 @ X3 @ X4))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln)).
% 13.85/2.47 thf(f188,axiom,(
% 13.85/2.47 (! [X3 : $i,X2 : ($i > $i > $o),X0 : $i,X1 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (X2 @ X3 @ X4)))) = dpsetconstrERa)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa)).
% 13.85/2.47 thf(f189,axiom,(
% 13.85/2.47 (! [X0 : $i,X4 : $i,X1 : $i,X3 : $i,X2 : ($i > $i > $o)] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X3 @ X0)) = dpsetconstrEL1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1)).
% 13.85/2.47 thf(f190,axiom,(
% 13.85/2.47 (! [X4 : $i,X1 : $i,X0 : $i,X3 : $i,X2 : ($i > $i > $o)] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X4 @ X1)) = dpsetconstrEL2)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2)).
% 13.85/2.47 thf(f192,axiom,(
% 13.85/2.47 (funcImageSingleton = ! [X0 : $i,X2 : $i,X1 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton)).
% 13.85/2.47 thf(f193,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) @ X1))) = apProp)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp)).
% 13.85/2.47 thf(f194,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))) = app)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',app)).
% 13.85/2.47 thf(f196,axiom,(
% 13.85/2.47 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))) = ap2p)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p)).
% 13.85/2.47 thf(f197,axiom,(
% 13.85/2.47 (! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => (in @ X2 @ (funcSet @ X0 @ X1))) = funcinfuncset)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset)).
% 13.85/2.47 thf(f198,axiom,(
% 13.85/2.47 (lamProp = ! [X1 : $i,X2 : ($i > $i),X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((((X2 @ X3)) = X4)))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp)).
% 13.85/2.47 thf(f199,axiom,(
% 13.85/2.47 (! [X0 : $i,X2 : ($i > $i),X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3)))))) = lamp)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp)).
% 13.85/2.47 thf(f200,axiom,(
% 13.85/2.47 (lam2p = ! [X1 : $i,X0 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (in @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3)))) @ (funcSet @ X0 @ X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p)).
% 13.85/2.47 thf(f208,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X2) => (((ap @ X0 @ X1 @ X2 @ X3)) = X4))))) = funcGraphProp4)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4)).
% 13.85/2.47 thf(f210,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X3) => (in @ (kpair @ X4 @ X5) @ X2)))) => (X2 = X3))))) = eqbreln)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln)).
% 13.85/2.47 thf(f214,axiom,(
% 13.85/2.47 (ap2apEq2 = ! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ X2 @ X3)) = ((ap @ X0 @ X1 @ X2 @ X3))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2)).
% 13.85/2.47 thf(f217,axiom,(
% 13.85/2.47 (! [X0 : $i,X2 : ($i > $i),X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (((lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3))))) = ((lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3))))))) = lam2lamEq)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq)).
% 13.85/2.47 thf(f219,axiom,(
% 13.85/2.47 (eta2 = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (((lam @ X0 @ X1 @ (^[X3 : $i] : ((ap @ X0 @ X1 @ X2 @ X3))))) = X2)))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2)).
% 13.85/2.47 thf(f223,axiom,(
% 13.85/2.47 (iftrueProp2 = ! [X0 : $i,X2 : $i,X1 : $o] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (((setadjoin @ X2 @ emptyset)) = ((dsetconstr @ X0 @ (^[X4 : $i] : ((~X1 & (X4 = X3)) | ((X4 = X2) & X1))))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2)).
% 13.85/2.47 thf(f225,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (if @ X0 @ X1 @ X2 @ X3) @ X0))) = ifp)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp)).
% 13.85/2.47 thf(f226,axiom,(
% 13.85/2.47 (theeq = ! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq)).
% 13.85/2.47 thf(f227,axiom,(
% 13.85/2.47 (iftrue = ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (((if @ X0 @ X1 @ X2 @ X3)) = X2)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue)).
% 13.85/2.47 thf(f229,axiom,(
% 13.85/2.47 (iftrueorfalse = ! [X2 : $i,X0 : $i,X1 : $o] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (if @ X0 @ X1 @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse)).
% 13.85/2.47 thf(f230,axiom,(
% 13.85/2.47 (binintersectT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem)).
% 13.85/2.47 thf(f231,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem)).
% 13.85/2.47 thf(f232,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) = powersetT_lem)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem)).
% 13.85/2.47 thf(f233,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X0)))) = setminusT_lem)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem)).
% 13.85/2.47 thf(f234,axiom,(
% 13.85/2.47 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem)).
% 13.85/2.47 thf(f237,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))) = powersetTI1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1)).
% 13.85/2.47 thf(f238,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X1 @ (powerset @ X2)) => ((in @ X3 @ X1) => (in @ X3 @ X2)))))) = powersetTE1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1)).
% 13.85/2.47 thf(f240,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X1)))) = complementTE1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1)).
% 13.85/2.47 thf(f243,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ((in @ X3 @ X2) => ~(in @ X3 @ X1)))))) = contrasubsetT)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT)).
% 13.85/2.47 thf(f245,axiom,(
% 13.85/2.47 (contrasubsetT2 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ X2) => (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT2)).
% 13.85/2.47 thf(f247,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))) = doubleComplementI1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementI1)).
% 13.85/2.47 thf(f249,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = doubleComplementSub1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1)).
% 13.85/2.47 thf(f250,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1)) = doubleComplementSub2)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2)).
% 13.85/2.47 thf(f251,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (X1 = ((setminus @ X0 @ (setminus @ X0 @ X1))))) = doubleComplementEq)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq)).
% 13.85/2.47 thf(f253,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = complementImpComplementIntersect)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect)).
% 13.85/2.47 thf(f255,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))) = complementInPowersetComplementIntersect)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect)).
% 13.85/2.47 thf(f256,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ (setminus @ X0 @ X1))))))) = contraSubsetComplement)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',contraSubsetComplement)).
% 13.85/2.47 thf(f257,axiom,(
% 13.85/2.47 (complementTcontraSubset = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTcontraSubset)).
% 13.85/2.47 thf(f258,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ (binunion @ X1 @ X2)) => ~(in @ X3 @ X1))))) = binunionTILcontra)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTILcontra)).
% 13.85/2.47 thf(f265,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))) = inComplementUnionImpInComplement1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpInComplement1)).
% 13.85/2.47 thf(f268,axiom,(
% 13.85/2.47 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))) = demorgan2a1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a1)).
% 13.85/2.47 thf(f271,axiom,(
% 13.85/2.47 (demorgan1a = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1a)).
% 13.85/2.47 thf(f276,axiom,(
% 13.85/2.47 (demorgan2b = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) => (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b)).
% 13.85/2.47 thf(f277,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (((setminus @ X0 @ (binunion @ X1 @ X2))) = ((binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))) = demorgan2)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2)).
% 13.85/2.47 thf(f278,axiom,(
% 13.85/2.47 (woz13rule0 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (binintersect @ X1 @ X2)) => (in @ X3 @ X0)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule0)).
% 13.85/2.47 thf(f279,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))) = woz13rule1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule1)).
% 13.85/2.47 thf(f280,axiom,(
% 13.85/2.47 (woz13rule2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule2)).
% 13.85/2.47 thf(f283,axiom,(
% 13.85/2.47 (woz1_1 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_1)).
% 13.85/2.47 thf(f286,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))) = woz1_4)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_4)).
% 13.85/2.47 thf(f288,axiom,(
% 13.85/2.47 ((^[X0 : $i, X1 : $i] : ((breln @ X0 @ X0 @ X1))) = breln1)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1)).
% 13.85/2.47 thf(f289,axiom,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X3 : $i] : ((in @ X3 @ X1) => (X2 @ X3)))) = breln1all2)),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1all2)).
% 13.85/2.47 thf(f292,axiom,(
% 13.85/2.47 (setOfPairsIsBReln1 = ! [X0 : $i,X1 : ($i > $i > $o)] : (breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : ((X1 @ X2 @ X3))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln1)).
% 13.85/2.47 thf(f293,axiom,(
% 13.85/2.47 (breln1all1 = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X3 : $i] : ((in @ X3 @ X1) => (X2 @ X3)))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1all1)).
% 13.85/2.47 thf(f295,conjecture,(
% 13.85/2.47 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ X1)))) => (X1 = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.85/2.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln1)).
% 13.85/2.47 thf(f296,negated_conjecture,(
% 13.85/2.47 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ X1)))) => (X1 = X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.85/2.47 inference(negated_conjecture,[status(cth)],[f295])).
% 13.85/2.47 thf(f299,plain,(
% 13.85/2.47 (! [X0 : ($i > $o),X1 : $i] : ((in @ X1 @ emptyset) => (X0 @ X1)) = vacuousDall)),
% 13.85/2.47 inference(rectify,[],[f54])).
% 13.85/2.47 thf(f300,plain,(
% 13.85/2.47 (vacuousDall = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f299])).
% 13.85/2.47 thf(f301,plain,(
% 13.85/2.47 (setoftrueEq = ! [X0 : $i] : (X0 = ((dsetconstr @ X0 @ (^[X1 : $i] : ($true))))))),
% 13.85/2.47 inference(rectify,[],[f36])).
% 13.85/2.47 thf(f302,plain,(
% 13.85/2.47 (setoftrueEq = ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f301])).
% 13.85/2.47 thf(f303,plain,(
% 13.85/2.47 (sepInPowerset = ! [X0 : ($i > $o),X1 : $i] : (in @ (dsetconstr @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) @ (powerset @ X1)))),
% 13.85/2.47 inference(rectify,[],[f99])).
% 13.85/2.47 thf(f304,plain,(
% 13.85/2.47 (sepInPowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f303])).
% 13.85/2.47 thf(f307,plain,(
% 13.85/2.47 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 13.85/2.47 inference(rectify,[],[f93])).
% 13.85/2.47 thf(f308,plain,(
% 13.85/2.47 (setextsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f307])).
% 13.85/2.47 thf(f311,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : ($i > $i > $o)] : ((in @ (kpair @ X3 @ X1) @ (dpsetconstr @ X0 @ X2 @ (^[X5 : $i, X6 : $i] : ((X4 @ X5 @ X6))))) => (in @ X3 @ X0)) = dpsetconstrEL1)),
% 13.85/2.47 inference(rectify,[],[f189])).
% 13.85/2.47 thf(f312,plain,(
% 13.85/2.47 (dpsetconstrEL1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y4 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (in @ Y1 @ Y4))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f311])).
% 13.85/2.47 thf(f313,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) <=> (in @ X2 @ X0)) => (X0 = X1)) = setextAx)),
% 13.85/2.47 inference(rectify,[],[f2])).
% 13.85/2.47 thf(f314,plain,(
% 13.85/2.47 (setextAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f313])).
% 13.85/2.47 thf(f315,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ (setminus @ X0 @ X1))))))) = contraSubsetComplement)),
% 13.85/2.47 inference(rectify,[],[f256])).
% 13.85/2.47 thf(f316,plain,(
% 13.85/2.47 (contraSubsetComplement = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y1 @ Y0)))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f315])).
% 13.85/2.47 thf(f317,plain,(
% 13.85/2.47 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 13.85/2.47 inference(fool_elimination,[],[f288])).
% 13.85/2.47 thf(f318,plain,(
% 13.85/2.47 (setOfPairsIsBReln1 = ! [X0 : $i,X1 : ($i > $i > $o)] : (breln1 @ X0 @ (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : ((X1 @ X2 @ X3))))))),
% 13.85/2.47 inference(rectify,[],[f292])).
% 13.85/2.47 thf(f319,plain,(
% 13.85/2.47 (setOfPairsIsBReln1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (breln1 @ Y1 @ (dpsetconstr @ Y1 @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y2 @ Y3))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f318])).
% 13.85/2.47 thf(f326,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (if @ X0 @ X1 @ X2 @ X3) @ X0))) = ifp)),
% 13.85/2.47 inference(rectify,[],[f225])).
% 13.85/2.47 thf(f327,plain,(
% 13.85/2.47 (ifp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (if @ Y2 @ Y1 @ Y0 @ Y3) @ Y2)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f326])).
% 13.85/2.47 thf(f330,plain,(
% 13.85/2.47 (setunionsingleton1 = ! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))),
% 13.85/2.47 inference(rectify,[],[f153])).
% 13.85/2.47 thf(f331,plain,(
% 13.85/2.47 (setunionsingleton1 = ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0)))))),
% 13.85/2.47 inference(fool_elimination,[],[f330])).
% 13.85/2.47 thf(f332,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) @ X0))) = apProp)),
% 13.85/2.47 inference(rectify,[],[f193])).
% 13.85/2.47 thf(f333,plain,(
% 13.85/2.47 (apProp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f332])).
% 13.85/2.47 thf(f346,plain,(
% 13.85/2.47 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 13.85/2.47 inference(fool_elimination,[],[f27])).
% 13.85/2.47 thf(f347,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (((setminus @ X1 @ (setminus @ X1 @ X0))) = X0)) = doubleComplementEq)),
% 13.85/2.47 inference(rectify,[],[f251])).
% 13.85/2.47 thf(f348,plain,(
% 13.85/2.47 (doubleComplementEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f347])).
% 13.85/2.47 thf(f353,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : ($i > $i),X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X1 @ X3) @ X2)) => (func @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[X4 : $i] : ((X1 @ X4)))))) = lamp)),
% 13.85/2.47 inference(rectify,[],[f199])).
% 13.85/2.47 thf(f354,plain,(
% 13.85/2.47 (lamp = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (func @ Y2 @ Y0 @ (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f353])).
% 13.85/2.47 thf(f355,plain,(
% 13.85/2.47 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 13.85/2.47 inference(rectify,[],[f19])).
% 13.85/2.47 thf(f356,plain,(
% 13.85/2.47 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f355])).
% 13.85/2.47 thf(f359,plain,(
% 13.85/2.47 (exuI2 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2)) => (exu @ (^[X3 : $i] : ((X0 @ X3))))))),
% 13.85/2.47 inference(rectify,[],[f65])).
% 13.85/2.47 thf(f360,plain,(
% 13.85/2.47 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f359])).
% 13.85/2.47 thf(f361,plain,(
% 13.85/2.47 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 13.85/2.47 inference(rectify,[],[f37])).
% 13.85/2.47 thf(f362,plain,(
% 13.85/2.47 (powersetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f361])).
% 13.85/2.47 thf(f363,plain,(
% 13.85/2.47 (binunionIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (binunion @ X2 @ X0))))),
% 13.85/2.47 inference(rectify,[],[f103])).
% 13.85/2.47 thf(f364,plain,(
% 13.85/2.47 (binunionIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f363])).
% 13.85/2.47 thf(f369,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (((binintersect @ X0 @ X1)) = emptyset)) = disjointsetsI1)),
% 13.85/2.47 inference(rectify,[],[f115])).
% 13.85/2.47 thf(f370,plain,(
% 13.85/2.47 (disjointsetsI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f369])).
% 13.85/2.47 thf(f371,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)) = doubleComplementSub2)),
% 13.85/2.47 inference(rectify,[],[f250])).
% 13.85/2.47 thf(f372,plain,(
% 13.85/2.47 (doubleComplementSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ (setminus @ Y0 @ Y1)) @ Y1))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f371])).
% 13.85/2.47 thf(f373,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : (((X2 = X0) | (in @ X0 @ X1)) <=> (in @ X0 @ (setadjoin @ X2 @ X1))) = setadjoinAx)),
% 13.85/2.47 inference(rectify,[],[f4])).
% 13.85/2.47 thf(f374,plain,(
% 13.85/2.47 (setadjoinAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y2 @ Y1) | (Y2 = Y0)) = (in @ Y2 @ (setadjoin @ Y0 @ Y1)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f373])).
% 13.85/2.47 thf(f377,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X1)))) = complementTE1)),
% 13.85/2.47 inference(rectify,[],[f240])).
% 13.85/2.47 thf(f378,plain,(
% 13.85/2.47 (complementTE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f377])).
% 13.85/2.47 thf(f381,plain,(
% 13.85/2.47 (! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))) = setunionsingleton2)),
% 13.85/2.47 inference(rectify,[],[f154])).
% 13.85/2.47 thf(f382,plain,(
% 13.85/2.47 (setunionsingleton2 = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset)))))))),
% 13.85/2.47 inference(fool_elimination,[],[f381])).
% 13.85/2.47 thf(f383,plain,(
% 13.85/2.47 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))) = nonemptyImpWitness)),
% 13.85/2.47 inference(rectify,[],[f45])).
% 13.85/2.47 thf(f384,plain,(
% 13.85/2.47 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f383])).
% 13.85/2.47 thf(f385,plain,(
% 13.85/2.47 (subsetTrans = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))))),
% 13.85/2.47 inference(rectify,[],[f89])).
% 13.85/2.47 thf(f386,plain,(
% 13.85/2.47 (subsetTrans = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y1 @ Y0) => (subset @ Y2 @ Y0)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f385])).
% 13.85/2.47 thf(f387,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : ($i > $o)] : (~ ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ~(X1 @ X3))) = quantDeMorgan3)),
% 13.85/2.47 inference(rectify,[],[f57])).
% 13.85/2.47 thf(f388,plain,(
% 13.85/2.47 (quantDeMorgan3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f387])).
% 13.85/2.47 thf(f389,plain,(
% 13.85/2.47 (cartprodsndpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (((ksnd @ (kpair @ X0 @ X3))) = X3))))),
% 13.85/2.47 inference(rectify,[],[f182])).
% 13.85/2.47 thf(f390,plain,(
% 13.85/2.47 (cartprodsndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f389])).
% 13.85/2.47 thf(f391,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (~(subset @ X1 @ X0) => (X0 != X1)) = notequalI1)),
% 13.85/2.47 inference(rectify,[],[f86])).
% 13.85/2.47 thf(f392,plain,(
% 13.85/2.47 (notequalI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f391])).
% 13.85/2.47 thf(f393,plain,(
% 13.85/2.47 (ksndsingleton = ! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : ((X0 = ((kpair @ (kfst @ X0) @ X1)))))))))),
% 13.85/2.47 inference(rectify,[],[f174])).
% 13.85/2.47 thf(f394,plain,(
% 13.85/2.47 (ksndsingleton = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f393])).
% 13.85/2.47 thf(f399,plain,(
% 13.85/2.47 (upairsetIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 13.85/2.47 inference(rectify,[],[f51])).
% 13.85/2.47 thf(f400,plain,(
% 13.85/2.47 (upairsetIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f399])).
% 13.85/2.47 thf(f405,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0)))) = singletoninpowunion)),
% 13.85/2.47 inference(rectify,[],[f142])).
% 13.85/2.47 thf(f406,plain,(
% 13.85/2.47 (singletoninpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f405])).
% 13.85/2.47 thf(f407,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((subset @ X0 @ (setminus @ X1 @ X2)) => ((in @ X3 @ X2) => ~(in @ X3 @ X0)))))) = contrasubsetT)),
% 13.85/2.47 inference(rectify,[],[f243])).
% 13.85/2.47 thf(f408,plain,(
% 13.85/2.47 (contrasubsetT = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((subset @ Y1 @ (setminus @ Y0 @ Y2)) => ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y1)))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f407])).
% 13.85/2.47 thf(f413,plain,(
% 13.85/2.47 (binintersectRsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1))),
% 13.85/2.47 inference(rectify,[],[f116])).
% 13.85/2.47 thf(f414,plain,(
% 13.85/2.47 (binintersectRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y0)))))))),
% 13.85/2.47 inference(fool_elimination,[],[f413])).
% 13.85/2.47 thf(f415,plain,(
% 13.85/2.47 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 13.85/2.47 inference(rectify,[],[f3])).
% 13.85/2.47 thf(f416,plain,(
% 13.85/2.47 (emptysetAx = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.85/2.47 inference(fool_elimination,[],[f415])).
% 13.85/2.47 thf(f417,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ (setminus @ X1 @ (setminus @ X1 @ X0)))) = doubleComplementSub1)),
% 13.85/2.47 inference(rectify,[],[f249])).
% 13.85/2.47 thf(f418,plain,(
% 13.85/2.47 (doubleComplementSub1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f417])).
% 13.85/2.47 thf(f419,plain,(
% 13.85/2.47 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 13.85/2.47 inference(rectify,[],[f163])).
% 13.85/2.47 thf(f420,plain,(
% 13.85/2.47 (theprop = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0))))))),
% 13.85/2.47 inference(fool_elimination,[],[f419])).
% 13.85/2.47 thf(f421,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)) = setadjoinSub)),
% 13.85/2.47 inference(rectify,[],[f90])).
% 13.85/2.47 thf(f422,plain,(
% 13.85/2.47 (setadjoinSub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f421])).
% 13.85/2.47 thf(f423,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X0 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
% 13.85/2.47 inference(rectify,[],[f47])).
% 13.85/2.47 thf(f424,plain,(
% 13.85/2.47 (notinsingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f423])).
% 13.85/2.47 thf(f427,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X1 @ X0)) = X1)) = binintersectSubset2)),
% 13.85/2.47 inference(rectify,[],[f112])).
% 13.85/2.47 thf(f428,plain,(
% 13.85/2.47 (binintersectSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f427])).
% 13.85/2.47 thf(f429,plain,(
% 13.85/2.47 (theeq = ! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))))),
% 13.85/2.47 inference(rectify,[],[f226])).
% 13.85/2.47 thf(f430,plain,(
% 13.85/2.47 (theeq = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f429])).
% 13.85/2.47 thf(f433,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (((setminus @ X0 @ (binunion @ X1 @ X2))) = ((binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))) = demorgan2)),
% 13.85/2.47 inference(rectify,[],[f277])).
% 13.85/2.47 thf(f434,plain,(
% 13.85/2.47 (demorgan2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((setminus @ Y1 @ (binunion @ Y0 @ Y2)) = (binintersect @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ Y2)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f433])).
% 13.85/2.47 thf(f435,plain,(
% 13.85/2.47 (woz1_1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ (setminus @ X1 @ (binintersect @ X0 @ X2)))))))),
% 13.85/2.47 inference(rectify,[],[f283])).
% 13.85/2.47 thf(f436,plain,(
% 13.85/2.47 (woz1_1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f435])).
% 13.85/2.47 thf(f437,plain,(
% 13.85/2.47 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 13.85/2.47 inference(rectify,[],[f106])).
% 13.85/2.47 thf(f438,plain,(
% 13.85/2.47 (binunionLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f437])).
% 13.85/2.47 thf(f439,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))) = woz13rule1)),
% 13.85/2.47 inference(rectify,[],[f279])).
% 13.85/2.47 thf(f440,plain,(
% 13.85/2.47 (woz13rule1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f439])).
% 13.85/2.47 thf(f441,plain,(
% 13.85/2.47 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 13.85/2.47 inference(rectify,[],[f82])).
% 13.85/2.47 thf(f442,plain,(
% 13.85/2.47 (emptysetsubset = ((!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0)))))),
% 13.85/2.47 inference(fool_elimination,[],[f441])).
% 13.85/2.47 thf(f443,plain,(
% 13.85/2.47 (! [X0 : $i] : ((in @ X0 @ omega) => (in @ (setadjoin @ X0 @ X0) @ omega)) = omegaSAx)),
% 13.85/2.47 inference(rectify,[],[f8])).
% 13.85/2.47 thf(f444,plain,(
% 13.85/2.47 (omegaSAx = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega))))))),
% 13.85/2.47 inference(fool_elimination,[],[f443])).
% 13.85/2.47 thf(f445,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (~(in @ X1 @ X0) => (in @ X1 @ (setminus @ X2 @ X0)))) = setminusI)),
% 13.85/2.47 inference(rectify,[],[f120])).
% 13.85/2.47 thf(f446,plain,(
% 13.85/2.47 (setminusI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (in @ Y1 @ (setminus @ Y0 @ Y2))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f445])).
% 13.85/2.47 thf(f447,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)) = eqimpsubset2)),
% 13.85/2.47 inference(rectify,[],[f79])).
% 13.85/2.47 thf(f448,plain,(
% 13.85/2.47 (eqimpsubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f447])).
% 13.85/2.47 thf(f449,plain,(
% 13.85/2.47 (! [X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X3 : $i] : ((X0 @ X3))))) = exuI1)),
% 13.85/2.47 inference(rectify,[],[f63])).
% 13.85/2.47 thf(f450,plain,(
% 13.85/2.47 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f449])).
% 13.85/2.47 thf(f451,plain,(
% 13.85/2.47 (notdexE = ! [X0 : $i,X1 : ($i > $o)] : (~ ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ~(X1 @ X3))))),
% 13.85/2.47 inference(rectify,[],[f61])).
% 13.85/2.47 thf(f452,plain,(
% 13.85/2.47 (notdexE = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f451])).
% 13.85/2.47 thf(f453,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
% 13.85/2.47 inference(rectify,[],[f231])).
% 13.85/2.47 thf(f454,plain,(
% 13.85/2.47 (binunionT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binunion @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f453])).
% 13.85/2.47 thf(f461,plain,(
% 13.85/2.47 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 13.85/2.47 inference(fool_elimination,[],[f32])).
% 13.85/2.47 thf(f462,plain,(
% 13.85/2.47 (kpairp = ! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X1 @ X0)))),
% 13.85/2.47 inference(rectify,[],[f139])).
% 13.85/2.47 thf(f463,plain,(
% 13.85/2.47 (kpairp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f462])).
% 13.85/2.47 thf(f464,plain,(
% 13.85/2.47 (exuE3u = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X3 : $i] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))))),
% 13.85/2.47 inference(rectify,[],[f68])).
% 13.85/2.47 thf(f465,plain,(
% 13.85/2.47 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f464])).
% 13.85/2.47 thf(f468,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => (((kfst @ (kpair @ X1 @ X3))) = X1))) = cartprodfstpairEq)),
% 13.85/2.47 inference(rectify,[],[f181])).
% 13.85/2.47 thf(f469,plain,(
% 13.85/2.47 (cartprodfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f468])).
% 13.85/2.47 thf(f470,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 13.85/2.47 inference(rectify,[],[f135])).
% 13.85/2.47 thf(f471,plain,(
% 13.85/2.47 (secondinupair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f470])).
% 13.85/2.47 thf(f474,plain,(
% 13.85/2.47 (! [X0 : ($i > $o),X1 : ($i > $o)] : (! [X2 : $i,X3 : $i] : ((X2 = X3) => ((X0 @ X3) <=> (X1 @ X2))) => ((exu @ (^[X4 : $i] : ((X0 @ X4)))) <=> (exu @ (^[X5 : $i] : ((X1 @ X5)))))) = exu__Cong)),
% 13.85/2.47 inference(rectify,[],[f69])).
% 13.85/2.47 thf(f475,plain,(
% 13.85/2.47 (exu__Cong = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) = (exu @ (^[Y2 : $i]: (Y0 @ Y2)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f474])).
% 13.85/2.47 thf(f478,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 13.85/2.47 inference(rectify,[],[f95])).
% 13.85/2.47 thf(f479,plain,(
% 13.85/2.47 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f478])).
% 13.85/2.47 thf(f480,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X1 @ X0)) = ((kpair @ X3 @ X2))) => (X0 = X2)) = setukpairinjR)),
% 13.85/2.47 inference(rectify,[],[f173])).
% 13.85/2.47 thf(f481,plain,(
% 13.85/2.47 (setukpairinjR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y3) = (kpair @ Y0 @ Y1)) => (Y3 = Y1))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f480])).
% 13.85/2.47 thf(f482,plain,(
% 13.85/2.47 (emptyInPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 13.85/2.47 inference(rectify,[],[f39])).
% 13.85/2.47 thf(f483,plain,(
% 13.85/2.47 (emptyInPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.85/2.47 inference(fool_elimination,[],[f482])).
% 13.85/2.47 thf(f484,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X1 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => (((ap @ X1 @ X0 @ X2 @ X3)) = X4))))) = funcGraphProp4)),
% 13.85/2.47 inference(rectify,[],[f208])).
% 13.85/2.47 thf(f485,plain,(
% 13.85/2.47 (funcGraphProp4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4)))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f484])).
% 13.85/2.47 thf(f488,plain,(
% 13.85/2.47 (setminusSubset1 = ! [X0 : $i,X1 : $i] : ((emptyset = ((setminus @ X1 @ X0))) => (subset @ X1 @ X0)))),
% 13.85/2.47 inference(rectify,[],[f129])).
% 13.85/2.47 thf(f489,plain,(
% 13.85/2.47 (setminusSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f488])).
% 13.85/2.47 thf(f490,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X0)))) = setminusT_lem)),
% 13.85/2.47 inference(rectify,[],[f233])).
% 13.85/2.47 thf(f491,plain,(
% 13.85/2.47 (setminusT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f490])).
% 13.85/2.47 thf(f496,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X1 @ X0)) = X0)) = binintersectSubset4)),
% 13.85/2.47 inference(rectify,[],[f117])).
% 13.85/2.47 thf(f497,plain,(
% 13.85/2.47 (binintersectSubset4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f496])).
% 13.85/2.47 thf(f500,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : ($i > $o),X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((X4 = X5) => ((X2 @ X4) <=> (X3 @ X5))))) => (((dsetconstr @ X0 @ (^[X6 : $i] : ((X2 @ X6))))) = ((dsetconstr @ X1 @ (^[X7 : $i] : ((X3 @ X7)))))))) = dsetconstr__Cong)),
% 13.85/2.47 inference(rectify,[],[f77])).
% 13.85/2.47 thf(f501,plain,(
% 13.85/2.47 (dsetconstr__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y3 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f500])).
% 13.85/2.47 thf(f502,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) = powersetT_lem)),
% 13.85/2.47 inference(rectify,[],[f232])).
% 13.85/2.47 thf(f503,plain,(
% 13.85/2.47 (powersetT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (powerset @ Y0) @ (powerset @ (powerset @ Y1))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f502])).
% 13.85/2.47 thf(f504,plain,(
% 13.85/2.47 (demorgan1a = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))))))))),
% 13.85/2.47 inference(rectify,[],[f271])).
% 13.85/2.47 thf(f505,plain,(
% 13.85/2.47 (demorgan1a = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))) => (in @ Y3 @ (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2)))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f504])).
% 13.85/2.47 thf(f506,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X1 @ (powerset @ X2)) => ((in @ X3 @ X1) => (in @ X3 @ X2)))))) = powersetTE1)),
% 13.85/2.47 inference(rectify,[],[f238])).
% 13.85/2.47 thf(f507,plain,(
% 13.85/2.47 (powersetTE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f506])).
% 13.85/2.47 thf(f508,plain,(
% 13.85/2.47 (omega0Ax = ((in @ emptyset @ omega)))),
% 13.85/2.47 inference(fool_elimination,[],[f7])).
% 13.85/2.47 thf(f511,plain,(
% 13.85/2.47 (upairequniteq = ! [X0 : $i,X1 : $i,X2 : $i] : ((((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) => (X1 = X2)))),
% 13.85/2.47 inference(rectify,[],[f171])).
% 13.85/2.47 thf(f512,plain,(
% 13.85/2.47 (upairequniteq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f511])).
% 13.85/2.47 thf(f515,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))) = powersetTI1)),
% 13.85/2.47 inference(rectify,[],[f237])).
% 13.85/2.47 thf(f516,plain,(
% 13.85/2.47 (powersetTI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f515])).
% 13.85/2.47 thf(f521,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = singletonsswitch)),
% 13.85/2.47 inference(rectify,[],[f49])).
% 13.85/2.47 thf(f522,plain,(
% 13.85/2.47 (singletonsswitch = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f521])).
% 13.85/2.47 thf(f525,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : ($i > $i > $o),X2 : $i,X3 : $i] : ((in @ X0 @ X2) => ! [X4 : $i] : ((in @ X4 @ X3) => ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X2 @ X3 @ (^[X5 : $i, X6 : $i] : ((X1 @ X5 @ X6))))) => (X1 @ X0 @ X4)))) = dpsetconstrERa)),
% 13.85/2.47 inference(rectify,[],[f188])).
% 13.85/2.47 thf(f526,plain,(
% 13.85/2.47 (dpsetconstrERa = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y3 @ Y4))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f525])).
% 13.85/2.47 thf(f527,plain,(
% 13.85/2.47 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 13.85/2.47 inference(rectify,[],[f108])).
% 13.85/2.47 thf(f528,plain,(
% 13.85/2.47 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f527])).
% 13.85/2.47 thf(f529,plain,(
% 13.85/2.47 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 13.85/2.47 inference(rectify,[],[f31])).
% 13.85/2.47 thf(f530,plain,(
% 13.85/2.47 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f529])).
% 13.85/2.47 thf(f531,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ X0)) => ((in @ X1 @ X0) | (X1 = X2))) = setadjoinOr)),
% 13.85/2.47 inference(rectify,[],[f35])).
% 13.85/2.47 thf(f532,plain,(
% 13.85/2.47 (setadjoinOr = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f531])).
% 13.85/2.47 thf(f533,plain,(
% 13.85/2.47 (setbeta = ! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((in @ X1 @ X0) => ((X2 @ X1) <=> (in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X2 @ X3))))))))),
% 13.85/2.47 inference(rectify,[],[f26])).
% 13.85/2.47 thf(f534,plain,(
% 13.85/2.47 (setbeta = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) = (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f533])).
% 13.85/2.47 thf(f535,plain,(
% 13.85/2.47 (nonemptyI1 = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))),
% 13.85/2.47 inference(rectify,[],[f30])).
% 13.85/2.47 thf(f536,plain,(
% 13.85/2.47 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0))))))),
% 13.85/2.47 inference(fool_elimination,[],[f535])).
% 13.85/2.47 thf(f537,plain,(
% 13.85/2.47 (emptyset__Cong = ((emptyset = emptyset)))),
% 13.85/2.47 inference(fool_elimination,[],[f70])).
% 13.85/2.47 thf(f538,plain,(
% 13.85/2.47 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)))),
% 13.85/2.47 inference(rectify,[],[f46])).
% 13.85/2.47 thf(f539,plain,(
% 13.85/2.47 (uniqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f538])).
% 13.85/2.47 thf(f540,plain,(
% 13.85/2.47 (powerset__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f72])).
% 13.85/2.47 thf(f541,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))) = app)),
% 13.85/2.47 inference(rectify,[],[f194])).
% 13.85/2.47 thf(f542,plain,(
% 13.85/2.47 (app = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y1 @ Y0 @ Y3) @ Y1)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f541])).
% 13.85/2.47 thf(f543,plain,(
% 13.85/2.47 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X2 @ X0)) => ~(in @ X1 @ X0)))),
% 13.85/2.47 inference(rectify,[],[f122])).
% 13.85/2.47 thf(f544,plain,(
% 13.85/2.47 (setminusER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f543])).
% 13.85/2.47 thf(f547,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setadjoin @ X1 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))) = setukpairinjR11)),
% 13.85/2.47 inference(rectify,[],[f168])).
% 13.85/2.47 thf(f548,plain,(
% 13.85/2.47 (setukpairinjR11 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f547])).
% 13.85/2.47 thf(f551,plain,(
% 13.85/2.47 (setukpairIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 13.85/2.47 inference(rectify,[],[f136])).
% 13.85/2.47 thf(f552,plain,(
% 13.85/2.47 (setukpairIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f551])).
% 13.85/2.47 thf(f553,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X1 @ X0)) => (in @ (ksnd @ X2) @ X0)) = cartprodsndin)),
% 13.85/2.47 inference(rectify,[],[f177])).
% 13.85/2.47 thf(f554,plain,(
% 13.85/2.47 (cartprodsndin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (ksnd @ Y0) @ Y2))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f553])).
% 13.85/2.47 thf(f555,plain,(
% 13.85/2.47 (! [X0 : $i] : (in @ emptyset @ (powerset @ X0)) = emptyinPowerset)),
% 13.85/2.47 inference(rectify,[],[f38])).
% 13.85/2.47 thf(f556,plain,(
% 13.85/2.47 (emptyinPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.85/2.47 inference(fool_elimination,[],[f555])).
% 13.85/2.47 thf(f557,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)) = binunionRsub)),
% 13.85/2.47 inference(rectify,[],[f107])).
% 13.85/2.47 thf(f558,plain,(
% 13.85/2.47 (binunionRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f557])).
% 13.85/2.47 thf(f561,plain,(
% 13.85/2.47 (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
% 13.85/2.47 inference(rectify,[],[f111])).
% 13.85/2.47 thf(f562,plain,(
% 13.85/2.47 (binintersectLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1)))))))),
% 13.85/2.47 inference(fool_elimination,[],[f561])).
% 13.85/2.47 thf(f567,plain,(
% 13.85/2.47 (ex1E1 = ! [X0 : $i,X1 : ($i > $o)] : ((ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) => ? [X3 : $i] : ((in @ X3 @ X0) & (X1 @ X3))))),
% 13.85/2.47 inference(rectify,[],[f157])).
% 13.85/2.47 thf(f568,plain,(
% 13.85/2.47 (ex1E1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f567])).
% 13.85/2.47 thf(f569,plain,(
% 13.85/2.47 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 13.85/2.47 inference(rectify,[],[f78])).
% 13.85/2.47 thf(f570,plain,(
% 13.85/2.47 (subsetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f569])).
% 13.85/2.47 thf(f573,plain,(
% 13.85/2.47 (setunionE2 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ? [X2 : $i] : ((in @ X0 @ X2) & (in @ X2 @ X1))))),
% 13.85/2.47 inference(rectify,[],[f152])).
% 13.85/2.47 thf(f574,plain,(
% 13.85/2.47 (setunionE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f573])).
% 13.85/2.47 thf(f575,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = complementImpComplementIntersect)),
% 13.85/2.47 inference(rectify,[],[f253])).
% 13.85/2.47 thf(f576,plain,(
% 13.85/2.47 (complementImpComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f575])).
% 13.85/2.47 thf(f579,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) <=> (in @ X0 @ (powerset @ X1))) = powersetAx)),
% 13.85/2.47 inference(rectify,[],[f5])).
% 13.85/2.47 thf(f580,plain,(
% 13.85/2.47 (powersetAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f579])).
% 13.85/2.47 thf(f581,plain,(
% 13.85/2.47 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))),
% 13.85/2.47 inference(rectify,[],[f230])).
% 13.85/2.47 thf(f582,plain,(
% 13.85/2.47 (binintersectT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ Y0))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f581])).
% 13.85/2.47 thf(f583,plain,(
% 13.85/2.47 (setminusERneg = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ (setminus @ X1 @ X2)) => ((in @ X0 @ X1) => (in @ X0 @ X2))))),
% 13.85/2.47 inference(rectify,[],[f124])).
% 13.85/2.47 thf(f584,plain,(
% 13.85/2.47 (setminusERneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f583])).
% 13.85/2.47 thf(f587,plain,(
% 13.85/2.47 (powersetsubset = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (subset @ (powerset @ X1) @ (powerset @ X0))))),
% 13.85/2.47 inference(rectify,[],[f98])).
% 13.85/2.47 thf(f588,plain,(
% 13.85/2.47 (powersetsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f587])).
% 13.85/2.47 thf(f589,plain,(
% 13.85/2.47 (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)))),
% 13.85/2.47 inference(rectify,[],[f96])).
% 13.85/2.47 thf(f590,plain,(
% 13.85/2.47 (powersetE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f589])).
% 13.85/2.47 thf(f591,plain,(
% 13.85/2.47 (breln1all1 = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X1) => (X2 @ X5)))))),
% 13.85/2.47 inference(rectify,[],[f293])).
% 13.85/2.47 thf(f592,plain,(
% 13.85/2.47 (breln1all1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f591])).
% 13.85/2.47 thf(f593,plain,(
% 13.85/2.47 (noeltsimpempty = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 13.85/2.47 inference(rectify,[],[f25])).
% 13.85/2.47 thf(f594,plain,(
% 13.85/2.47 (noeltsimpempty = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.85/2.47 inference(fool_elimination,[],[f593])).
% 13.85/2.47 thf(f595,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))) = woz1_4)),
% 13.85/2.47 inference(rectify,[],[f286])).
% 13.85/2.47 thf(f596,plain,(
% 13.85/2.47 (woz1_4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (subset @ Y2 @ (setminus @ Y1 @ Y0)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f595])).
% 13.85/2.47 thf(f597,plain,(
% 13.85/2.47 (ksndpairEq = ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X1 @ X0))) = X0))),
% 13.85/2.47 inference(rectify,[],[f175])).
% 13.85/2.47 thf(f598,plain,(
% 13.85/2.47 (ksndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1)))))))),
% 13.85/2.47 inference(fool_elimination,[],[f597])).
% 13.85/2.47 thf(f599,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (funcSet @ X1 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (ap @ X1 @ X2 @ X0 @ X3) @ X2))) = ap2p)),
% 13.85/2.47 inference(rectify,[],[f196])).
% 13.85/2.47 thf(f600,plain,(
% 13.85/2.47 (ap2p = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ Y1 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (ap @ Y1 @ Y0 @ Y2 @ Y3) @ Y0)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f599])).
% 13.85/2.47 thf(f601,plain,(
% 13.85/2.47 (! [X0 : $i] : ((in @ X0 @ emptyset) => $false) = emptysetimpfalse)),
% 13.85/2.47 inference(rectify,[],[f20])).
% 13.85/2.47 thf(f602,plain,(
% 13.85/2.47 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false)))))),
% 13.85/2.47 inference(fool_elimination,[],[f601])).
% 13.85/2.47 thf(f603,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (powerset @ (setunion @ X1)))) = subPowSU)),
% 13.85/2.47 inference(rectify,[],[f43])).
% 13.85/2.47 thf(f604,plain,(
% 13.85/2.47 (subPowSU = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f603])).
% 13.85/2.47 thf(f605,plain,(
% 13.85/2.47 (omega__Cong = ((omega = omega)))),
% 13.85/2.47 inference(fool_elimination,[],[f74])).
% 13.85/2.47 thf(f606,plain,(
% 13.85/2.47 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => (! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (in @ (kpair @ X3 @ X4) @ X2)))) => (! [X5 : $i] : ((in @ X5 @ X1) => ! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X2) => (in @ (kpair @ X5 @ X6) @ X0)))) => (X0 = X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.85/2.47 inference(rectify,[],[f296])).
% 13.85/2.47 thf(f607,plain,(
% 13.85/2.47 (((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ Y1)))))))) => (Y1 = Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 13.85/2.47 inference(fool_elimination,[],[f606])).
% 13.85/2.47 thf(f608,plain,(
% 13.85/2.47 (kfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1)))))))),
% 13.85/2.47 inference(fool_elimination,[],[f164])).
% 13.85/2.47 thf(f609,plain,(
% 13.85/2.47 (! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)) = subsetemptysetimpeq)),
% 13.85/2.47 inference(rectify,[],[f94])).
% 13.85/2.47 thf(f610,plain,(
% 13.85/2.47 (subsetemptysetimpeq = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0))))))),
% 13.85/2.47 inference(fool_elimination,[],[f609])).
% 13.85/2.47 thf(f613,plain,(
% 13.85/2.47 (nonemptyI = ! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((in @ X1 @ X0) => ((X2 @ X1) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X2 @ X3))))))))),
% 13.85/2.47 inference(rectify,[],[f29])).
% 13.85/2.47 thf(f614,plain,(
% 13.85/2.47 (nonemptyI = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (nonempty @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f613])).
% 13.85/2.47 thf(f615,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => (in @ X0 @ (funcSet @ X2 @ X1))) = funcinfuncset)),
% 13.85/2.47 inference(rectify,[],[f197])).
% 13.85/2.47 thf(f616,plain,(
% 13.85/2.47 (funcinfuncset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (in @ Y2 @ (funcSet @ Y0 @ Y1)))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f615])).
% 13.85/2.47 thf(f617,plain,(
% 13.85/2.47 (ubforcartprodlem3 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X1 @ X3) @ (powerset @ (powerset @ (binunion @ X2 @ X0)))))))),
% 13.85/2.47 inference(rectify,[],[f148])).
% 13.85/2.47 thf(f618,plain,(
% 13.85/2.47 (ubforcartprodlem3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f617])).
% 13.85/2.47 thf(f623,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X0 @ X2) => ! [X3 : $i] : ((breln @ X1 @ X0 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X6 : $i] : ((in @ X6 @ X1) => ! [X7 : $i] : ((in @ X7 @ X0) => ((in @ (kpair @ X6 @ X7) @ X3) => (in @ (kpair @ X6 @ X7) @ X2)))) => (X2 = X3))))) = eqbreln)),
% 13.85/2.47 inference(rectify,[],[f210])).
% 13.85/2.47 thf(f624,plain,(
% 13.85/2.47 (eqbreln = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3)))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f623])).
% 13.85/2.47 thf(f625,plain,(
% 13.85/2.47 (ubforcartprodlem2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X0)))))))),
% 13.85/2.47 inference(rectify,[],[f147])).
% 13.85/2.47 thf(f626,plain,(
% 13.85/2.47 (ubforcartprodlem2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f625])).
% 13.85/2.47 thf(f627,plain,(
% 13.85/2.47 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 13.85/2.47 inference(rectify,[],[f23])).
% 13.85/2.47 thf(f628,plain,(
% 13.85/2.47 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f627])).
% 13.85/2.47 thf(f633,plain,(
% 13.85/2.47 (woz13rule2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 13.85/2.47 inference(rectify,[],[f280])).
% 13.85/2.47 thf(f634,plain,(
% 13.85/2.47 (woz13rule2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f633])).
% 13.85/2.47 thf(f637,plain,(
% 13.85/2.47 (setukpairinjR2 = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = ((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) => (X1 = X2)))),
% 13.85/2.47 inference(rectify,[],[f172])).
% 13.85/2.47 thf(f638,plain,(
% 13.85/2.47 (setukpairinjR2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y1))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f637])).
% 13.85/2.47 thf(f641,plain,(
% 13.85/2.47 (quantDeMorgan4 = ! [X0 : ($i > $o),X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X1) & ~(X0 @ X2)) => ~ ! [X3 : $i] : ((in @ X3 @ X1) => (X0 @ X3))))),
% 13.85/2.47 inference(rectify,[],[f58])).
% 13.85/2.47 thf(f642,plain,(
% 13.85/2.47 (quantDeMorgan4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f641])).
% 13.85/2.47 thf(f643,plain,(
% 13.85/2.47 (complementTcontraSubset = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))))),
% 13.85/2.47 inference(rectify,[],[f257])).
% 13.85/2.47 thf(f644,plain,(
% 13.85/2.47 (complementTcontraSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (subset @ Y2 @ (setminus @ Y1 @ Y0)))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f643])).
% 13.85/2.47 thf(f655,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X1 @ emptyset))) => (X0 = X1)) = singletonsuniq)),
% 13.85/2.47 inference(rectify,[],[f160])).
% 13.85/2.47 thf(f656,plain,(
% 13.85/2.47 (singletonsuniq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f655])).
% 13.85/2.47 thf(f657,plain,(
% 13.85/2.47 (setminusELneg = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X1 @ (setminus @ X0 @ X2)) => (~(in @ X1 @ X2) => ~(in @ X1 @ X0))))),
% 13.85/2.47 inference(rectify,[],[f125])).
% 13.85/2.47 thf(f658,plain,(
% 13.85/2.47 (setminusELneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f657])).
% 13.85/2.47 thf(f659,plain,(
% 13.85/2.47 (lamProp = ! [X0 : $i,X1 : ($i > $i),X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X1 @ X3) @ X0)) => (func @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[X4 : $i, X5 : $i] : ((((X1 @ X4)) = X5)))))))),
% 13.85/2.47 inference(rectify,[],[f198])).
% 13.85/2.47 thf(f660,plain,(
% 13.85/2.47 (lamProp = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (func @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y1 @ Y3) = Y4)))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f659])).
% 13.85/2.47 thf(f663,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0)))))) = doubleComplementI1)),
% 13.85/2.47 inference(rectify,[],[f247])).
% 13.85/2.47 thf(f664,plain,(
% 13.85/2.47 (doubleComplementI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f663])).
% 13.85/2.47 thf(f667,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X1 @ X0))))) = upairinpowunion)),
% 13.85/2.47 inference(rectify,[],[f145])).
% 13.85/2.47 thf(f668,plain,(
% 13.85/2.47 (upairinpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f667])).
% 13.85/2.47 thf(f671,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X0 @ X2)) = ((kpair @ X1 @ X3))) => (X0 = X1)) = setukpairinjL)),
% 13.85/2.47 inference(rectify,[],[f167])).
% 13.85/2.47 thf(f672,plain,(
% 13.85/2.47 (setukpairinjL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y2 @ Y0)) => (Y3 = Y2))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f671])).
% 13.85/2.47 thf(f673,plain,(
% 13.85/2.47 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 13.85/2.47 inference(rectify,[],[f234])).
% 13.85/2.47 thf(f674,plain,(
% 13.85/2.47 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f673])).
% 13.85/2.47 thf(f679,plain,(
% 13.85/2.47 ((^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 13.85/2.47 inference(rectify,[],[f1])).
% 13.85/2.47 thf(f680,plain,(
% 13.85/2.47 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f679])).
% 13.85/2.47 thf(f685,plain,(
% 13.85/2.47 (subsetRefl = ! [X0 : $i] : (subset @ X0 @ X0))),
% 13.85/2.47 inference(rectify,[],[f88])).
% 13.85/2.47 thf(f686,plain,(
% 13.85/2.47 (subsetRefl = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))))),
% 13.85/2.47 inference(fool_elimination,[],[f685])).
% 13.85/2.47 thf(f687,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ (setminus @ X1 @ (binintersect @ X0 @ X2)))))) = complementInPowersetComplementIntersect)),
% 13.85/2.47 inference(rectify,[],[f255])).
% 13.85/2.47 thf(f688,plain,(
% 13.85/2.47 (complementInPowersetComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f687])).
% 13.85/2.47 thf(f689,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : ($i > $i > $o)] : ((in @ (kpair @ X3 @ X0) @ (dpsetconstr @ X2 @ X1 @ (^[X5 : $i, X6 : $i] : ((X4 @ X5 @ X6))))) => (in @ X0 @ X1)) = dpsetconstrEL2)),
% 13.85/2.47 inference(rectify,[],[f190])).
% 13.85/2.47 thf(f690,plain,(
% 13.85/2.47 (dpsetconstrEL2 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (in @ Y4 @ Y3))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f689])).
% 13.85/2.47 thf(f691,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (((kpair @ X2 @ X3)) = ((kpair @ X2 @ X3))))) = cartprodmempaircEq)),
% 13.85/2.47 inference(rectify,[],[f180])).
% 13.85/2.47 thf(f692,plain,(
% 13.85/2.47 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f691])).
% 13.85/2.47 thf(f693,plain,(
% 13.85/2.47 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 13.85/2.47 inference(rectify,[],[f21])).
% 13.85/2.47 thf(f694,plain,(
% 13.85/2.47 (notinemptyset = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.85/2.47 inference(fool_elimination,[],[f693])).
% 13.85/2.47 thf(f699,plain,(
% 13.85/2.47 (singletonsubset = ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1)))),
% 13.85/2.47 inference(rectify,[],[f140])).
% 13.85/2.47 thf(f700,plain,(
% 13.85/2.47 (singletonsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f699])).
% 13.85/2.47 thf(f701,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (~(in @ X1 @ X0) => (X0 != X2))) = notequalI2)),
% 13.85/2.47 inference(rectify,[],[f87])).
% 13.85/2.47 thf(f702,plain,(
% 13.85/2.47 (notequalI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (~ (Y2 = Y0))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f701])).
% 13.85/2.47 thf(f703,plain,(
% 13.85/2.47 (setunionsingleton = ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0)))))),
% 13.85/2.47 inference(fool_elimination,[],[f155])).
% 13.85/2.47 thf(f704,plain,(
% 13.85/2.47 (funcImageSingleton = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X2 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X1))))))))),
% 13.85/2.47 inference(rectify,[],[f192])).
% 13.85/2.47 thf(f705,plain,(
% 13.85/2.47 (funcImageSingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1))))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f704])).
% 13.85/2.47 thf(f710,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = upairset2IR)),
% 13.85/2.47 inference(rectify,[],[f102])).
% 13.85/2.47 thf(f711,plain,(
% 13.85/2.47 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f710])).
% 13.85/2.47 thf(f712,plain,(
% 13.85/2.47 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X2 @ X1)) => (in @ X0 @ X1)))),
% 13.85/2.47 inference(rectify,[],[f114])).
% 13.85/2.47 thf(f713,plain,(
% 13.85/2.47 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f712])).
% 13.85/2.47 thf(f714,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = subset2powerset)),
% 13.85/2.47 inference(rectify,[],[f92])).
% 13.85/2.47 thf(f715,plain,(
% 13.85/2.47 (subset2powerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f714])).
% 13.85/2.47 thf(f716,plain,(
% 13.85/2.47 (inPowerset = ! [X0 : $i] : (in @ X0 @ (powerset @ X0)))),
% 13.85/2.47 inference(rectify,[],[f97])).
% 13.85/2.47 thf(f717,plain,(
% 13.85/2.47 (inPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0))))))),
% 13.85/2.47 inference(fool_elimination,[],[f716])).
% 13.85/2.47 thf(f718,plain,(
% 13.85/2.47 (ap2apEq2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => (((ap @ X2 @ X1 @ X0 @ X3)) = ((ap @ X2 @ X1 @ X0 @ X3))))))),
% 13.85/2.47 inference(rectify,[],[f214])).
% 13.85/2.47 thf(f719,plain,(
% 13.85/2.47 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ Y2 @ Y3) = (ap @ Y0 @ Y1 @ Y2 @ Y3))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f718])).
% 13.85/2.47 thf(f722,plain,(
% 13.85/2.47 (exuEu = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X3 : $i] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))))),
% 13.85/2.47 inference(rectify,[],[f75])).
% 13.85/2.47 thf(f723,plain,(
% 13.85/2.47 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f722])).
% 13.85/2.47 thf(f726,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)) = setukpairinjL1)),
% 13.85/2.47 inference(rectify,[],[f161])).
% 13.85/2.47 thf(f727,plain,(
% 13.85/2.47 (setukpairinjL1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f726])).
% 13.85/2.47 thf(f728,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ((in @ X2 @ X1) => (in @ X0 @ (setunion @ X1)))) = setunionI)),
% 13.85/2.47 inference(rectify,[],[f41])).
% 13.85/2.47 thf(f729,plain,(
% 13.85/2.47 (setunionI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f728])).
% 13.85/2.47 thf(f730,plain,(
% 13.85/2.47 (exuE1 = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : (! [X3 : $i] : ((X0 @ X3) => (X2 = X3)) & (X0 @ X2))))),
% 13.85/2.47 inference(rectify,[],[f17])).
% 13.85/2.47 thf(f731,plain,(
% 13.85/2.47 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f730])).
% 13.85/2.47 thf(f732,plain,(
% 13.85/2.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => (in @ X0 @ X2)) = setminusEL)),
% 13.85/2.47 inference(rectify,[],[f121])).
% 13.85/2.47 thf(f733,plain,(
% 13.85/2.47 (setminusEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f732])).
% 13.85/2.47 thf(f734,plain,(
% 13.85/2.47 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))))))),
% 13.85/2.47 inference(fool_elimination,[],[f71])).
% 13.85/2.47 thf(f737,plain,(
% 13.85/2.47 (! [X0 : $i] : ((iskpair @ X0) => (((kpair @ (kfst @ X0) @ (ksnd @ X0))) = X0)) = kpairsurjEq)),
% 13.85/2.47 inference(rectify,[],[f176])).
% 13.85/2.47 thf(f738,plain,(
% 13.85/2.47 (kpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0))))))),
% 13.85/2.48 inference(fool_elimination,[],[f737])).
% 13.85/2.48 thf(f739,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)) = binintersectSubset1)),
% 13.85/2.48 inference(rectify,[],[f118])).
% 13.85/2.48 thf(f740,plain,(
% 13.85/2.48 (binintersectSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f739])).
% 13.85/2.48 thf(f743,plain,(
% 13.85/2.48 (setadjoinIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (setadjoin @ X1 @ X0))))),
% 13.85/2.48 inference(rectify,[],[f33])).
% 13.85/2.48 thf(f744,plain,(
% 13.85/2.48 (setadjoinIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2)))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f743])).
% 13.85/2.48 thf(f745,plain,(
% 13.85/2.48 (binintersectSubset5 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((subset @ X1 @ X0) => (subset @ X1 @ (binintersect @ X2 @ X0)))))),
% 13.85/2.48 inference(rectify,[],[f109])).
% 13.85/2.48 thf(f746,plain,(
% 13.85/2.48 (binintersectSubset5 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f745])).
% 13.85/2.48 thf(f747,plain,(
% 13.85/2.48 (singletonprop = ! [X0 : ($i > $o),X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((in @ X4 @ X1) & (X0 @ X4)) => (singleton @ (dsetconstr @ X1 @ (^[X5 : $i] : ((X0 @ X5))))))))),
% 13.85/2.48 inference(rectify,[],[f156])).
% 13.85/2.48 thf(f748,plain,(
% 13.85/2.48 (singletonprop = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f747])).
% 13.85/2.48 thf(f749,plain,(
% 13.85/2.48 (symdiffIneg2 = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X1 @ X0) => (~(in @ X1 @ X2) => ~(in @ X1 @ (symdiff @ X0 @ X2)))))),
% 13.85/2.48 inference(rectify,[],[f134])).
% 13.85/2.48 thf(f750,plain,(
% 13.85/2.48 (symdiffIneg2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0)))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f749])).
% 13.85/2.48 thf(f751,plain,(
% 13.85/2.48 (eqinunit = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 13.85/2.48 inference(rectify,[],[f48])).
% 13.85/2.48 thf(f752,plain,(
% 13.85/2.48 (eqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f751])).
% 13.85/2.48 thf(f753,plain,(
% 13.85/2.48 (setminusILneg = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X0 @ X1))))),
% 13.85/2.48 inference(rectify,[],[f126])).
% 13.85/2.48 thf(f754,plain,(
% 13.85/2.48 (setminusILneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f753])).
% 13.85/2.48 thf(f759,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X0 @ X2)) => (in @ (kfst @ X1) @ X0)) = cartprodfstin)),
% 13.85/2.48 inference(rectify,[],[f165])).
% 13.85/2.48 thf(f760,plain,(
% 13.85/2.48 (cartprodfstin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (kfst @ Y1) @ Y2))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f759])).
% 13.85/2.48 thf(f761,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (powerset @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = powersetE)),
% 13.85/2.48 inference(rectify,[],[f40])).
% 13.85/2.48 thf(f762,plain,(
% 13.85/2.48 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f761])).
% 13.85/2.48 thf(f763,plain,(
% 13.85/2.48 (demorgan2b = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) => (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))))))),
% 13.85/2.48 inference(rectify,[],[f276])).
% 13.85/2.48 thf(f764,plain,(
% 13.85/2.48 (demorgan2b = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (binintersect @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2)))))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f763])).
% 13.85/2.48 thf(f765,plain,(
% 13.85/2.48 (cartprodpairmemEL = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((in @ (kpair @ X1 @ X0) @ (cartprod @ X3 @ X2)) => (in @ X1 @ X3)))),
% 13.85/2.48 inference(rectify,[],[f178])).
% 13.85/2.48 thf(f766,plain,(
% 13.85/2.48 (cartprodpairmemEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f765])).
% 13.85/2.48 thf(f767,plain,(
% 13.85/2.48 (setminusLsub = ! [X0 : $i,X1 : $i] : (subset @ (setminus @ X1 @ X0) @ X1))),
% 13.85/2.48 inference(rectify,[],[f128])).
% 13.85/2.48 thf(f768,plain,(
% 13.85/2.48 (setminusLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0)))))))),
% 13.85/2.48 inference(fool_elimination,[],[f767])).
% 13.85/2.48 thf(f769,plain,(
% 13.85/2.48 (eta2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X2 @ X0)) => (((lam @ X2 @ X0 @ (^[X3 : $i] : ((ap @ X2 @ X0 @ X1 @ X3))))) = X1)))),
% 13.85/2.48 inference(rectify,[],[f219])).
% 13.85/2.48 thf(f770,plain,(
% 13.85/2.48 (eta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => ((lam @ Y0 @ Y2 @ (^[Y3 : $i]: (ap @ Y0 @ Y2 @ Y1 @ Y3))) = Y1))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f769])).
% 13.85/2.48 thf(f771,plain,(
% 13.85/2.48 (! [X0 : ($i > $i > $o),X1 : $i,X2 : $i,X3 : $i] : ((in @ X3 @ X2) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X0 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X2 @ X1 @ (^[X5 : $i, X6 : $i] : ((X0 @ X5 @ X6)))))))) = dpsetconstrI)),
% 13.85/2.48 inference(rectify,[],[f185])).
% 13.85/2.48 thf(f772,plain,(
% 13.85/2.48 (dpsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))))))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f771])).
% 13.85/2.48 thf(f775,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X1) => (X2 @ X5)))) = breln1all2)),
% 13.85/2.48 inference(rectify,[],[f289])).
% 13.85/2.48 thf(f776,plain,(
% 13.85/2.48 (breln1all2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f775])).
% 13.85/2.48 thf(f779,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) => (in @ X3 @ (setminus @ X1 @ X0)))))) = demorgan2a1)),
% 13.85/2.48 inference(rectify,[],[f268])).
% 13.85/2.48 thf(f780,plain,(
% 13.85/2.48 (demorgan2a1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f779])).
% 13.85/2.48 thf(f783,plain,(
% 13.85/2.48 (contrasubsetT2 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((subset @ X0 @ X2) => (subset @ (setminus @ X1 @ X2) @ (setminus @ X1 @ X0))))))),
% 13.85/2.48 inference(rectify,[],[f245])).
% 13.85/2.48 thf(f784,plain,(
% 13.85/2.48 (contrasubsetT2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => (subset @ (setminus @ Y0 @ Y2) @ (setminus @ Y0 @ Y1)))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f783])).
% 13.85/2.48 thf(f785,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (((kpair @ (kfst @ X1) @ (ksnd @ X1))) = X1)) = cartprodpairsurjEq)),
% 13.85/2.48 inference(rectify,[],[f183])).
% 13.85/2.48 thf(f786,plain,(
% 13.85/2.48 (cartprodpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f785])).
% 13.85/2.48 thf(f789,plain,(
% 13.85/2.48 (iftrueProp2 = ! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X2 => (((setadjoin @ X1 @ emptyset)) = ((dsetconstr @ X0 @ (^[X4 : $i] : ((~X2 & (X4 = X3)) | ((X1 = X4) & X2))))))))))),
% 13.85/2.48 inference(rectify,[],[f223])).
% 13.85/2.48 thf(f790,plain,(
% 13.85/2.48 (iftrueProp2 = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (Y0 => ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y0 & (Y1 = Y4)) | ((Y3 = Y4) & (~ Y0)))))))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f789])).
% 13.85/2.48 thf(f795,plain,(
% 13.85/2.48 (setOfPairsIsBReln = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o)] : (breln @ X0 @ X1 @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((X2 @ X3 @ X4))))))),
% 13.85/2.48 inference(rectify,[],[f187])).
% 13.85/2.48 thf(f796,plain,(
% 13.85/2.48 (setOfPairsIsBReln = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y2 @ Y1 @ (dpsetconstr @ Y2 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y0 @ Y3 @ Y4))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f795])).
% 13.85/2.48 thf(f797,plain,(
% 13.85/2.48 (iftrue = ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X0 => (((if @ X2 @ X0 @ X1 @ X3)) = X1)))))),
% 13.85/2.48 inference(rectify,[],[f227])).
% 13.85/2.48 thf(f798,plain,(
% 13.85/2.48 (iftrue = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((if @ Y0 @ Y2 @ Y1 @ Y3) = Y1))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f797])).
% 13.85/2.48 thf(f799,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)) = setunionE)),
% 13.85/2.48 inference(rectify,[],[f42])).
% 13.85/2.48 thf(f800,plain,(
% 13.85/2.48 (setunionE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f799])).
% 13.85/2.48 thf(f803,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0)) = binintersectSubset3)),
% 13.85/2.48 inference(rectify,[],[f113])).
% 13.85/2.48 thf(f804,plain,(
% 13.85/2.48 (binintersectSubset3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f803])).
% 13.85/2.48 thf(f805,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2))) = subsetE)),
% 13.85/2.48 inference(rectify,[],[f83])).
% 13.85/2.48 thf(f806,plain,(
% 13.85/2.48 (subsetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f805])).
% 13.85/2.48 thf(f807,plain,(
% 13.85/2.48 (! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3))) => (exu @ (^[X4 : $i] : ((X0 @ X4)))))) = exuI3)),
% 13.85/2.48 inference(rectify,[],[f64])).
% 13.85/2.48 thf(f808,plain,(
% 13.85/2.48 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f807])).
% 13.85/2.48 thf(f813,plain,(
% 13.85/2.48 (lam2p = ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X2 @ X3) @ X0)) => (in @ (lam @ X1 @ X0 @ (^[X4 : $i] : ((X2 @ X4)))) @ (funcSet @ X1 @ X0))))),
% 13.85/2.48 inference(rectify,[],[f200])).
% 13.85/2.48 thf(f814,plain,(
% 13.85/2.48 (lam2p = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (in @ (lam @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))) @ (funcSet @ Y1 @ Y2)))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f813])).
% 13.85/2.48 thf(f815,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) => (in @ X3 @ (setminus @ X1 @ X0)))))) = inComplementUnionImpInComplement1)),
% 13.85/2.48 inference(rectify,[],[f265])).
% 13.85/2.48 thf(f816,plain,(
% 13.85/2.48 (inComplementUnionImpInComplement1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f815])).
% 13.85/2.48 thf(f819,plain,(
% 13.85/2.48 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 13.85/2.48 inference(rectify,[],[f59])).
% 13.85/2.48 thf(f820,plain,(
% 13.85/2.48 (prop2setI = ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))))))),
% 13.85/2.48 inference(fool_elimination,[],[f819])).
% 13.85/2.48 thf(f821,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = upairsetIR)),
% 13.85/2.48 inference(rectify,[],[f52])).
% 13.85/2.48 thf(f822,plain,(
% 13.85/2.48 (upairsetIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f821])).
% 13.85/2.48 thf(f825,plain,(
% 13.85/2.48 (setadjoinSub2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => (subset @ X1 @ (setadjoin @ X2 @ X0))))),
% 13.85/2.48 inference(rectify,[],[f91])).
% 13.85/2.48 thf(f826,plain,(
% 13.85/2.48 (setadjoinSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2)))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f825])).
% 13.85/2.48 thf(f827,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : ($i > $i),X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X1 @ X3) @ X2)) => (((lam @ X0 @ X2 @ (^[X4 : $i] : ((X1 @ X4))))) = ((lam @ X0 @ X2 @ (^[X5 : $i] : ((X1 @ X5))))))) = lam2lamEq)),
% 13.85/2.48 inference(rectify,[],[f217])).
% 13.85/2.48 thf(f828,plain,(
% 13.85/2.48 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => ((lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))) = (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f827])).
% 13.85/2.48 thf(f835,plain,(
% 13.85/2.48 (prop2setE = ! [X0 : $i,X1 : $o] : ((in @ X0 @ (prop2set @ X1)) => X1))),
% 13.85/2.48 inference(rectify,[],[f18])).
% 13.85/2.48 thf(f836,plain,(
% 13.85/2.48 (prop2setE = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0)))))))),
% 13.85/2.48 inference(fool_elimination,[],[f835])).
% 13.85/2.48 thf(f839,plain,(
% 13.85/2.48 (inCongP = ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X2 @ X1) => (in @ X3 @ X0)))))),
% 13.85/2.48 inference(rectify,[],[f66])).
% 13.85/2.48 thf(f840,plain,(
% 13.85/2.48 (inCongP = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f839])).
% 13.85/2.48 thf(f841,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i,X2 : $i] : (((binintersect @ X0 @ (binunion @ X2 @ X1))) = ((binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1)))) = bs114d)),
% 13.85/2.48 inference(rectify,[],[f119])).
% 13.85/2.48 thf(f842,plain,(
% 13.85/2.48 (bs114d = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y0 @ Y1)) = (binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f841])).
% 13.85/2.48 thf(f843,plain,(
% 13.85/2.48 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 13.85/2.48 inference(rectify,[],[f81])).
% 13.85/2.48 thf(f844,plain,(
% 13.85/2.48 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f843])).
% 13.85/2.48 thf(f853,plain,(
% 13.85/2.48 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = emptyI)),
% 13.85/2.48 inference(rectify,[],[f24])).
% 13.85/2.48 thf(f854,plain,(
% 13.85/2.48 (emptyI = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.85/2.48 inference(fool_elimination,[],[f853])).
% 13.85/2.48 thf(f855,plain,(
% 13.85/2.48 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f184])).
% 13.85/2.48 thf(f856,plain,(
% 13.85/2.48 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 13.85/2.48 inference(rectify,[],[f28])).
% 13.85/2.48 thf(f857,plain,(
% 13.85/2.48 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f856])).
% 13.85/2.48 thf(f860,plain,(
% 13.85/2.48 (sepSubset = ! [X0 : ($i > $o),X1 : $i] : (subset @ (dsetconstr @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) @ X1))),
% 13.85/2.48 inference(rectify,[],[f100])).
% 13.85/2.48 thf(f861,plain,(
% 13.85/2.48 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ Y0)))))))),
% 13.85/2.48 inference(fool_elimination,[],[f860])).
% 13.85/2.48 thf(f862,plain,(
% 13.85/2.48 (woz13rule0 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (binintersect @ X1 @ X2)) => (in @ X3 @ X0)))))),
% 13.85/2.48 inference(rectify,[],[f278])).
% 13.85/2.48 thf(f863,plain,(
% 13.85/2.48 (woz13rule0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y0 @ Y2)) => (in @ Y3 @ Y1))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f862])).
% 13.85/2.48 thf(f864,plain,(
% 13.85/2.48 (iftrueorfalse = ! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (if @ X1 @ X2 @ X0 @ X3) @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset))))))),
% 13.85/2.48 inference(rectify,[],[f229])).
% 13.85/2.48 thf(f865,plain,(
% 13.85/2.48 (iftrueorfalse = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (if @ Y1 @ Y0 @ Y2 @ Y3) @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f864])).
% 13.85/2.48 thf(f870,plain,(
% 13.85/2.48 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => (~(in @ X3 @ (binunion @ X0 @ X2)) => ~(in @ X3 @ X0))))) = binunionTILcontra)),
% 13.85/2.48 inference(rectify,[],[f258])).
% 13.85/2.48 thf(f871,plain,(
% 13.85/2.48 (binunionTILcontra = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1))))))))))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f870])).
% 13.85/2.48 thf(f874,plain,(
% 13.85/2.48 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 13.85/2.48 inference(rectify,[],[f80])).
% 13.85/2.48 thf(f875,plain,(
% 13.85/2.48 (eqimpsubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(fool_elimination,[],[f874])).
% 13.85/2.48 thf(f876,plain,(
% 13.85/2.48 (apProp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f333])).
% 13.85/2.48 thf(f878,plain,(
% 13.85/2.48 (setukpairinjL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y2 @ Y0)) => (Y3 = Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f672])).
% 13.85/2.48 thf(f879,plain,(
% 13.85/2.48 (powersetTE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f507])).
% 13.85/2.48 thf(f880,plain,(
% 13.85/2.48 (eqbreln = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3)))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f624])).
% 13.85/2.48 thf(f883,plain,(
% 13.85/2.48 (setadjoinSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f826])).
% 13.85/2.48 thf(f884,plain,(
% 13.85/2.48 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f674])).
% 13.85/2.48 thf(f885,plain,(
% 13.85/2.48 (inCongP = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f840])).
% 13.85/2.48 thf(f886,plain,(
% 13.85/2.48 (disjointsetsI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f370])).
% 13.85/2.48 thf(f887,plain,(
% 13.85/2.48 (lam2p = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (in @ (lam @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))) @ (funcSet @ Y1 @ Y2)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f814])).
% 13.85/2.48 thf(f889,plain,(
% 13.85/2.48 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f844])).
% 13.85/2.48 thf(f890,plain,(
% 13.85/2.48 (iftrueorfalse = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (if @ Y1 @ Y0 @ Y2 @ Y3) @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f865])).
% 13.85/2.48 thf(f891,plain,(
% 13.85/2.48 (setunionsingleton = ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0)))))),
% 13.85/2.48 inference(cnf_transformation,[],[f703])).
% 13.85/2.48 thf(f894,plain,(
% 13.85/2.48 (notinsingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f424])).
% 13.85/2.48 thf(f895,plain,(
% 13.85/2.48 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ Y2 @ Y3) = (ap @ Y0 @ Y1 @ Y2 @ Y3))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f719])).
% 13.85/2.48 thf(f897,plain,(
% 13.85/2.48 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f360])).
% 13.85/2.48 thf(f899,plain,(
% 13.85/2.48 (setOfPairsIsBReln = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y2 @ Y1 @ (dpsetconstr @ Y2 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y0 @ Y3 @ Y4))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f796])).
% 13.85/2.48 thf(f900,plain,(
% 13.85/2.48 (setminusLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f768])).
% 13.85/2.48 thf(f902,plain,(
% 13.85/2.48 (cartprodsndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f390])).
% 13.85/2.48 thf(f903,plain,(
% 13.85/2.48 (setukpairinjR2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f638])).
% 13.85/2.48 thf(f904,plain,(
% 13.85/2.48 (emptyinPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f556])).
% 13.85/2.48 thf(f905,plain,(
% 13.85/2.48 (setminusSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f489])).
% 13.85/2.48 thf(f907,plain,(
% 13.85/2.48 (singletonsswitch = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f522])).
% 13.85/2.48 thf(f908,plain,(
% 13.85/2.48 (setminusER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f544])).
% 13.85/2.48 thf(f909,plain,(
% 13.85/2.48 (binintersectSubset4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f497])).
% 13.85/2.48 thf(f910,plain,(
% 13.85/2.48 (bs114d = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y0 @ Y1)) = (binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f842])).
% 13.85/2.48 thf(f916,plain,(
% 13.85/2.48 (upairinpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f668])).
% 13.85/2.48 thf(f918,plain,(
% 13.85/2.48 (cartprodpairmemEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f766])).
% 13.85/2.48 thf(f920,plain,(
% 13.85/2.48 (upairequniteq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f512])).
% 13.85/2.48 thf(f922,plain,(
% 13.85/2.48 (complementInPowersetComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f688])).
% 13.85/2.48 thf(f923,plain,(
% 13.85/2.48 (upairsetIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f822])).
% 13.85/2.48 thf(f924,plain,(
% 13.85/2.48 (setunionsingleton1 = ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0)))))),
% 13.85/2.48 inference(cnf_transformation,[],[f331])).
% 13.85/2.48 thf(f925,plain,(
% 13.85/2.48 (setminusILneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f754])).
% 13.85/2.48 thf(f927,plain,(
% 13.85/2.48 (lamp = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (func @ Y2 @ Y0 @ (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f354])).
% 13.85/2.48 thf(f929,plain,(
% 13.85/2.48 (inComplementUnionImpInComplement1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f816])).
% 13.85/2.48 thf(f931,plain,(
% 13.85/2.48 (setoftrueEq = ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f302])).
% 13.85/2.48 thf(f932,plain,(
% 13.85/2.48 (upairsetIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f400])).
% 13.85/2.48 thf(f933,plain,(
% 13.85/2.48 (eqimpsubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f875])).
% 13.85/2.48 thf(f935,plain,(
% 13.85/2.48 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f479])).
% 13.85/2.48 thf(f937,plain,(
% 13.85/2.48 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f356])).
% 13.85/2.48 thf(f940,plain,(
% 13.85/2.48 (subsetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f570])).
% 13.85/2.48 thf(f941,plain,(
% 13.85/2.48 (woz1_1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f436])).
% 13.85/2.48 thf(f942,plain,(
% 13.85/2.48 (omega__Cong = ((omega = omega)))),
% 13.85/2.48 inference(cnf_transformation,[],[f605])).
% 13.85/2.48 thf(f944,plain,(
% 13.85/2.48 (subsetemptysetimpeq = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f610])).
% 13.85/2.48 thf(f945,plain,(
% 13.85/2.48 (sepInPowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f304])).
% 13.85/2.48 thf(f948,plain,(
% 13.85/2.48 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f857])).
% 13.85/2.48 thf(f949,plain,(
% 13.85/2.48 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f528])).
% 13.85/2.48 thf(f950,plain,(
% 13.85/2.48 (binintersectSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f740])).
% 13.85/2.48 thf(f951,plain,(
% 13.85/2.48 (iftrue = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((if @ Y0 @ Y2 @ Y1 @ Y3) = Y1))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f798])).
% 13.85/2.48 thf(f952,plain,(
% 13.85/2.48 (demorgan1a = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))) => (in @ Y3 @ (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2)))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f505])).
% 13.85/2.48 thf(f953,plain,(
% 13.85/2.48 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f734])).
% 13.85/2.48 thf(f955,plain,(
% 13.85/2.48 (dpsetconstrEL1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y4 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (in @ Y1 @ Y4))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f312])).
% 13.85/2.48 thf(f956,plain,(
% 13.85/2.48 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f723])).
% 13.85/2.48 thf(f957,plain,(
% 13.85/2.48 (ex1E1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f568])).
% 13.85/2.48 thf(f958,plain,(
% 13.85/2.48 (singletoninpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f406])).
% 13.85/2.48 thf(f959,plain,(
% 13.85/2.48 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f762])).
% 13.85/2.48 thf(f960,plain,(
% 13.85/2.48 (powersetT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (powerset @ Y0) @ (powerset @ (powerset @ Y1))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f503])).
% 13.85/2.48 thf(f961,plain,(
% 13.85/2.48 (setextAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f314])).
% 13.85/2.48 thf(f962,plain,(
% 13.85/2.48 (setadjoinSub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f422])).
% 13.85/2.48 thf(f963,plain,(
% 13.85/2.48 (funcinfuncset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (in @ Y2 @ (funcSet @ Y0 @ Y1)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f616])).
% 13.85/2.48 thf(f965,plain,(
% 13.85/2.48 (contrasubsetT2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => (subset @ (setminus @ Y0 @ Y2) @ (setminus @ Y0 @ Y1)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f784])).
% 13.85/2.48 thf(f969,plain,(
% 13.85/2.48 (notequalI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (~ (Y2 = Y0))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f702])).
% 13.85/2.48 thf(f970,plain,(
% 13.85/2.48 (binintersectSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f428])).
% 13.85/2.48 thf(f972,plain,(
% 13.85/2.48 (quantDeMorgan4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f642])).
% 13.85/2.48 thf(f973,plain,(
% 13.85/2.48 (uniqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f539])).
% 13.85/2.48 thf(f974,plain,(
% 13.85/2.48 (complementTE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f378])).
% 13.85/2.48 thf(f975,plain,(
% 13.85/2.48 (binunionIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f364])).
% 13.85/2.48 thf(f976,plain,(
% 13.85/2.48 (demorgan2b = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (binintersect @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2)))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f764])).
% 13.85/2.48 thf(f977,plain,(
% 13.85/2.48 (subsetTrans = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y1 @ Y0) => (subset @ Y2 @ Y0)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f386])).
% 13.85/2.48 thf(f980,plain,(
% 13.85/2.48 (dsetconstr__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y3 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f501])).
% 13.85/2.48 thf(f981,plain,(
% 13.85/2.48 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ Y0)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f861])).
% 13.85/2.48 thf(f983,plain,(
% 13.85/2.48 (setunionE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f574])).
% 13.85/2.48 thf(f984,plain,(
% 13.85/2.48 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 13.85/2.48 inference(cnf_transformation,[],[f461])).
% 13.85/2.48 thf(f985,plain,(
% 13.85/2.48 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f628])).
% 13.85/2.48 thf(f986,plain,(
% 13.85/2.48 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f692])).
% 13.85/2.48 thf(f987,plain,(
% 13.85/2.48 (prop2setE = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f836])).
% 13.85/2.48 thf(f988,plain,(
% 13.85/2.48 (ifp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (if @ Y2 @ Y1 @ Y0 @ Y3) @ Y2)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f327])).
% 13.85/2.48 thf(f989,plain,(
% 13.85/2.48 (demorgan2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((setminus @ Y1 @ (binunion @ Y0 @ Y2)) = (binintersect @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ Y2)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f434])).
% 13.85/2.48 thf(f990,plain,(
% 13.85/2.48 (setminusT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f491])).
% 13.85/2.48 thf(f992,plain,(
% 13.85/2.48 (subPowSU = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f604])).
% 13.85/2.48 thf(f993,plain,(
% 13.85/2.48 (binintersectT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ Y0))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f582])).
% 13.85/2.48 thf(f994,plain,(
% 13.85/2.48 (setextsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f308])).
% 13.85/2.48 thf(f998,plain,(
% 13.85/2.48 (powersetAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f580])).
% 13.85/2.48 thf(f999,plain,(
% 13.85/2.48 (prop2setI = ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f820])).
% 13.85/2.48 thf(f1000,plain,(
% 13.85/2.48 (lamProp = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (func @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y1 @ Y3) = Y4)))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f660])).
% 13.85/2.48 thf(f1004,plain,(
% 13.85/2.48 (powersetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f362])).
% 13.85/2.48 thf(f1006,plain,(
% 13.85/2.48 (setOfPairsIsBReln1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (breln1 @ Y1 @ (dpsetconstr @ Y1 @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y2 @ Y3))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f319])).
% 13.85/2.48 thf(f1007,plain,(
% 13.85/2.48 (notequalI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f392])).
% 13.85/2.48 thf(f1008,plain,(
% 13.85/2.48 (breln1all2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f776])).
% 13.85/2.48 thf(f1009,plain,(
% 13.85/2.48 (contraSubsetComplement = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y1 @ Y0)))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f316])).
% 13.85/2.48 thf(f1010,plain,(
% 13.85/2.48 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f711])).
% 13.85/2.48 thf(f1013,plain,(
% 13.85/2.48 (emptyInPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f483])).
% 13.85/2.48 thf(f1014,plain,(
% 13.85/2.48 (eqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f752])).
% 13.85/2.48 thf(f1016,plain,(
% 13.85/2.48 (dpsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f772])).
% 13.85/2.48 thf(f1017,plain,(
% 13.85/2.48 (doubleComplementSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ (setminus @ Y0 @ Y1)) @ Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f372])).
% 13.85/2.48 thf(f1018,plain,(
% 13.85/2.48 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f530])).
% 13.85/2.48 thf(f1023,plain,(
% 13.85/2.48 (setadjoinOr = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f532])).
% 13.85/2.48 thf(f1024,plain,(
% 13.85/2.48 (emptyI = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f854])).
% 13.85/2.48 thf(f1025,plain,(
% 13.85/2.48 (app = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y1 @ Y0 @ Y3) @ Y1)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f542])).
% 13.85/2.48 thf(f1027,plain,(
% 13.85/2.48 (powersetsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f588])).
% 13.85/2.48 thf(f1028,plain,(
% 13.85/2.48 (ubforcartprodlem2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f626])).
% 13.85/2.48 thf(f1029,plain,(
% 13.85/2.48 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false)))))),
% 13.85/2.48 inference(cnf_transformation,[],[f602])).
% 13.85/2.48 thf(f1030,plain,(
% 13.85/2.48 (setminusERneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f584])).
% 13.85/2.48 thf(f1033,plain,(
% 13.85/2.48 (breln1all1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f592])).
% 13.85/2.48 thf(f1035,plain,(
% 13.85/2.48 (setadjoinIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f744])).
% 13.85/2.48 thf(f1036,plain,(
% 13.85/2.48 (dpsetconstrEL2 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (in @ Y4 @ Y3))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f690])).
% 13.85/2.48 thf(f1039,plain,(
% 13.85/2.48 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f808])).
% 13.85/2.48 thf(f1040,plain,(
% 13.85/2.48 (subset2powerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f715])).
% 13.85/2.48 thf(f1041,plain,(
% 13.85/2.48 (quantDeMorgan3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f388])).
% 13.85/2.48 thf(f1042,plain,(
% 13.85/2.48 (cartprodfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f469])).
% 13.85/2.48 thf(f1044,plain,(
% 13.85/2.48 (setminusELneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f658])).
% 13.85/2.48 thf(f1045,plain,(
% 13.85/2.48 (demorgan2a1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f780])).
% 13.85/2.48 thf(f1046,plain,(
% 13.85/2.48 (subsetRefl = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))))),
% 13.85/2.48 inference(cnf_transformation,[],[f686])).
% 13.85/2.48 thf(f1048,plain,(
% 13.85/2.48 (setunionsingleton2 = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f382])).
% 13.85/2.48 thf(f1052,plain,(
% 13.85/2.48 (binunionTILcontra = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f871])).
% 13.85/2.48 thf(f1053,plain,(
% 13.85/2.48 (theprop = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f420])).
% 13.85/2.48 thf(f1054,plain,(
% 13.85/2.48 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f855])).
% 13.85/2.48 thf(f1055,plain,(
% 13.85/2.48 (subsetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f806])).
% 13.85/2.48 thf(f1057,plain,(
% 13.85/2.48 (setminusI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (in @ Y1 @ (setminus @ Y0 @ Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f446])).
% 13.85/2.48 thf(f1058,plain,(
% 13.85/2.48 (setbeta = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) = (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f534])).
% 13.85/2.48 thf(f1061,plain,(
% 13.85/2.48 (setunionE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f800])).
% 13.85/2.48 thf(f1063,plain,(
% 13.85/2.48 (doubleComplementSub1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f418])).
% 13.85/2.48 thf(f1064,plain,(
% 13.85/2.48 (funcImageSingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f705])).
% 13.85/2.48 thf(f1065,plain,(
% 13.85/2.48 (vacuousDall = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f300])).
% 13.85/2.48 thf(f1066,plain,(
% 13.85/2.48 (binunionLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f438])).
% 13.85/2.48 thf(f1067,plain,(
% 13.85/2.48 (emptysetAx = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f416])).
% 13.85/2.48 thf(f1068,plain,(
% 13.85/2.48 (contrasubsetT = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((subset @ Y1 @ (setminus @ Y0 @ Y2)) => ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y1)))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f408])).
% 13.85/2.48 thf(f1069,plain,(
% 13.85/2.48 (binintersectSubset5 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f746])).
% 13.85/2.48 thf(f1070,plain,(
% 13.85/2.48 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f384])).
% 13.85/2.48 thf(f1071,plain,(
% 13.85/2.48 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f731])).
% 13.85/2.48 thf(f1072,plain,(
% 13.85/2.48 (doubleComplementEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f348])).
% 13.85/2.48 thf(f1073,plain,(
% 13.85/2.48 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f465])).
% 13.85/2.48 thf(f1074,plain,(
% 13.85/2.48 (singletonsuniq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f656])).
% 13.85/2.48 thf(f1075,plain,(
% 13.85/2.48 (binunionRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f558])).
% 13.85/2.48 thf(f1078,plain,(
% 13.85/2.48 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 13.85/2.48 inference(cnf_transformation,[],[f346])).
% 13.85/2.48 thf(f1080,plain,(
% 13.85/2.48 (woz13rule1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f440])).
% 13.85/2.48 thf(f1081,plain,(
% 13.85/2.48 (inPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f717])).
% 13.85/2.48 thf(f1082,plain,(
% 13.85/2.48 (notdexE = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f452])).
% 13.85/2.48 thf(f1085,plain,(
% 13.85/2.48 (ap2p = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ Y1 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (ap @ Y1 @ Y0 @ Y2 @ Y3) @ Y0)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f600])).
% 13.85/2.48 thf(f1086,plain,(
% 13.85/2.48 (ksndsingleton = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f394])).
% 13.85/2.48 thf(f1089,plain,(
% 13.85/2.48 (setadjoinAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y2 @ Y1) | (Y2 = Y0)) = (in @ Y2 @ (setadjoin @ Y0 @ Y1)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f374])).
% 13.85/2.48 thf(f1090,plain,(
% 13.85/2.48 (doubleComplementI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f664])).
% 13.85/2.48 thf(f1091,plain,(
% 13.85/2.48 (cartprodpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f786])).
% 13.85/2.48 thf(f1092,plain,(
% 13.85/2.48 (funcGraphProp4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4)))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f485])).
% 13.85/2.48 thf(f1093,plain,(
% 13.85/2.48 (cartprodfstin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (kfst @ Y1) @ Y2))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f760])).
% 13.85/2.48 thf(f1095,plain,(
% 13.85/2.48 (ubforcartprodlem3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f618])).
% 13.85/2.48 thf(f1096,plain,(
% 13.85/2.48 (setukpairinjR11 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f548])).
% 13.85/2.48 thf(f1097,plain,(
% 13.85/2.48 (ksndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f598])).
% 13.85/2.48 thf(f1099,plain,(
% 13.85/2.48 (notinemptyset = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f694])).
% 13.85/2.48 thf(f1100,plain,(
% 13.85/2.48 (singletonsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f700])).
% 13.85/2.48 thf(f1101,plain,(
% 13.85/2.48 (binintersectSubset3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f804])).
% 13.85/2.48 thf(f1102,plain,(
% 13.85/2.48 (omega0Ax = ((in @ emptyset @ omega)))),
% 13.85/2.48 inference(cnf_transformation,[],[f508])).
% 13.85/2.48 thf(f1103,plain,(
% 13.85/2.48 (emptysetsubset = ((!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0)))))),
% 13.85/2.48 inference(cnf_transformation,[],[f442])).
% 13.85/2.48 thf(f1104,plain,(
% 13.85/2.48 (noeltsimpempty = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f594])).
% 13.85/2.48 thf(f1105,plain,(
% 13.85/2.48 (woz13rule2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3)))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f634])).
% 13.85/2.48 thf(f1106,plain,(
% 13.85/2.48 (cartprodsndin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (ksnd @ Y0) @ Y2))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f554])).
% 13.85/2.48 thf(f1107,plain,(
% 13.85/2.48 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f536])).
% 13.85/2.48 thf(f1109,plain,(
% 13.85/2.48 (theeq = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f430])).
% 13.85/2.48 thf(f1110,plain,(
% 13.85/2.48 (exu__Cong = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) = (exu @ (^[Y2 : $i]: (Y0 @ Y2)))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f475])).
% 13.85/2.48 thf(f1111,plain,(
% 13.85/2.48 (powersetTI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f516])).
% 13.85/2.48 thf(f1112,plain,(
% 13.85/2.48 (powerset__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f540])).
% 13.85/2.48 thf(f1116,plain,(
% 13.85/2.48 (nonemptyI = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (nonempty @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f614])).
% 13.85/2.48 thf(f1118,plain,(
% 13.85/2.48 (dpsetconstrERa = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y3 @ Y4))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f526])).
% 13.85/2.48 thf(f1120,plain,(
% 13.85/2.48 (binintersectRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y0)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f414])).
% 13.85/2.48 thf(f1121,plain,(
% 13.85/2.48 (eqimpsubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f448])).
% 13.85/2.48 thf(f1122,plain,(
% 13.85/2.48 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f713])).
% 13.85/2.48 thf(f1123,plain,(
% 13.85/2.48 (((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ Y1)))))))) => (Y1 = Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 13.85/2.48 inference(cnf_transformation,[],[f607])).
% 13.85/2.48 thf(f1125,plain,(
% 13.85/2.48 (powersetE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f590])).
% 13.85/2.48 thf(f1127,plain,(
% 13.85/2.48 (emptyset__Cong = ((emptyset = emptyset)))),
% 13.85/2.48 inference(cnf_transformation,[],[f537])).
% 13.85/2.48 thf(f1128,plain,(
% 13.85/2.48 (kpairp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f463])).
% 13.85/2.48 thf(f1129,plain,(
% 13.85/2.48 (complementTcontraSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (subset @ Y2 @ (setminus @ Y1 @ Y0)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f644])).
% 13.85/2.48 thf(f1130,plain,(
% 13.85/2.48 (kfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f608])).
% 13.85/2.48 thf(f1131,plain,(
% 13.85/2.48 (kpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f738])).
% 13.85/2.48 thf(f1132,plain,(
% 13.85/2.48 (complementImpComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f576])).
% 13.85/2.48 thf(f1136,plain,(
% 13.85/2.48 (setukpairIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f552])).
% 13.85/2.48 thf(f1138,plain,(
% 13.85/2.48 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f680])).
% 13.85/2.48 thf(f1139,plain,(
% 13.85/2.48 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 13.85/2.48 inference(cnf_transformation,[],[f317])).
% 13.85/2.48 thf(f1143,plain,(
% 13.85/2.48 (singletonprop = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f748])).
% 13.85/2.48 thf(f1144,plain,(
% 13.85/2.48 (setukpairinjR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y3) = (kpair @ Y0 @ Y1)) => (Y3 = Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f481])).
% 13.85/2.48 thf(f1145,plain,(
% 13.85/2.48 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => ((lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))) = (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f828])).
% 13.85/2.48 thf(f1149,plain,(
% 13.85/2.48 (woz1_4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (subset @ Y2 @ (setminus @ Y1 @ Y0)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f596])).
% 13.85/2.48 thf(f1150,plain,(
% 13.85/2.48 (iftrueProp2 = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (Y0 => ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y0 & (Y1 = Y4)) | ((Y3 = Y4) & (~ Y0)))))))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f790])).
% 13.85/2.48 thf(f1151,plain,(
% 13.85/2.48 (secondinupair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f471])).
% 13.85/2.48 thf(f1153,plain,(
% 13.85/2.48 (omegaSAx = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f444])).
% 13.85/2.48 thf(f1155,plain,(
% 13.85/2.48 (binintersectLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1)))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f562])).
% 13.85/2.48 thf(f1157,plain,(
% 13.85/2.48 (setminusEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f733])).
% 13.85/2.48 thf(f1158,plain,(
% 13.85/2.48 (binunionT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binunion @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f454])).
% 13.85/2.48 thf(f1159,plain,(
% 13.85/2.48 (setukpairinjL1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f727])).
% 13.85/2.48 thf(f1161,plain,(
% 13.85/2.48 (setunionI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f729])).
% 13.85/2.48 thf(f1162,plain,(
% 13.85/2.48 (eta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => ((lam @ Y0 @ Y2 @ (^[Y3 : $i]: (ap @ Y0 @ Y2 @ Y1 @ Y3))) = Y1))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f770])).
% 13.85/2.48 thf(f1167,plain,(
% 13.85/2.48 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f450])).
% 13.85/2.48 thf(f1169,plain,(
% 13.85/2.48 (woz13rule0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y0 @ Y2)) => (in @ Y3 @ Y1))))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f863])).
% 13.85/2.48 thf(f1170,plain,(
% 13.85/2.48 (symdiffIneg2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0)))))))))))))),
% 13.85/2.48 inference(cnf_transformation,[],[f750])).
% 13.85/2.48 thf(f1172,definition,(
% 13.85/2.48 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 13.85/2.48 introduced(theory,[fool_exhaustiveness_axiom])).
% 13.85/2.48 thf(f1173,plain,(
% 13.85/2.48 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1139,f1054])).
% 13.85/2.48 thf(f1174,plain,(
% 13.85/2.48 (eqbreln = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3)))))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f880,f1054,f1054])).
% 13.85/2.48 thf(f1176,plain,(
% 13.85/2.48 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f897,f1138])).
% 13.85/2.48 thf(f1177,plain,(
% 13.85/2.48 (setOfPairsIsBReln = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y1 @ (dpsetconstr @ Y2 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y0 @ Y3 @ Y4))))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f899,f1054])).
% 13.85/2.48 thf(f1179,plain,(
% 13.85/2.48 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f948,f1078])).
% 13.85/2.48 thf(f1180,plain,(
% 13.85/2.48 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f956,f1138])).
% 13.85/2.48 thf(f1183,plain,(
% 13.85/2.48 (setOfPairsIsBReln1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y1 @ (dpsetconstr @ Y1 @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y2 @ Y3))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1006,f1173])).
% 13.85/2.48 thf(f1184,plain,(
% 13.85/2.48 (breln1all2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1008,f1173])).
% 13.85/2.48 thf(f1186,plain,(
% 13.85/2.48 (breln1all1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1033,f1173])).
% 13.85/2.48 thf(f1187,plain,(
% 13.85/2.48 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1039,f1138])).
% 13.85/2.48 thf(f1190,plain,(
% 13.85/2.48 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1070,f1078])).
% 13.85/2.48 thf(f1191,plain,(
% 13.85/2.48 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1071,f1138])).
% 13.85/2.48 thf(f1192,plain,(
% 13.85/2.48 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1073,f1138])).
% 13.85/2.48 thf(f1195,plain,(
% 13.85/2.48 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => ((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1107,f1078])).
% 13.85/2.48 thf(f1196,plain,(
% 13.85/2.48 (exu__Cong = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y1 @ Y2))) = ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y0 @ Y2)))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1110,f1138,f1138])).
% 13.85/2.48 thf(f1198,plain,(
% 13.85/2.48 (nonemptyI = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => ((^[Y3 : $i]: (~ (emptyset = Y3))) @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1116,f1078])).
% 13.85/2.48 thf(f1199,plain,(
% 13.85/2.48 ($true = ((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (subset @ Y7 @ (cartprod @ Y5 @ Y6))))))) @ Y3 @ Y3 @ Y4)))) @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ Y1)))))))) => (Y1 = Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1123,f1173,f1173])).
% 13.85/2.48 thf(f1200,plain,(
% 13.85/2.48 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.85/2.48 inference(definition_unfolding,[],[f1167,f1138])).
% 13.85/2.48 thf(f1201,definition,(
% 13.85/2.48 (sF0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (subset @ Y7 @ (cartprod @ Y5 @ Y6))))))) @ Y3 @ Y3 @ Y4)))) @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ Y1)))))))) => (Y1 = Y2)))))))))))))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 13.85/2.48 thf(f1202,plain,(
% 13.85/2.48 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (subset @ Y7 @ (cartprod @ Y5 @ Y6))))))) @ Y3 @ Y3 @ Y4)))) @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ Y1)))))))) => (Y1 = Y2)))))))))))) = sF0)),
% 13.85/2.48 inference(reorient_equations,[],[f1201])).
% 13.85/2.48 thf(f1203,definition,(
% 13.85/2.48 (sF1 = ((subbreln1 => sF0)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 13.85/2.48 thf(f1204,definition,(
% 13.85/2.48 (sF2 = ((breln1all1 => sF1)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 13.85/2.48 thf(f1205,definition,(
% 13.85/2.48 (sF3 = ((setOfPairsIsBReln1 => sF2)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 13.85/2.48 thf(f1206,definition,(
% 13.85/2.48 (sF4 = ((choice2fnsingleton => sF3)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 13.85/2.48 thf(f1207,plain,(
% 13.85/2.48 (((choice2fnsingleton => sF3)) = sF4)),
% 13.85/2.48 inference(reorient_equations,[],[f1206])).
% 13.85/2.48 thf(f1208,definition,(
% 13.85/2.48 (sF5 = ((breln1SetBreln1 => sF4)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 13.85/2.48 thf(f1209,plain,(
% 13.85/2.48 (((breln1SetBreln1 => sF4)) = sF5)),
% 13.85/2.48 inference(reorient_equations,[],[f1208])).
% 13.85/2.48 thf(f1210,definition,(
% 13.85/2.48 (sF6 = ((breln1all2 => sF5)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 13.85/2.48 thf(f1211,plain,(
% 13.85/2.48 (((breln1all2 => sF5)) = sF6)),
% 13.85/2.48 inference(reorient_equations,[],[f1210])).
% 13.85/2.48 thf(f1212,definition,(
% 13.85/2.48 (sF7 = ((woz1_5 => sF6)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 13.85/2.48 thf(f1213,plain,(
% 13.85/2.48 (((woz1_5 => sF6)) = sF7)),
% 13.85/2.48 inference(reorient_equations,[],[f1212])).
% 13.85/2.48 thf(f1214,definition,(
% 13.85/2.48 (sF8 = ((woz1_4 => sF7)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
% 13.85/2.48 thf(f1215,definition,(
% 13.85/2.48 (sF9 = ((woz1_3 => sF8)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
% 13.85/2.48 thf(f1216,definition,(
% 13.85/2.48 (sF10 = ((woz1_2 => sF9)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
% 13.85/2.48 thf(f1217,plain,(
% 13.85/2.48 (((woz1_2 => sF9)) = sF10)),
% 13.85/2.48 inference(reorient_equations,[],[f1216])).
% 13.85/2.48 thf(f1218,definition,(
% 13.85/2.48 (sF11 = ((woz1_1 => sF10)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
% 13.85/2.48 thf(f1219,definition,(
% 13.85/2.48 (sF12 = ((woz13rule4 => sF11)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 13.85/2.48 thf(f1220,plain,(
% 13.85/2.48 (((woz13rule4 => sF11)) = sF12)),
% 13.85/2.48 inference(reorient_equations,[],[f1219])).
% 13.85/2.48 thf(f1221,definition,(
% 13.85/2.48 (sF13 = ((woz13rule3 => sF12)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
% 13.85/2.48 thf(f1222,definition,(
% 13.85/2.48 (sF14 = ((woz13rule2 => sF13)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
% 13.85/2.48 thf(f1223,plain,(
% 13.85/2.48 (((woz13rule2 => sF13)) = sF14)),
% 13.85/2.48 inference(reorient_equations,[],[f1222])).
% 13.85/2.48 thf(f1224,definition,(
% 13.85/2.48 (sF15 = ((woz13rule1 => sF14)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
% 13.85/2.48 thf(f1225,definition,(
% 13.85/2.48 (sF16 = ((woz13rule0 => sF15)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF16])],[function_definition])).
% 13.85/2.48 thf(f1226,definition,(
% 13.85/2.48 (sF17 = ((demorgan2 => sF16)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF17])],[function_definition])).
% 13.85/2.48 thf(f1227,definition,(
% 13.85/2.48 (sF18 = ((demorgan2b => sF17)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF18])],[function_definition])).
% 13.85/2.48 thf(f1228,definition,(
% 13.85/2.48 (sF19 = ((demorgan2b2 => sF18)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF19])],[function_definition])).
% 13.85/2.48 thf(f1229,definition,(
% 13.85/2.48 (sF20 = ((demorgan2a => sF19)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF20])],[function_definition])).
% 13.85/2.48 thf(f1230,plain,(
% 13.85/2.48 (((demorgan2a => sF19)) = sF20)),
% 13.85/2.48 inference(reorient_equations,[],[f1229])).
% 13.85/2.48 thf(f1231,definition,(
% 13.85/2.48 (sF21 = ((demorgan1 => sF20)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF21])],[function_definition])).
% 13.85/2.48 thf(f1232,definition,(
% 13.85/2.48 (sF22 = ((demorgan1b => sF21)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF22])],[function_definition])).
% 13.85/2.48 thf(f1233,plain,(
% 13.85/2.48 (((demorgan1b => sF21)) = sF22)),
% 13.85/2.48 inference(reorient_equations,[],[f1232])).
% 13.85/2.48 thf(f1234,definition,(
% 13.85/2.48 (sF23 = ((demorgan1a => sF22)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF23])],[function_definition])).
% 13.85/2.48 thf(f1235,plain,(
% 13.85/2.48 (((demorgan1a => sF22)) = sF23)),
% 13.85/2.48 inference(reorient_equations,[],[f1234])).
% 13.85/2.48 thf(f1236,definition,(
% 13.85/2.48 (sF24 = ((demorgan2a2 => sF23)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF24])],[function_definition])).
% 13.85/2.48 thf(f1237,plain,(
% 13.85/2.48 (((demorgan2a2 => sF23)) = sF24)),
% 13.85/2.48 inference(reorient_equations,[],[f1236])).
% 13.85/2.48 thf(f1238,definition,(
% 13.85/2.48 (sF25 = ((complementUnionInPowersetComplement => sF24)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF25])],[function_definition])).
% 13.85/2.48 thf(f1239,definition,(
% 13.85/2.48 (sF26 = ((demorgan2a1 => sF25)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF26])],[function_definition])).
% 13.85/2.48 thf(f1240,definition,(
% 13.85/2.48 (sF27 = ((binunionTEcontra => sF26)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF27])],[function_definition])).
% 13.85/2.48 thf(f1241,plain,(
% 13.85/2.48 (((binunionTEcontra => sF26)) = sF27)),
% 13.85/2.48 inference(reorient_equations,[],[f1240])).
% 13.85/2.48 thf(f1242,definition,(
% 13.85/2.48 (sF28 = ((binunionTE => sF27)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF28])],[function_definition])).
% 13.85/2.48 thf(f1243,plain,(
% 13.85/2.48 (((binunionTE => sF27)) = sF28)),
% 13.85/2.48 inference(reorient_equations,[],[f1242])).
% 13.85/2.48 thf(f1244,definition,(
% 13.85/2.48 (sF29 = ((inComplementUnionImpInComplement1 => sF28)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF29])],[function_definition])).
% 13.85/2.48 thf(f1245,definition,(
% 13.85/2.48 (sF30 = ((inComplementUnionImpNotIn1 => sF29)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF30])],[function_definition])).
% 13.85/2.48 thf(f1246,plain,(
% 13.85/2.48 (((inComplementUnionImpNotIn1 => sF29)) = sF30)),
% 13.85/2.48 inference(reorient_equations,[],[f1245])).
% 13.85/2.48 thf(f1247,definition,(
% 13.85/2.48 (sF31 = ((intersectInPowersetIntersectUnions => sF30)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF31])],[function_definition])).
% 13.85/2.48 thf(f1248,plain,(
% 13.85/2.48 (((intersectInPowersetIntersectUnions => sF30)) = sF31)),
% 13.85/2.48 inference(reorient_equations,[],[f1247])).
% 13.85/2.48 thf(f1249,definition,(
% 13.85/2.48 (sF32 = ((inIntersectImpInIntersectUnions => sF31)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF32])],[function_definition])).
% 13.85/2.48 thf(f1250,plain,(
% 13.85/2.48 (((inIntersectImpInIntersectUnions => sF31)) = sF32)),
% 13.85/2.48 inference(reorient_equations,[],[f1249])).
% 13.85/2.48 thf(f1251,definition,(
% 13.85/2.48 (sF33 = ((inIntersectImpInUnion2 => sF32)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF33])],[function_definition])).
% 13.85/2.48 thf(f1252,plain,(
% 13.85/2.48 (((inIntersectImpInUnion2 => sF32)) = sF33)),
% 13.85/2.48 inference(reorient_equations,[],[f1251])).
% 13.85/2.48 thf(f1253,definition,(
% 13.85/2.48 (sF34 = ((inIntersectImpInUnion => sF33)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF34])],[function_definition])).
% 13.85/2.48 thf(f1254,definition,(
% 13.85/2.48 (sF35 = ((binunionTIRcontra => sF34)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF35])],[function_definition])).
% 13.85/2.48 thf(f1255,definition,(
% 13.85/2.48 (sF36 = ((binunionTILcontra => sF35)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF36])],[function_definition])).
% 13.85/2.48 thf(f1256,definition,(
% 13.85/2.48 (sF37 = ((complementTcontraSubset => sF36)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF37])],[function_definition])).
% 13.85/2.48 thf(f1257,definition,(
% 13.85/2.48 (sF38 = ((contraSubsetComplement => sF37)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF38])],[function_definition])).
% 13.85/2.48 thf(f1258,definition,(
% 13.85/2.48 (sF39 = ((complementInPowersetComplementIntersect => sF38)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF39])],[function_definition])).
% 13.85/2.48 thf(f1259,definition,(
% 13.85/2.48 (sF40 = ((complementSubsetComplementIntersect => sF39)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF40])],[function_definition])).
% 13.85/2.48 thf(f1260,definition,(
% 13.85/2.48 (sF41 = ((complementImpComplementIntersect => sF40)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF41])],[function_definition])).
% 13.85/2.48 thf(f1261,plain,(
% 13.85/2.48 (((complementImpComplementIntersect => sF40)) = sF41)),
% 13.85/2.48 inference(reorient_equations,[],[f1260])).
% 13.85/2.48 thf(f1262,definition,(
% 13.85/2.48 (sF42 = ((complementTnotintersectT => sF41)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF42])],[function_definition])).
% 13.85/2.48 thf(f1263,definition,(
% 13.85/2.48 (sF43 = ((doubleComplementEq => sF42)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF43])],[function_definition])).
% 13.85/2.48 thf(f1264,plain,(
% 13.85/2.48 (((doubleComplementEq => sF42)) = sF43)),
% 13.85/2.48 inference(reorient_equations,[],[f1263])).
% 13.85/2.48 thf(f1265,definition,(
% 13.85/2.48 (sF44 = ((doubleComplementSub2 => sF43)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF44])],[function_definition])).
% 13.85/2.48 thf(f1266,definition,(
% 13.85/2.48 (sF45 = ((doubleComplementSub1 => sF44)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF45])],[function_definition])).
% 13.85/2.48 thf(f1267,definition,(
% 13.85/2.48 (sF46 = ((doubleComplementE1 => sF45)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF46])],[function_definition])).
% 13.85/2.48 thf(f1268,definition,(
% 13.85/2.48 (sF47 = ((doubleComplementI1 => sF46)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF47])],[function_definition])).
% 13.85/2.48 thf(f1269,definition,(
% 13.85/2.48 (sF48 = ((contrasubsetT3 => sF47)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF48])],[function_definition])).
% 13.85/2.48 thf(f1270,definition,(
% 13.85/2.48 (sF49 = ((contrasubsetT2 => sF48)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF49])],[function_definition])).
% 13.85/2.48 thf(f1271,definition,(
% 13.85/2.48 (sF50 = ((contrasubsetT1 => sF49)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF50])],[function_definition])).
% 13.85/2.48 thf(f1272,definition,(
% 13.85/2.48 (sF51 = ((contrasubsetT => sF50)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF51])],[function_definition])).
% 13.85/2.48 thf(f1273,definition,(
% 13.85/2.48 (sF52 = ((binintersectTERcontra => sF51)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF52])],[function_definition])).
% 13.85/2.48 thf(f1274,plain,(
% 13.85/2.48 (((binintersectTERcontra => sF51)) = sF52)),
% 13.85/2.48 inference(reorient_equations,[],[f1273])).
% 13.85/2.48 thf(f1275,definition,(
% 13.85/2.48 (sF53 = ((binintersectTELcontra => sF52)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF53])],[function_definition])).
% 13.85/2.48 thf(f1276,plain,(
% 13.85/2.48 (((binintersectTELcontra => sF52)) = sF53)),
% 13.85/2.48 inference(reorient_equations,[],[f1275])).
% 13.85/2.48 thf(f1277,definition,(
% 13.85/2.48 (sF54 = ((complementTE1 => sF53)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF54])],[function_definition])).
% 13.85/2.48 thf(f1278,plain,(
% 13.85/2.48 (((complementTE1 => sF53)) = sF54)),
% 13.85/2.48 inference(reorient_equations,[],[f1277])).
% 13.85/2.48 thf(f1279,definition,(
% 13.85/2.48 (sF55 = ((complementTI1 => sF54)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF55])],[function_definition])).
% 13.85/2.48 thf(f1280,plain,(
% 13.85/2.48 (((complementTI1 => sF54)) = sF55)),
% 13.85/2.48 inference(reorient_equations,[],[f1279])).
% 13.85/2.48 thf(f1281,definition,(
% 13.85/2.48 (sF56 = ((powersetTE1 => sF55)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF56])],[function_definition])).
% 13.85/2.48 thf(f1282,definition,(
% 13.85/2.48 (sF57 = ((powersetTI1 => sF56)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF57])],[function_definition])).
% 13.85/2.48 thf(f1283,plain,(
% 13.85/2.48 (((powersetTI1 => sF56)) = sF57)),
% 13.85/2.48 inference(reorient_equations,[],[f1282])).
% 13.85/2.48 thf(f1284,definition,(
% 13.85/2.48 (sF58 = ((subsetTI => sF57)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF58])],[function_definition])).
% 13.85/2.48 thf(f1285,definition,(
% 13.85/2.48 (sF59 = ((setextT => sF58)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF59])],[function_definition])).
% 13.85/2.48 thf(f1286,definition,(
% 13.85/2.48 (sF60 = ((complementT_lem => sF59)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF60])],[function_definition])).
% 13.85/2.48 thf(f1287,definition,(
% 13.85/2.48 (sF61 = ((setminusT_lem => sF60)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF61])],[function_definition])).
% 13.85/2.48 thf(f1288,plain,(
% 13.85/2.48 (((setminusT_lem => sF60)) = sF61)),
% 13.85/2.48 inference(reorient_equations,[],[f1287])).
% 13.85/2.48 thf(f1289,definition,(
% 13.85/2.48 (sF62 = ((powersetT_lem => sF61)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF62])],[function_definition])).
% 13.85/2.48 thf(f1290,definition,(
% 13.85/2.48 (sF63 = ((binunionT_lem => sF62)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF63])],[function_definition])).
% 13.85/2.48 thf(f1291,plain,(
% 13.85/2.48 (((binunionT_lem => sF62)) = sF63)),
% 13.85/2.48 inference(reorient_equations,[],[f1290])).
% 13.85/2.48 thf(f1292,definition,(
% 13.85/2.48 (sF64 = ((binintersectT_lem => sF63)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF64])],[function_definition])).
% 13.85/2.48 thf(f1293,definition,(
% 13.85/2.48 (sF65 = ((iftrueorfalse => sF64)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF65])],[function_definition])).
% 13.85/2.48 thf(f1294,plain,(
% 13.85/2.48 (((iftrueorfalse => sF64)) = sF65)),
% 13.85/2.48 inference(reorient_equations,[],[f1293])).
% 13.85/2.48 thf(f1295,definition,(
% 13.85/2.48 (sF66 = ((iffalse => sF65)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF66])],[function_definition])).
% 13.85/2.48 thf(f1296,definition,(
% 13.85/2.48 (sF67 = ((iftrue => sF66)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF67])],[function_definition])).
% 13.85/2.48 thf(f1297,plain,(
% 13.85/2.48 (((iftrue => sF66)) = sF67)),
% 13.85/2.48 inference(reorient_equations,[],[f1296])).
% 13.85/2.48 thf(f1298,definition,(
% 13.85/2.48 (sF68 = ((theeq => sF67)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF68])],[function_definition])).
% 13.85/2.48 thf(f1299,plain,(
% 13.85/2.48 (((theeq => sF67)) = sF68)),
% 13.85/2.48 inference(reorient_equations,[],[f1298])).
% 13.85/2.48 thf(f1300,definition,(
% 13.85/2.48 (sF69 = ((ifp => sF68)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF69])],[function_definition])).
% 13.85/2.48 thf(f1301,plain,(
% 13.85/2.48 (((ifp => sF68)) = sF69)),
% 13.85/2.48 inference(reorient_equations,[],[f1300])).
% 13.85/2.48 thf(f1302,definition,(
% 13.85/2.48 (sF70 = ((ifSingleton => sF69)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF70])],[function_definition])).
% 13.85/2.48 thf(f1303,plain,(
% 13.85/2.48 (((ifSingleton => sF69)) = sF70)),
% 13.85/2.48 inference(reorient_equations,[],[f1302])).
% 13.85/2.48 thf(f1304,definition,(
% 13.85/2.48 (sF71 = ((iftrueProp2 => sF70)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF71])],[function_definition])).
% 13.85/2.48 thf(f1305,plain,(
% 13.85/2.48 (((iftrueProp2 => sF70)) = sF71)),
% 13.85/2.48 inference(reorient_equations,[],[f1304])).
% 13.85/2.48 thf(f1306,definition,(
% 13.85/2.48 (sF72 = ((iftrueProp1 => sF71)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF72])],[function_definition])).
% 13.85/2.48 thf(f1307,plain,(
% 13.85/2.48 (((iftrueProp1 => sF71)) = sF72)),
% 13.85/2.48 inference(reorient_equations,[],[f1306])).
% 13.85/2.48 thf(f1308,definition,(
% 13.85/2.48 (sF73 = ((iffalseProp2 => sF72)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF73])],[function_definition])).
% 13.85/2.48 thf(f1309,definition,(
% 13.85/2.48 (sF74 = ((iffalseProp1 => sF73)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF74])],[function_definition])).
% 13.85/2.48 thf(f1310,definition,(
% 13.85/2.48 (sF75 = ((eta2 => sF74)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF75])],[function_definition])).
% 13.85/2.48 thf(f1311,definition,(
% 13.85/2.48 (sF76 = ((beta2 => sF75)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF76])],[function_definition])).
% 13.85/2.48 thf(f1312,definition,(
% 13.85/2.48 (sF77 = ((lam2lamEq => sF76)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF77])],[function_definition])).
% 13.85/2.48 thf(f1313,plain,(
% 13.85/2.48 (((lam2lamEq => sF76)) = sF77)),
% 13.85/2.48 inference(reorient_equations,[],[f1312])).
% 13.85/2.48 thf(f1314,definition,(
% 13.85/2.48 (sF78 = ((eta1 => sF77)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF78])],[function_definition])).
% 13.85/2.48 thf(f1315,definition,(
% 13.85/2.48 (sF79 = ((beta1 => sF78)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF79])],[function_definition])).
% 13.85/2.48 thf(f1316,definition,(
% 13.85/2.48 (sF80 = ((ap2apEq2 => sF79)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF80])],[function_definition])).
% 13.85/2.48 thf(f1317,plain,(
% 13.85/2.48 (((ap2apEq2 => sF79)) = sF80)),
% 13.85/2.48 inference(reorient_equations,[],[f1316])).
% 13.85/2.48 thf(f1318,definition,(
% 13.85/2.48 (sF81 = ((ap2apEq1 => sF80)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF81])],[function_definition])).
% 13.85/2.48 thf(f1319,definition,(
% 13.85/2.48 (sF82 = ((funcext2 => sF81)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF82])],[function_definition])).
% 13.85/2.48 thf(f1320,plain,(
% 13.85/2.48 (((funcext2 => sF81)) = sF82)),
% 13.85/2.48 inference(reorient_equations,[],[f1319])).
% 13.85/2.48 thf(f1321,definition,(
% 13.85/2.48 (sF83 = ((funcext => sF82)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF83])],[function_definition])).
% 13.85/2.48 thf(f1322,definition,(
% 13.85/2.48 (sF84 = ((eqbreln => sF83)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF84])],[function_definition])).
% 13.85/2.48 thf(f1323,plain,(
% 13.85/2.48 (((eqbreln => sF83)) = sF84)),
% 13.85/2.48 inference(reorient_equations,[],[f1322])).
% 13.85/2.48 thf(f1324,definition,(
% 13.85/2.48 (sF85 = ((subbreln => sF84)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF85])],[function_definition])).
% 13.85/2.48 thf(f1325,plain,(
% 13.85/2.48 (((subbreln => sF84)) = sF85)),
% 13.85/2.48 inference(reorient_equations,[],[f1324])).
% 13.85/2.48 thf(f1326,definition,(
% 13.85/2.48 (sF86 = ((funcGraphProp4 => sF85)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF86])],[function_definition])).
% 13.85/2.48 thf(f1327,plain,(
% 13.85/2.48 (((funcGraphProp4 => sF85)) = sF86)),
% 13.85/2.48 inference(reorient_equations,[],[f1326])).
% 13.85/2.48 thf(f1328,definition,(
% 13.85/2.48 (sF87 = ((funcextLem => sF86)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF87])],[function_definition])).
% 13.85/2.48 thf(f1329,definition,(
% 13.85/2.48 (sF88 = ((funcGraphProp2 => sF87)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF88])],[function_definition])).
% 13.85/2.48 thf(f1330,plain,(
% 13.85/2.48 (((funcGraphProp2 => sF87)) = sF88)),
% 13.85/2.48 inference(reorient_equations,[],[f1329])).
% 13.85/2.48 thf(f1331,definition,(
% 13.85/2.48 (sF89 = ((funcGraphProp3 => sF88)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF89])],[function_definition])).
% 13.85/2.48 thf(f1332,definition,(
% 13.85/2.48 (sF90 = ((funcGraphProp1 => sF89)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF90])],[function_definition])).
% 13.85/2.48 thf(f1333,definition,(
% 13.85/2.48 (sF91 = ((ex1E2 => sF90)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF91])],[function_definition])).
% 13.85/2.48 thf(f1334,plain,(
% 13.85/2.48 (((ex1E2 => sF90)) = sF91)),
% 13.85/2.48 inference(reorient_equations,[],[f1333])).
% 13.85/2.48 thf(f1335,definition,(
% 13.85/2.48 (sF92 = ((brelnall2 => sF91)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF92])],[function_definition])).
% 13.85/2.48 thf(f1336,definition,(
% 13.85/2.48 (sF93 = ((brelnall1 => sF92)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF93])],[function_definition])).
% 13.85/2.48 thf(f1337,plain,(
% 13.85/2.48 (((brelnall1 => sF92)) = sF93)),
% 13.85/2.48 inference(reorient_equations,[],[f1336])).
% 13.85/2.48 thf(f1338,definition,(
% 13.85/2.48 (sF94 = ((lam2p => sF93)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF94])],[function_definition])).
% 13.85/2.48 thf(f1339,plain,(
% 13.85/2.48 (((lam2p => sF93)) = sF94)),
% 13.85/2.48 inference(reorient_equations,[],[f1338])).
% 13.85/2.48 thf(f1340,definition,(
% 13.85/2.48 (sF95 = ((lamp => sF94)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF95])],[function_definition])).
% 13.85/2.48 thf(f1341,plain,(
% 13.85/2.48 (((lamp => sF94)) = sF95)),
% 13.85/2.48 inference(reorient_equations,[],[f1340])).
% 13.85/2.48 thf(f1342,definition,(
% 13.85/2.48 (sF96 = ((lamProp => sF95)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF96])],[function_definition])).
% 13.85/2.48 thf(f1343,plain,(
% 13.85/2.48 (((lamProp => sF95)) = sF96)),
% 13.85/2.48 inference(reorient_equations,[],[f1342])).
% 13.85/2.48 thf(f1344,definition,(
% 13.85/2.48 (sF97 = ((funcinfuncset => sF96)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF97])],[function_definition])).
% 13.85/2.48 thf(f1345,definition,(
% 13.85/2.48 (sF98 = ((ap2p => sF97)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF98])],[function_definition])).
% 13.85/2.48 thf(f1346,definition,(
% 13.85/2.48 (sF99 = ((infuncsetfunc => sF98)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF99])],[function_definition])).
% 13.85/2.48 thf(f1347,plain,(
% 13.85/2.48 (((infuncsetfunc => sF98)) = sF99)),
% 13.85/2.48 inference(reorient_equations,[],[f1346])).
% 13.85/2.48 thf(f1348,definition,(
% 13.85/2.48 (sF100 = ((app => sF99)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF100])],[function_definition])).
% 13.85/2.48 thf(f1349,plain,(
% 13.85/2.48 (((app => sF99)) = sF100)),
% 13.85/2.48 inference(reorient_equations,[],[f1348])).
% 13.85/2.48 thf(f1350,definition,(
% 13.85/2.48 (sF101 = ((apProp => sF100)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF101])],[function_definition])).
% 13.85/2.48 thf(f1351,plain,(
% 13.85/2.48 (((apProp => sF100)) = sF101)),
% 13.85/2.48 inference(reorient_equations,[],[f1350])).
% 13.85/2.48 thf(f1352,definition,(
% 13.85/2.48 (sF102 = ((funcImageSingleton => sF101)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF102])],[function_definition])).
% 13.85/2.48 thf(f1353,plain,(
% 13.85/2.48 (((funcImageSingleton => sF101)) = sF102)),
% 13.85/2.48 inference(reorient_equations,[],[f1352])).
% 13.85/2.48 thf(f1354,definition,(
% 13.85/2.48 (sF103 = ((dpsetconstrER => sF102)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF103])],[function_definition])).
% 13.85/2.48 thf(f1355,plain,(
% 13.85/2.48 (((dpsetconstrER => sF102)) = sF103)),
% 13.85/2.48 inference(reorient_equations,[],[f1354])).
% 13.85/2.48 thf(f1356,definition,(
% 13.85/2.48 (sF104 = ((dpsetconstrEL2 => sF103)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF104])],[function_definition])).
% 13.85/2.48 thf(f1357,definition,(
% 13.85/2.48 (sF105 = ((dpsetconstrEL1 => sF104)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF105])],[function_definition])).
% 13.85/2.48 thf(f1358,plain,(
% 13.85/2.48 (((dpsetconstrEL1 => sF104)) = sF105)),
% 13.85/2.48 inference(reorient_equations,[],[f1357])).
% 13.85/2.48 thf(f1359,definition,(
% 13.85/2.48 (sF106 = ((dpsetconstrERa => sF105)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF106])],[function_definition])).
% 13.85/2.48 thf(f1360,definition,(
% 13.85/2.48 (sF107 = ((setOfPairsIsBReln => sF106)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF107])],[function_definition])).
% 13.85/2.48 thf(f1361,plain,(
% 13.85/2.48 (((setOfPairsIsBReln => sF106)) = sF107)),
% 13.85/2.48 inference(reorient_equations,[],[f1360])).
% 13.85/2.48 thf(f1362,definition,(
% 13.85/2.48 (sF108 = ((dpsetconstrSub => sF107)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF108])],[function_definition])).
% 13.85/2.48 thf(f1363,plain,(
% 13.85/2.48 (((dpsetconstrSub => sF107)) = sF108)),
% 13.85/2.48 inference(reorient_equations,[],[f1362])).
% 13.85/2.48 thf(f1364,definition,(
% 13.85/2.48 (sF109 = ((dpsetconstrI => sF108)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF109])],[function_definition])).
% 13.85/2.48 thf(f1365,plain,(
% 13.85/2.48 (((dpsetconstrI => sF108)) = sF109)),
% 13.85/2.48 inference(reorient_equations,[],[f1364])).
% 13.85/2.48 thf(f1366,definition,(
% 13.85/2.48 (sF110 = ((cartprodpairsurjEq => sF109)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF110])],[function_definition])).
% 13.85/2.48 thf(f1367,plain,(
% 13.85/2.48 (((cartprodpairsurjEq => sF109)) = sF110)),
% 13.85/2.48 inference(reorient_equations,[],[f1366])).
% 13.85/2.48 thf(f1368,definition,(
% 13.85/2.48 (sF111 = ((cartprodsndpairEq => sF110)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF111])],[function_definition])).
% 13.85/2.48 thf(f1369,plain,(
% 13.85/2.48 (((cartprodsndpairEq => sF110)) = sF111)),
% 13.85/2.48 inference(reorient_equations,[],[f1368])).
% 13.85/2.48 thf(f1370,definition,(
% 13.85/2.48 (sF112 = ((cartprodfstpairEq => sF111)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF112])],[function_definition])).
% 13.85/2.48 thf(f1371,plain,(
% 13.85/2.48 (((cartprodfstpairEq => sF111)) = sF112)),
% 13.85/2.48 inference(reorient_equations,[],[f1370])).
% 13.85/2.48 thf(f1372,definition,(
% 13.85/2.48 (sF113 = ((cartprodmempaircEq => sF112)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF113])],[function_definition])).
% 13.85/2.48 thf(f1373,plain,(
% 13.85/2.48 (((cartprodmempaircEq => sF112)) = sF113)),
% 13.85/2.48 inference(reorient_equations,[],[f1372])).
% 13.85/2.48 thf(f1374,definition,(
% 13.85/2.48 (sF114 = ((cartprodpairmemER => sF113)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF114])],[function_definition])).
% 13.85/2.48 thf(f1375,plain,(
% 13.85/2.48 (((cartprodpairmemER => sF113)) = sF114)),
% 13.85/2.48 inference(reorient_equations,[],[f1374])).
% 13.85/2.48 thf(f1376,definition,(
% 13.85/2.48 (sF115 = ((cartprodpairmemEL => sF114)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF115])],[function_definition])).
% 13.85/2.48 thf(f1377,definition,(
% 13.85/2.48 (sF116 = ((cartprodsndin => sF115)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF116])],[function_definition])).
% 13.85/2.48 thf(f1378,plain,(
% 13.85/2.48 (((cartprodsndin => sF115)) = sF116)),
% 13.85/2.48 inference(reorient_equations,[],[f1377])).
% 13.85/2.48 thf(f1379,definition,(
% 13.85/2.48 (sF117 = ((kpairsurjEq => sF116)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF117])],[function_definition])).
% 13.85/2.48 thf(f1380,definition,(
% 13.85/2.48 (sF118 = ((ksndpairEq => sF117)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF118])],[function_definition])).
% 13.85/2.48 thf(f1381,definition,(
% 13.85/2.48 (sF119 = ((ksndsingleton => sF118)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF119])],[function_definition])).
% 13.85/2.48 thf(f1382,plain,(
% 13.85/2.48 (((ksndsingleton => sF118)) = sF119)),
% 13.85/2.48 inference(reorient_equations,[],[f1381])).
% 13.85/2.48 thf(f1383,definition,(
% 13.85/2.48 (sF120 = ((setukpairinjR => sF119)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF120])],[function_definition])).
% 13.85/2.48 thf(f1384,plain,(
% 13.85/2.48 (((setukpairinjR => sF119)) = sF120)),
% 13.85/2.48 inference(reorient_equations,[],[f1383])).
% 13.85/2.48 thf(f1385,definition,(
% 13.85/2.48 (sF121 = ((setukpairinjR2 => sF120)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF121])],[function_definition])).
% 13.85/2.48 thf(f1386,plain,(
% 13.85/2.48 (((setukpairinjR2 => sF120)) = sF121)),
% 13.85/2.48 inference(reorient_equations,[],[f1385])).
% 13.85/2.48 thf(f1387,definition,(
% 13.85/2.48 (sF122 = ((upairequniteq => sF121)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF122])],[function_definition])).
% 13.85/2.48 thf(f1388,plain,(
% 13.85/2.48 (((upairequniteq => sF121)) = sF122)),
% 13.85/2.48 inference(reorient_equations,[],[f1387])).
% 13.85/2.48 thf(f1389,definition,(
% 13.85/2.48 (sF123 = ((setukpairinjR1 => sF122)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF123])],[function_definition])).
% 13.85/2.48 thf(f1390,definition,(
% 13.85/2.48 (sF124 = ((setukpairinjR12 => sF123)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF124])],[function_definition])).
% 13.85/2.48 thf(f1391,definition,(
% 13.85/2.48 (sF125 = ((setukpairinjR11 => sF124)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF125])],[function_definition])).
% 13.85/2.48 thf(f1392,definition,(
% 13.85/2.48 (sF126 = ((setukpairinjL => sF125)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF126])],[function_definition])).
% 13.85/2.48 thf(f1393,plain,(
% 13.85/2.48 (((setukpairinjL => sF125)) = sF126)),
% 13.85/2.48 inference(reorient_equations,[],[f1392])).
% 13.85/2.48 thf(f1394,definition,(
% 13.85/2.48 (sF127 = ((setukpairinjL2 => sF126)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF127])],[function_definition])).
% 13.85/2.48 thf(f1395,definition,(
% 13.85/2.48 (sF128 = ((cartprodfstin => sF127)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF128])],[function_definition])).
% 13.85/2.48 thf(f1396,definition,(
% 13.85/2.48 (sF129 = ((kfstpairEq => sF128)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF129])],[function_definition])).
% 13.85/2.48 thf(f1397,definition,(
% 13.85/2.48 (sF130 = ((theprop => sF129)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF130])],[function_definition])).
% 13.85/2.48 thf(f1398,plain,(
% 13.85/2.48 (((theprop => sF129)) = sF130)),
% 13.85/2.48 inference(reorient_equations,[],[f1397])).
% 13.85/2.48 thf(f1399,definition,(
% 13.85/2.48 (sF131 = ((kfstsingleton => sF130)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF131])],[function_definition])).
% 13.85/2.48 thf(f1400,plain,(
% 13.85/2.48 (((kfstsingleton => sF130)) = sF131)),
% 13.85/2.48 inference(reorient_equations,[],[f1399])).
% 13.85/2.48 thf(f1401,definition,(
% 13.85/2.48 (sF132 = ((setukpairinjL1 => sF131)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF132])],[function_definition])).
% 13.85/2.48 thf(f1402,plain,(
% 13.85/2.48 (((setukpairinjL1 => sF131)) = sF132)),
% 13.85/2.48 inference(reorient_equations,[],[f1401])).
% 13.85/2.48 thf(f1403,definition,(
% 13.85/2.48 (sF133 = ((singletonsuniq => sF132)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF133])],[function_definition])).
% 13.85/2.48 thf(f1404,definition,(
% 13.85/2.48 (sF134 = ((ex1I2 => sF133)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF134])],[function_definition])).
% 13.85/2.48 thf(f1405,definition,(
% 13.85/2.48 (sF135 = ((ex1I => sF134)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF135])],[function_definition])).
% 13.85/2.48 thf(f1406,definition,(
% 13.85/2.48 (sF136 = ((ex1E1 => sF135)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF136])],[function_definition])).
% 13.85/2.48 thf(f1407,definition,(
% 13.85/2.48 (sF137 = ((singletonprop => sF136)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF137])],[function_definition])).
% 13.85/2.48 thf(f1408,plain,(
% 13.85/2.48 (((singletonprop => sF136)) = sF137)),
% 13.85/2.48 inference(reorient_equations,[],[f1407])).
% 13.85/2.48 thf(f1409,definition,(
% 13.85/2.48 (sF138 = ((setunionsingleton => sF137)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF138])],[function_definition])).
% 13.85/2.48 thf(f1410,definition,(
% 13.85/2.48 (sF139 = ((setunionsingleton2 => sF138)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF139])],[function_definition])).
% 13.85/2.48 thf(f1411,plain,(
% 13.85/2.48 (((setunionsingleton2 => sF138)) = sF139)),
% 13.85/2.48 inference(reorient_equations,[],[f1410])).
% 13.85/2.48 thf(f1412,definition,(
% 13.85/2.48 (sF140 = ((setunionsingleton1 => sF139)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF140])],[function_definition])).
% 13.85/2.48 thf(f1413,plain,(
% 13.85/2.48 (((setunionsingleton1 => sF139)) = sF140)),
% 13.85/2.48 inference(reorient_equations,[],[f1412])).
% 13.85/2.48 thf(f1414,definition,(
% 13.85/2.48 (sF141 = ((setunionE2 => sF140)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF141])],[function_definition])).
% 13.85/2.48 thf(f1415,definition,(
% 13.85/2.48 (sF142 = ((cartprodmempair => sF141)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF142])],[function_definition])).
% 13.85/2.48 thf(f1416,definition,(
% 13.85/2.48 (sF143 = ((cartprodmempair1 => sF142)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF143])],[function_definition])).
% 13.85/2.48 thf(f1417,plain,(
% 13.85/2.48 (((cartprodmempair1 => sF142)) = sF143)),
% 13.85/2.48 inference(reorient_equations,[],[f1416])).
% 13.85/2.48 thf(f1418,definition,(
% 13.85/2.48 (sF144 = ((cartprodpairin => sF143)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF144])],[function_definition])).
% 13.85/2.48 thf(f1419,definition,(
% 13.85/2.48 (sF145 = ((ubforcartprodlem3 => sF144)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF145])],[function_definition])).
% 13.85/2.48 thf(f1420,plain,(
% 13.85/2.48 (((ubforcartprodlem3 => sF144)) = sF145)),
% 13.85/2.48 inference(reorient_equations,[],[f1419])).
% 13.85/2.48 thf(f1421,definition,(
% 13.85/2.48 (sF146 = ((ubforcartprodlem2 => sF145)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF146])],[function_definition])).
% 13.85/2.48 thf(f1422,definition,(
% 13.85/2.48 (sF147 = ((ubforcartprodlem1 => sF146)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF147])],[function_definition])).
% 13.85/2.48 thf(f1423,plain,(
% 13.85/2.48 (((ubforcartprodlem1 => sF146)) = sF147)),
% 13.85/2.48 inference(reorient_equations,[],[f1422])).
% 13.85/2.48 thf(f1424,definition,(
% 13.85/2.48 (sF148 = ((upairinpowunion => sF147)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF148])],[function_definition])).
% 13.85/2.48 thf(f1425,plain,(
% 13.85/2.48 (((upairinpowunion => sF147)) = sF148)),
% 13.85/2.48 inference(reorient_equations,[],[f1424])).
% 13.85/2.48 thf(f1426,definition,(
% 13.85/2.48 (sF149 = ((upairsubunion => sF148)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF149])],[function_definition])).
% 13.85/2.48 thf(f1427,plain,(
% 13.85/2.48 (((upairsubunion => sF148)) = sF149)),
% 13.85/2.48 inference(reorient_equations,[],[f1426])).
% 13.85/2.48 thf(f1428,definition,(
% 13.85/2.48 (sF150 = ((upairset2E => sF149)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF150])],[function_definition])).
% 13.85/2.48 thf(f1429,definition,(
% 13.85/2.48 (sF151 = ((singletoninpowunion => sF150)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF151])],[function_definition])).
% 13.85/2.48 thf(f1430,plain,(
% 13.85/2.48 (((singletoninpowunion => sF150)) = sF151)),
% 13.85/2.48 inference(reorient_equations,[],[f1429])).
% 13.85/2.48 thf(f1431,definition,(
% 13.85/2.48 (sF152 = ((singletoninpowerset => sF151)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF152])],[function_definition])).
% 13.85/2.48 thf(f1432,definition,(
% 13.85/2.48 (sF153 = ((singletonsubset => sF152)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF153])],[function_definition])).
% 13.85/2.48 thf(f1433,definition,(
% 13.85/2.48 (sF154 = ((kpairp => sF153)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF154])],[function_definition])).
% 13.85/2.48 thf(f1434,definition,(
% 13.85/2.48 (sF155 = ((kpairiskpair => sF154)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF155])],[function_definition])).
% 13.85/2.48 thf(f1435,definition,(
% 13.85/2.48 (sF156 = ((setukpairIR => sF155)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF156])],[function_definition])).
% 13.85/2.48 thf(f1436,plain,(
% 13.85/2.48 (((setukpairIR => sF155)) = sF156)),
% 13.85/2.48 inference(reorient_equations,[],[f1435])).
% 13.85/2.48 thf(f1437,definition,(
% 13.85/2.48 (sF157 = ((setukpairIL => sF156)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF157])],[function_definition])).
% 13.85/2.48 thf(f1438,definition,(
% 13.85/2.48 (sF158 = ((secondinupair => sF157)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF158])],[function_definition])).
% 13.85/2.48 thf(f1439,definition,(
% 13.85/2.48 (sF159 = ((symdiffIneg2 => sF158)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF159])],[function_definition])).
% 13.85/2.48 thf(f1440,definition,(
% 13.85/2.48 (sF160 = ((symdiffIneg1 => sF159)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF160])],[function_definition])).
% 13.85/2.48 thf(f1441,plain,(
% 13.85/2.48 (((symdiffIneg1 => sF159)) = sF160)),
% 13.85/2.48 inference(reorient_equations,[],[f1440])).
% 13.85/2.48 thf(f1442,definition,(
% 13.85/2.48 (sF161 = ((symdiffI2 => sF160)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF161])],[function_definition])).
% 13.85/2.48 thf(f1443,definition,(
% 13.85/2.48 (sF162 = ((symdiffI1 => sF161)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF162])],[function_definition])).
% 13.85/2.48 thf(f1444,plain,(
% 13.85/2.48 (((symdiffI1 => sF161)) = sF162)),
% 13.85/2.48 inference(reorient_equations,[],[f1443])).
% 13.85/2.48 thf(f1445,definition,(
% 13.85/2.48 (sF163 = ((symdiffE => sF162)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF163])],[function_definition])).
% 13.85/2.48 thf(f1446,plain,(
% 13.85/2.48 (((symdiffE => sF162)) = sF163)),
% 13.85/2.48 inference(reorient_equations,[],[f1445])).
% 13.85/2.48 thf(f1447,definition,(
% 13.85/2.48 (sF164 = ((setminusSubset1 => sF163)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF164])],[function_definition])).
% 13.85/2.48 thf(f1448,definition,(
% 13.85/2.48 (sF165 = ((setminusLsub => sF164)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF165])],[function_definition])).
% 13.85/2.48 thf(f1449,plain,(
% 13.85/2.48 (((setminusLsub => sF164)) = sF165)),
% 13.85/2.48 inference(reorient_equations,[],[f1448])).
% 13.85/2.48 thf(f1450,definition,(
% 13.85/2.48 (sF166 = ((setminusIRneg => sF165)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF166])],[function_definition])).
% 13.85/2.48 thf(f1451,definition,(
% 13.85/2.48 (sF167 = ((setminusILneg => sF166)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF167])],[function_definition])).
% 13.85/2.48 thf(f1452,definition,(
% 13.85/2.48 (sF168 = ((setminusELneg => sF167)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF168])],[function_definition])).
% 13.85/2.48 thf(f1453,definition,(
% 13.85/2.48 (sF169 = ((setminusERneg => sF168)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF169])],[function_definition])).
% 13.85/2.48 thf(f1454,plain,(
% 13.85/2.48 (((setminusERneg => sF168)) = sF169)),
% 13.85/2.48 inference(reorient_equations,[],[f1453])).
% 13.85/2.48 thf(f1455,definition,(
% 13.85/2.48 (sF170 = ((setminusSubset2 => sF169)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF170])],[function_definition])).
% 13.85/2.48 thf(f1456,plain,(
% 13.85/2.48 (((setminusSubset2 => sF169)) = sF170)),
% 13.85/2.48 inference(reorient_equations,[],[f1455])).
% 13.85/2.48 thf(f1457,definition,(
% 13.85/2.48 (sF171 = ((setminusER => sF170)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF171])],[function_definition])).
% 13.85/2.48 thf(f1458,plain,(
% 13.85/2.48 (((setminusER => sF170)) = sF171)),
% 13.85/2.48 inference(reorient_equations,[],[f1457])).
% 13.85/2.48 thf(f1459,definition,(
% 13.85/2.48 (sF172 = ((setminusEL => sF171)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF172])],[function_definition])).
% 13.85/2.48 thf(f1460,plain,(
% 13.85/2.48 (((setminusEL => sF171)) = sF172)),
% 13.85/2.48 inference(reorient_equations,[],[f1459])).
% 13.85/2.48 thf(f1461,definition,(
% 13.85/2.48 (sF173 = ((setminusI => sF172)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF173])],[function_definition])).
% 13.85/2.48 thf(f1462,definition,(
% 13.85/2.48 (sF174 = ((bs114d => sF173)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF174])],[function_definition])).
% 13.85/2.48 thf(f1463,plain,(
% 13.85/2.48 (((bs114d => sF173)) = sF174)),
% 13.85/2.48 inference(reorient_equations,[],[f1462])).
% 13.85/2.48 thf(f1464,definition,(
% 13.85/2.48 (sF175 = ((binintersectSubset1 => sF174)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF175])],[function_definition])).
% 13.85/2.48 thf(f1465,definition,(
% 13.85/2.48 (sF176 = ((binintersectSubset4 => sF175)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF176])],[function_definition])).
% 13.85/2.48 thf(f1466,plain,(
% 13.85/2.48 (((binintersectSubset4 => sF175)) = sF176)),
% 13.85/2.48 inference(reorient_equations,[],[f1465])).
% 13.85/2.48 thf(f1467,definition,(
% 13.85/2.48 (sF177 = ((binintersectRsub => sF176)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF177])],[function_definition])).
% 13.85/2.48 thf(f1468,plain,(
% 13.85/2.48 (((binintersectRsub => sF176)) = sF177)),
% 13.85/2.48 inference(reorient_equations,[],[f1467])).
% 13.85/2.48 thf(f1469,definition,(
% 13.85/2.48 (sF178 = ((disjointsetsI1 => sF177)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF178])],[function_definition])).
% 13.85/2.48 thf(f1470,definition,(
% 13.85/2.48 (sF179 = ((binintersectER => sF178)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF179])],[function_definition])).
% 13.85/2.48 thf(f1471,plain,(
% 13.85/2.48 (((binintersectER => sF178)) = sF179)),
% 13.85/2.48 inference(reorient_equations,[],[f1470])).
% 13.85/2.48 thf(f1472,definition,(
% 13.85/2.48 (sF180 = ((binintersectSubset3 => sF179)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF180])],[function_definition])).
% 13.85/2.48 thf(f1473,plain,(
% 13.85/2.48 (((binintersectSubset3 => sF179)) = sF180)),
% 13.85/2.48 inference(reorient_equations,[],[f1472])).
% 13.85/2.48 thf(f1474,definition,(
% 13.85/2.48 (sF181 = ((binintersectSubset2 => sF180)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF181])],[function_definition])).
% 13.85/2.48 thf(f1475,plain,(
% 13.85/2.48 (((binintersectSubset2 => sF180)) = sF181)),
% 13.85/2.48 inference(reorient_equations,[],[f1474])).
% 13.85/2.48 thf(f1476,definition,(
% 13.85/2.48 (sF182 = ((binintersectLsub => sF181)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF182])],[function_definition])).
% 13.85/2.48 thf(f1477,plain,(
% 13.85/2.48 (((binintersectLsub => sF181)) = sF182)),
% 13.85/2.48 inference(reorient_equations,[],[f1476])).
% 13.85/2.48 thf(f1478,definition,(
% 13.85/2.48 (sF183 = ((binintersectEL => sF182)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF183])],[function_definition])).
% 13.85/2.48 thf(f1479,definition,(
% 13.85/2.48 (sF184 = ((binintersectSubset5 => sF183)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF184])],[function_definition])).
% 13.85/2.48 thf(f1480,definition,(
% 13.85/2.48 (sF185 = ((binintersectI => sF184)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF185])],[function_definition])).
% 13.85/2.48 thf(f1481,definition,(
% 13.85/2.48 (sF186 = ((binunionRsub => sF185)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF186])],[function_definition])).
% 13.85/2.48 thf(f1482,definition,(
% 13.85/2.48 (sF187 = ((binunionLsub => sF186)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF187])],[function_definition])).
% 13.85/2.48 thf(f1483,definition,(
% 13.85/2.48 (sF188 = ((binunionE => sF187)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF188])],[function_definition])).
% 13.85/2.48 thf(f1484,definition,(
% 13.85/2.48 (sF189 = ((binunionEcases => sF188)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF189])],[function_definition])).
% 13.85/2.48 thf(f1485,definition,(
% 13.85/2.48 (sF190 = ((binunionIR => sF189)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF190])],[function_definition])).
% 13.85/2.48 thf(f1486,definition,(
% 13.85/2.48 (sF191 = ((upairset2IR => sF190)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF191])],[function_definition])).
% 13.85/2.48 thf(f1487,definition,(
% 13.85/2.48 (sF192 = ((binunionIL => sF191)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF192])],[function_definition])).
% 13.85/2.48 thf(f1488,definition,(
% 13.85/2.48 (sF193 = ((sepSubset => sF192)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF193])],[function_definition])).
% 13.85/2.48 thf(f1489,plain,(
% 13.85/2.48 (((sepSubset => sF192)) = sF193)),
% 13.85/2.48 inference(reorient_equations,[],[f1488])).
% 13.85/2.48 thf(f1490,definition,(
% 13.85/2.48 (sF194 = ((sepInPowerset => sF193)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF194])],[function_definition])).
% 13.85/2.48 thf(f1491,definition,(
% 13.85/2.48 (sF195 = ((powersetsubset => sF194)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF195])],[function_definition])).
% 13.85/2.48 thf(f1492,plain,(
% 13.85/2.48 (((powersetsubset => sF194)) = sF195)),
% 13.85/2.48 inference(reorient_equations,[],[f1491])).
% 13.85/2.48 thf(f1493,definition,(
% 13.85/2.48 (sF196 = ((inPowerset => sF195)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF196])],[function_definition])).
% 13.85/2.48 thf(f1494,definition,(
% 13.85/2.48 (sF197 = ((powersetE1 => sF196)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF197])],[function_definition])).
% 13.85/2.48 thf(f1495,definition,(
% 13.85/2.48 (sF198 = ((powersetI1 => sF197)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF198])],[function_definition])).
% 13.85/2.48 thf(f1496,plain,(
% 13.85/2.48 (((powersetI1 => sF197)) = sF198)),
% 13.85/2.48 inference(reorient_equations,[],[f1495])).
% 13.85/2.48 thf(f1497,definition,(
% 13.85/2.48 (sF199 = ((subsetemptysetimpeq => sF198)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF199])],[function_definition])).
% 13.85/2.48 thf(f1498,definition,(
% 13.85/2.48 (sF200 = ((setextsub => sF199)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF200])],[function_definition])).
% 13.85/2.48 thf(f1499,plain,(
% 13.85/2.48 (((setextsub => sF199)) = sF200)),
% 13.85/2.48 inference(reorient_equations,[],[f1498])).
% 13.85/2.48 thf(f1500,definition,(
% 13.85/2.48 (sF201 = ((subset2powerset => sF200)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF201])],[function_definition])).
% 13.85/2.48 thf(f1501,plain,(
% 13.85/2.48 (((subset2powerset => sF200)) = sF201)),
% 13.85/2.48 inference(reorient_equations,[],[f1500])).
% 13.85/2.48 thf(f1502,definition,(
% 13.85/2.48 (sF202 = ((setadjoinSub2 => sF201)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF202])],[function_definition])).
% 13.85/2.48 thf(f1503,plain,(
% 13.85/2.48 (((setadjoinSub2 => sF201)) = sF202)),
% 13.85/2.48 inference(reorient_equations,[],[f1502])).
% 13.85/2.48 thf(f1504,definition,(
% 13.85/2.48 (sF203 = ((setadjoinSub => sF202)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF203])],[function_definition])).
% 13.85/2.48 thf(f1505,plain,(
% 13.85/2.48 (((setadjoinSub => sF202)) = sF203)),
% 13.85/2.48 inference(reorient_equations,[],[f1504])).
% 13.85/2.48 thf(f1506,definition,(
% 13.85/2.48 (sF204 = ((subsetTrans => sF203)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF204])],[function_definition])).
% 13.85/2.48 thf(f1507,definition,(
% 13.85/2.48 (sF205 = ((subsetRefl => sF204)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF205])],[function_definition])).
% 13.85/2.48 thf(f1508,plain,(
% 13.85/2.48 (((subsetRefl => sF204)) = sF205)),
% 13.85/2.48 inference(reorient_equations,[],[f1507])).
% 13.85/2.48 thf(f1509,definition,(
% 13.85/2.48 (sF206 = ((notequalI2 => sF205)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF206])],[function_definition])).
% 13.85/2.48 thf(f1510,definition,(
% 13.85/2.48 (sF207 = ((notequalI1 => sF206)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF207])],[function_definition])).
% 13.85/2.48 thf(f1511,plain,(
% 13.85/2.48 (((notequalI1 => sF206)) = sF207)),
% 13.85/2.48 inference(reorient_equations,[],[f1510])).
% 13.85/2.48 thf(f1512,definition,(
% 13.85/2.48 (sF208 = ((notsubsetI => sF207)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF208])],[function_definition])).
% 13.85/2.48 thf(f1513,definition,(
% 13.85/2.48 (sF209 = ((subsetE2 => sF208)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF209])],[function_definition])).
% 13.85/2.48 thf(f1514,plain,(
% 13.85/2.48 (((subsetE2 => sF208)) = sF209)),
% 13.85/2.48 inference(reorient_equations,[],[f1513])).
% 13.85/2.48 thf(f1515,definition,(
% 13.85/2.48 (sF210 = ((subsetE => sF209)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF210])],[function_definition])).
% 13.85/2.48 thf(f1516,definition,(
% 13.85/2.48 (sF211 = ((emptysetsubset => sF210)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF211])],[function_definition])).
% 13.85/2.48 thf(f1517,plain,(
% 13.85/2.48 (((emptysetsubset => sF210)) = sF211)),
% 13.85/2.48 inference(reorient_equations,[],[f1516])).
% 13.85/2.48 thf(f1518,definition,(
% 13.85/2.48 (sF212 = ((subsetI2 => sF211)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF212])],[function_definition])).
% 13.85/2.48 thf(f1519,definition,(
% 13.85/2.48 (sF213 = ((eqimpsubset1 => sF212)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF213])],[function_definition])).
% 13.85/2.48 thf(f1520,plain,(
% 13.85/2.48 (((eqimpsubset1 => sF212)) = sF213)),
% 13.85/2.48 inference(reorient_equations,[],[f1519])).
% 13.85/2.48 thf(f1521,definition,(
% 13.85/2.48 (sF214 = ((eqimpsubset2 => sF213)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF214])],[function_definition])).
% 13.85/2.48 thf(f1522,definition,(
% 13.85/2.48 (sF215 = ((subsetI1 => sF214)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF215])],[function_definition])).
% 13.85/2.48 thf(f1523,definition,(
% 13.85/2.48 (sF216 = ((dsetconstr__Cong => sF215)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF216])],[function_definition])).
% 13.85/2.48 thf(f1524,plain,(
% 13.85/2.48 (((dsetconstr__Cong => sF215)) = sF216)),
% 13.85/2.48 inference(reorient_equations,[],[f1523])).
% 13.85/2.48 thf(f1525,definition,(
% 13.85/2.48 (sF217 = ((descr__Cong => sF216)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF217])],[function_definition])).
% 13.85/2.48 thf(f1526,plain,(
% 13.85/2.48 (((descr__Cong => sF216)) = sF217)),
% 13.85/2.48 inference(reorient_equations,[],[f1525])).
% 13.85/2.48 thf(f1527,definition,(
% 13.85/2.48 (sF218 = ((exuEu => sF217)))),
% 13.85/2.48 introduced(definition,[new_symbols(definition,[sF218])],[function_definition])).
% 13.85/2.49 thf(f1528,definition,(
% 13.85/2.49 (sF219 = ((omega__Cong => sF218)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF219])],[function_definition])).
% 13.85/2.49 thf(f1529,definition,(
% 13.85/2.49 (sF220 = ((setunion__Cong => sF219)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF220])],[function_definition])).
% 13.85/2.49 thf(f1530,definition,(
% 13.85/2.49 (sF221 = ((powerset__Cong => sF220)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF221])],[function_definition])).
% 13.85/2.49 thf(f1531,definition,(
% 13.85/2.49 (sF222 = ((setadjoin__Cong => sF221)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF222])],[function_definition])).
% 13.85/2.49 thf(f1532,definition,(
% 13.85/2.49 (sF223 = ((emptyset__Cong => sF222)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF223])],[function_definition])).
% 13.85/2.49 thf(f1533,plain,(
% 13.85/2.49 (((emptyset__Cong => sF222)) = sF223)),
% 13.85/2.49 inference(reorient_equations,[],[f1532])).
% 13.85/2.49 thf(f1534,definition,(
% 13.85/2.49 (sF224 = ((exu__Cong => sF223)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF224])],[function_definition])).
% 13.85/2.49 thf(f1535,plain,(
% 13.85/2.49 (((exu__Cong => sF223)) = sF224)),
% 13.85/2.49 inference(reorient_equations,[],[f1534])).
% 13.85/2.49 thf(f1536,definition,(
% 13.85/2.49 (sF225 = ((exuE3u => sF224)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF225])],[function_definition])).
% 13.85/2.49 thf(f1537,definition,(
% 13.85/2.49 (sF226 = ((in__Cong => sF225)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF226])],[function_definition])).
% 13.85/2.49 thf(f1538,definition,(
% 13.85/2.49 (sF227 = ((inCongP => sF226)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF227])],[function_definition])).
% 13.85/2.49 thf(f1539,definition,(
% 13.85/2.49 (sF228 = ((exuI2 => sF227)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF228])],[function_definition])).
% 13.85/2.49 thf(f1540,definition,(
% 13.85/2.49 (sF229 = ((exuI3 => sF228)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF229])],[function_definition])).
% 13.85/2.49 thf(f1541,definition,(
% 13.85/2.49 (sF230 = ((exuI1 => sF229)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF230])],[function_definition])).
% 13.85/2.49 thf(f1542,definition,(
% 13.85/2.49 (sF231 = ((notdallE => sF230)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF231])],[function_definition])).
% 13.85/2.49 thf(f1543,plain,(
% 13.85/2.49 (((notdallE => sF230)) = sF231)),
% 13.85/2.49 inference(reorient_equations,[],[f1542])).
% 13.85/2.49 thf(f1544,definition,(
% 13.85/2.49 (sF232 = ((notdexE => sF231)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF232])],[function_definition])).
% 13.85/2.49 thf(f1545,plain,(
% 13.85/2.49 (((notdexE => sF231)) = sF232)),
% 13.85/2.49 inference(reorient_equations,[],[f1544])).
% 13.85/2.49 thf(f1546,definition,(
% 13.85/2.49 (sF233 = ((prop2set2propI => sF232)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF233])],[function_definition])).
% 13.85/2.49 thf(f1547,definition,(
% 13.85/2.49 (sF234 = ((prop2setI => sF233)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF234])],[function_definition])).
% 13.85/2.49 thf(f1548,definition,(
% 13.85/2.49 (sF235 = ((quantDeMorgan4 => sF234)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF235])],[function_definition])).
% 13.85/2.49 thf(f1549,definition,(
% 13.85/2.49 (sF236 = ((quantDeMorgan3 => sF235)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF236])],[function_definition])).
% 13.85/2.49 thf(f1550,definition,(
% 13.85/2.49 (sF237 = ((quantDeMorgan2 => sF236)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF237])],[function_definition])).
% 13.85/2.49 thf(f1551,plain,(
% 13.85/2.49 (((quantDeMorgan2 => sF236)) = sF237)),
% 13.85/2.49 inference(reorient_equations,[],[f1550])).
% 13.85/2.49 thf(f1552,definition,(
% 13.85/2.49 (sF238 = ((quantDeMorgan1 => sF237)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF238])],[function_definition])).
% 13.85/2.49 thf(f1553,definition,(
% 13.85/2.49 (sF239 = ((vacuousDall => sF238)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF239])],[function_definition])).
% 13.85/2.49 thf(f1554,definition,(
% 13.85/2.49 (sF240 = ((emptyE1 => sF239)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF240])],[function_definition])).
% 13.85/2.49 thf(f1555,definition,(
% 13.85/2.49 (sF241 = ((upairsetIR => sF240)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF241])],[function_definition])).
% 13.85/2.49 thf(f1556,definition,(
% 13.85/2.49 (sF242 = ((upairsetIL => sF241)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF242])],[function_definition])).
% 13.85/2.49 thf(f1557,definition,(
% 13.85/2.49 (sF243 = ((upairsetE => sF242)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF243])],[function_definition])).
% 13.85/2.49 thf(f1558,definition,(
% 13.85/2.49 (sF244 = ((singletonsswitch => sF243)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF244])],[function_definition])).
% 13.85/2.49 thf(f1559,definition,(
% 13.85/2.49 (sF245 = ((eqinunit => sF244)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF245])],[function_definition])).
% 13.85/2.49 thf(f1560,plain,(
% 13.85/2.49 (((eqinunit => sF244)) = sF245)),
% 13.85/2.49 inference(reorient_equations,[],[f1559])).
% 13.85/2.49 thf(f1561,definition,(
% 13.85/2.49 (sF246 = ((notinsingleton => sF245)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF246])],[function_definition])).
% 13.85/2.49 thf(f1562,plain,(
% 13.85/2.49 (((notinsingleton => sF245)) = sF246)),
% 13.85/2.49 inference(reorient_equations,[],[f1561])).
% 13.85/2.49 thf(f1563,definition,(
% 13.85/2.49 (sF247 = ((uniqinunit => sF246)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF247])],[function_definition])).
% 13.85/2.49 thf(f1564,plain,(
% 13.85/2.49 (((uniqinunit => sF246)) = sF247)),
% 13.85/2.49 inference(reorient_equations,[],[f1563])).
% 13.85/2.49 thf(f1565,definition,(
% 13.85/2.49 (sF248 = ((nonemptyImpWitness => sF247)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF248])],[function_definition])).
% 13.85/2.49 thf(f1566,definition,(
% 13.85/2.49 (sF249 = ((exuE2 => sF248)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF249])],[function_definition])).
% 13.85/2.49 thf(f1567,plain,(
% 13.85/2.49 (((exuE2 => sF248)) = sF249)),
% 13.85/2.49 inference(reorient_equations,[],[f1566])).
% 13.85/2.49 thf(f1568,definition,(
% 13.85/2.49 (sF250 = ((subPowSU => sF249)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF250])],[function_definition])).
% 13.85/2.49 thf(f1569,plain,(
% 13.85/2.49 (((subPowSU => sF249)) = sF250)),
% 13.85/2.49 inference(reorient_equations,[],[f1568])).
% 13.85/2.49 thf(f1570,definition,(
% 13.85/2.49 (sF251 = ((setunionE => sF250)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF251])],[function_definition])).
% 13.85/2.49 thf(f1571,definition,(
% 13.85/2.49 (sF252 = ((setunionI => sF251)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF252])],[function_definition])).
% 13.85/2.49 thf(f1572,plain,(
% 13.85/2.49 (((setunionI => sF251)) = sF252)),
% 13.85/2.49 inference(reorient_equations,[],[f1571])).
% 13.85/2.49 thf(f1573,definition,(
% 13.85/2.49 (sF253 = ((powersetE => sF252)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF253])],[function_definition])).
% 13.85/2.49 thf(f1574,definition,(
% 13.85/2.49 (sF254 = ((emptyInPowerset => sF253)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF254])],[function_definition])).
% 13.85/2.49 thf(f1575,definition,(
% 13.85/2.49 (sF255 = ((emptyinPowerset => sF254)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF255])],[function_definition])).
% 13.85/2.49 thf(f1576,definition,(
% 13.85/2.49 (sF256 = ((powersetI => sF255)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF256])],[function_definition])).
% 13.85/2.49 thf(f1577,definition,(
% 13.85/2.49 (sF257 = ((setoftrueEq => sF256)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF257])],[function_definition])).
% 13.85/2.49 thf(f1578,definition,(
% 13.85/2.49 (sF258 = ((setadjoinOr => sF257)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF258])],[function_definition])).
% 13.85/2.49 thf(f1579,definition,(
% 13.85/2.49 (sF259 = ((setadjoinE => sF258)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF259])],[function_definition])).
% 13.85/2.49 thf(f1580,plain,(
% 13.85/2.49 (((setadjoinE => sF258)) = sF259)),
% 13.85/2.49 inference(reorient_equations,[],[f1579])).
% 13.85/2.49 thf(f1581,definition,(
% 13.85/2.49 (sF260 = ((setadjoinIR => sF259)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF260])],[function_definition])).
% 13.85/2.49 thf(f1582,plain,(
% 13.85/2.49 (((setadjoinIR => sF259)) = sF260)),
% 13.85/2.49 inference(reorient_equations,[],[f1581])).
% 13.85/2.49 thf(f1583,definition,(
% 13.85/2.49 (sF261 = ((emptyinunitempty => sF260)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF261])],[function_definition])).
% 13.85/2.49 thf(f1584,plain,(
% 13.85/2.49 (((emptyinunitempty => sF260)) = sF261)),
% 13.85/2.49 inference(reorient_equations,[],[f1583])).
% 13.85/2.49 thf(f1585,definition,(
% 13.85/2.49 (sF262 = ((setadjoinIL => sF261)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF262])],[function_definition])).
% 13.85/2.49 thf(f1586,plain,(
% 13.85/2.49 (((setadjoinIL => sF261)) = sF262)),
% 13.85/2.49 inference(reorient_equations,[],[f1585])).
% 13.85/2.49 thf(f1587,definition,(
% 13.85/2.49 (sF263 = ((nonemptyI1 => sF262)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF263])],[function_definition])).
% 13.85/2.49 thf(f1588,definition,(
% 13.85/2.49 (sF264 = ((nonemptyI => sF263)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF264])],[function_definition])).
% 13.85/2.49 thf(f1589,definition,(
% 13.85/2.49 (sF265 = ((nonemptyE1 => sF264)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF265])],[function_definition])).
% 13.85/2.49 thf(f1590,plain,(
% 13.85/2.49 (((nonemptyE1 => sF264)) = sF265)),
% 13.85/2.49 inference(reorient_equations,[],[f1589])).
% 13.85/2.49 thf(f1591,definition,(
% 13.85/2.49 (sF266 = ((setbeta => sF265)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF266])],[function_definition])).
% 13.85/2.49 thf(f1592,definition,(
% 13.85/2.49 (sF267 = ((noeltsimpempty => sF266)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF267])],[function_definition])).
% 13.85/2.49 thf(f1593,plain,(
% 13.85/2.49 (((noeltsimpempty => sF266)) = sF267)),
% 13.85/2.49 inference(reorient_equations,[],[f1592])).
% 13.85/2.49 thf(f1594,definition,(
% 13.85/2.49 (sF268 = ((emptyI => sF267)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF268])],[function_definition])).
% 13.85/2.49 thf(f1595,plain,(
% 13.85/2.49 (((emptyI => sF267)) = sF268)),
% 13.85/2.49 inference(reorient_equations,[],[f1594])).
% 13.85/2.49 thf(f1596,definition,(
% 13.85/2.49 (sF269 = ((setext => sF268)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF269])],[function_definition])).
% 13.85/2.49 thf(f1597,plain,(
% 13.85/2.49 (((setext => sF268)) = sF269)),
% 13.85/2.49 inference(reorient_equations,[],[f1596])).
% 13.85/2.49 thf(f1598,definition,(
% 13.85/2.49 (sF270 = ((exuE3e => sF269)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF270])],[function_definition])).
% 13.85/2.49 thf(f1599,definition,(
% 13.85/2.49 (sF271 = ((notinemptyset => sF270)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF271])],[function_definition])).
% 13.85/2.49 thf(f1600,plain,(
% 13.85/2.49 (((notinemptyset => sF270)) = sF271)),
% 13.85/2.49 inference(reorient_equations,[],[f1599])).
% 13.85/2.49 thf(f1601,definition,(
% 13.85/2.49 (sF272 = ((emptysetimpfalse => sF271)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF272])],[function_definition])).
% 13.85/2.49 thf(f1602,definition,(
% 13.85/2.49 (sF273 = ((emptysetE => sF272)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF273])],[function_definition])).
% 13.85/2.49 thf(f1603,plain,(
% 13.85/2.49 (((emptysetE => sF272)) = sF273)),
% 13.85/2.49 inference(reorient_equations,[],[f1602])).
% 13.85/2.49 thf(f1604,definition,(
% 13.85/2.49 (sF274 = ((prop2setE => sF273)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF274])],[function_definition])).
% 13.85/2.49 thf(f1605,definition,(
% 13.85/2.49 (sF275 = ((exuE1 => sF274)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF275])],[function_definition])).
% 13.85/2.49 thf(f1606,definition,(
% 13.85/2.49 (sF276 = ((dsetconstrER => sF275)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF276])],[function_definition])).
% 13.85/2.49 thf(f1607,plain,(
% 13.85/2.49 (((dsetconstrER => sF275)) = sF276)),
% 13.85/2.49 inference(reorient_equations,[],[f1606])).
% 13.85/2.49 thf(f1608,definition,(
% 13.85/2.49 (sF277 = ((dsetconstrEL => sF276)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF277])],[function_definition])).
% 13.85/2.49 thf(f1609,definition,(
% 13.85/2.49 (sF278 = ((dsetconstrI => sF277)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF278])],[function_definition])).
% 13.85/2.49 thf(f1610,plain,(
% 13.85/2.49 (((dsetconstrI => sF277)) = sF278)),
% 13.85/2.49 inference(reorient_equations,[],[f1609])).
% 13.85/2.49 thf(f1611,definition,(
% 13.85/2.49 (sF279 = ((descrp => sF278)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF279])],[function_definition])).
% 13.85/2.49 thf(f1612,definition,(
% 13.85/2.49 (sF280 = ((wellorderingAx => sF279)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF280])],[function_definition])).
% 13.85/2.49 thf(f1613,plain,(
% 13.85/2.49 (((wellorderingAx => sF279)) = sF280)),
% 13.85/2.49 inference(reorient_equations,[],[f1612])).
% 13.85/2.49 thf(f1614,definition,(
% 13.85/2.49 (sF281 = ((foundationAx => sF280)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF281])],[function_definition])).
% 13.85/2.49 thf(f1615,definition,(
% 13.85/2.49 (sF282 = ((replAx => sF281)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF282])],[function_definition])).
% 13.85/2.49 thf(f1616,definition,(
% 13.85/2.49 (sF283 = ((omegaIndAx => sF282)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF283])],[function_definition])).
% 13.85/2.49 thf(f1617,plain,(
% 13.85/2.49 (((omegaIndAx => sF282)) = sF283)),
% 13.85/2.49 inference(reorient_equations,[],[f1616])).
% 13.85/2.49 thf(f1618,definition,(
% 13.85/2.49 (sF284 = ((omegaSAx => sF283)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF284])],[function_definition])).
% 13.85/2.49 thf(f1619,plain,(
% 13.85/2.49 (((omegaSAx => sF283)) = sF284)),
% 13.85/2.49 inference(reorient_equations,[],[f1618])).
% 13.85/2.49 thf(f1620,definition,(
% 13.85/2.49 (sF285 = ((omega0Ax => sF284)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF285])],[function_definition])).
% 13.85/2.49 thf(f1621,definition,(
% 13.85/2.49 (sF286 = ((setunionAx => sF285)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF286])],[function_definition])).
% 13.85/2.49 thf(f1622,plain,(
% 13.85/2.49 (((setunionAx => sF285)) = sF286)),
% 13.85/2.49 inference(reorient_equations,[],[f1621])).
% 13.85/2.49 thf(f1623,definition,(
% 13.85/2.49 (sF287 = ((powersetAx => sF286)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF287])],[function_definition])).
% 13.85/2.49 thf(f1624,plain,(
% 13.85/2.49 (((powersetAx => sF286)) = sF287)),
% 13.85/2.49 inference(reorient_equations,[],[f1623])).
% 13.85/2.49 thf(f1625,definition,(
% 13.85/2.49 (sF288 = ((setadjoinAx => sF287)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF288])],[function_definition])).
% 13.85/2.49 thf(f1626,plain,(
% 13.85/2.49 (((setadjoinAx => sF287)) = sF288)),
% 13.85/2.49 inference(reorient_equations,[],[f1625])).
% 13.85/2.49 thf(f1627,definition,(
% 13.85/2.49 (sF289 = ((emptysetAx => sF288)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF289])],[function_definition])).
% 13.85/2.49 thf(f1628,plain,(
% 13.85/2.49 (((emptysetAx => sF288)) = sF289)),
% 13.85/2.49 inference(reorient_equations,[],[f1627])).
% 13.85/2.49 thf(f1629,definition,(
% 13.85/2.49 (sF290 = ((setextAx => sF289)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF290])],[function_definition])).
% 13.85/2.49 thf(f1630,definition,(
% 13.85/2.49 (sF291 = ((~ sF290)))),
% 13.85/2.49 introduced(definition,[new_symbols(definition,[sF291])],[function_definition])).
% 13.85/2.49 thf(f1631,plain,(
% 13.85/2.49 (sF291 = $true)),
% 13.85/2.49 inference(definition_folding,[],[f1199,f1630,f1629,f1628,f1626,f1624,f1622,f1620,f1619,f1617,f1615,f1614,f1613,f1611,f1610,f1608,f1607,f1605,f1604,f1603,f1601,f1600,f1598,f1597,f1595,f1593,f1591,f1590,f1588,f1587,f1586,f1584,f1582,f1580,f1578,f1577,f1576,f1575,f1574,f1573,f1572,f1570,f1569,f1567,f1565,f1564,f1562,f1560,f1558,f1557,f1556,f1555,f1554,f1553,f1552,f1551,f1549,f1548,f1547,f1546,f1545,f1543,f1541,f1540,f1539,f1538,f1537,f1536,f1535,f1533,f1531,f1530,f1529,f1528,f1527,f1526,f1524,f1522,f1521,f1520,f1518,f1517,f1515,f1514,f1512,f1511,f1509,f1508,f1506,f1505,f1503,f1501,f1499,f1497,f1496,f1494,f1493,f1492,f1490,f1489,f1487,f1486,f1485,f1484,f1483,f1482,f1481,f1480,f1479,f1478,f1477,f1475,f1473,f1471,f1469,f1468,f1466,f1464,f1463,f1461,f1460,f1458,f1456,f1454,f1452,f1451,f1450,f1449,f1447,f1446,f1444,f1442,f1441,f1439,f1438,f1437,f1436,f1434,f1433,f1432,f1431,f1430,f1428,f1427,f1425,f1423,f1421,f1420,f1418,f1417,f1415,f1414,f1413,f1411,f1409,f1408,f1406,f1405,f1404,f1403,f1402,f1400,f1398,f1396,f1395,f1394,f1393,f1391,f1390,f1389,f1388,f1386,f1384,f1382,f1380,f1379,f1378,f1376,f1375,f1373,f1371,f1369,f1367,f1365,f1363,f1361,f1359,f1358,f1356,f1355,f1353,f1351,f1349,f1347,f1345,f1344,f1343,f1341,f1339,f1337,f1335,f1334,f1332,f1331,f1330,f1328,f1327,f1325,f1323,f1321,f1320,f1318,f1317,f1315,f1314,f1313,f1311,f1310,f1309,f1308,f1307,f1305,f1303,f1301,f1299,f1297,f1295,f1294,f1292,f1291,f1289,f1288,f1286,f1285,f1284,f1283,f1281,f1280,f1278,f1276,f1274,f1272,f1271,f1270,f1269,f1268,f1267,f1266,f1265,f1264,f1262,f1261,f1259,f1258,f1257,f1256,f1255,f1254,f1253,f1252,f1250,f1248,f1246,f1244,f1243,f1241,f1239,f1238,f1237,f1235,f1233,f1231,f1230,f1228,f1227,f1226,f1225,f1224,f1223,f1221,f1220,f1218,f1217,f1215,f1214,f1213,f1211,f1209,f1207,f1205,f1204,f1203,f1202])).
% 13.85/2.49 thf(f1632,plain,(
% 13.85/2.49 (setbeta = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) = (in @ Y1 @ (dsetconstr @ Y2 @ Y0))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1058])).
% 13.85/2.49 thf(f1634,plain,(
% 13.85/2.49 (dsetconstr__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f980])).
% 13.85/2.49 thf(f1636,plain,(
% 13.85/2.49 (eta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => ((lam @ Y0 @ Y2 @ (ap @ Y0 @ Y2 @ Y1)) = Y1))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1162])).
% 13.85/2.49 thf(f1642,plain,(
% 13.85/2.49 (ex1E1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f957])).
% 13.85/2.49 thf(f1643,plain,(
% 13.85/2.49 (breln1all2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y1)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1184])).
% 13.85/2.49 thf(f1645,plain,(
% 13.85/2.49 (dpsetconstrERa = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ Y2)) => (Y2 @ Y3 @ Y4))))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1118])).
% 13.85/2.49 thf(f1646,plain,(
% 13.85/2.49 (sepInPowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f945])).
% 13.85/2.49 thf(f1647,plain,(
% 13.85/2.49 (breln1all1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y1)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1186])).
% 13.85/2.49 thf(f1648,plain,(
% 13.85/2.49 (dpsetconstrEL1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y4 @ Y2 @ Y0)) => (in @ Y1 @ Y4))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f955])).
% 13.85/2.49 thf(f1649,plain,(
% 13.85/2.49 (eqbreln = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3)))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1174])).
% 13.85/2.49 thf(f1650,plain,(
% 13.85/2.49 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1179])).
% 13.85/2.49 thf(f1651,plain,(
% 13.85/2.49 (dpsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3)))))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1016])).
% 13.85/2.49 thf(f1653,plain,(
% 13.85/2.49 (lamProp = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (func @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: (= @ (Y1 @ Y3))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1000])).
% 13.85/2.49 thf(f1654,plain,(
% 13.85/2.49 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1191])).
% 13.85/2.49 thf(f1655,plain,(
% 13.85/2.49 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))))),
% 13.85/2.49 inference(boolean_simplification,[],[f1654])).
% 13.85/2.49 thf(f1658,plain,(
% 13.85/2.49 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1180])).
% 13.85/2.49 thf(f1659,plain,(
% 13.85/2.49 (exu__Cong = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1196])).
% 13.85/2.49 thf(f1660,plain,(
% 13.85/2.49 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1176])).
% 13.85/2.49 thf(f1661,plain,(
% 13.85/2.49 (setOfPairsIsBReln1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ Y1 @ Y0) @ (cartprod @ Y1 @ Y1))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1183])).
% 13.85/2.49 thf(f1662,plain,(
% 13.85/2.49 (dpsetconstrEL2 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ Y0)) => (in @ Y4 @ Y3))))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1036])).
% 13.85/2.49 thf(f1665,plain,(
% 13.85/2.49 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => $true))))))))))))),
% 13.85/2.49 inference(boolean_simplification,[],[f986])).
% 13.85/2.49 thf(f1666,plain,(
% 13.85/2.49 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 13.85/2.49 inference(boolean_simplification,[],[f1665])).
% 13.85/2.49 thf(f1667,plain,(
% 13.85/2.49 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1190])).
% 13.85/2.49 thf(f1668,plain,(
% 13.85/2.49 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.85/2.49 inference(boolean_simplification,[],[f1667])).
% 13.85/2.49 thf(f1669,plain,(
% 13.85/2.49 (lam2p = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (in @ (lam @ Y1 @ Y2 @ Y0) @ (funcSet @ Y1 @ Y2)))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f887])).
% 13.85/2.49 thf(f1672,plain,(
% 13.85/2.49 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0)))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f981])).
% 13.85/2.49 thf(f1677,plain,(
% 13.85/2.49 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1200])).
% 13.85/2.49 thf(f1678,plain,(
% 13.85/2.49 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))))),
% 13.85/2.49 inference(boolean_simplification,[],[f1677])).
% 13.85/2.49 thf(f1680,plain,(
% 13.85/2.49 (lamp = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (func @ Y2 @ Y0 @ (lam @ Y2 @ Y0 @ Y1)))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f927])).
% 13.85/2.49 thf(f1682,plain,(
% 13.85/2.49 (emptysetsubset = ((!! @ $i @ (subset @ emptyset))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1103])).
% 13.85/2.49 thf(f1683,plain,(
% 13.85/2.49 (singletonprop = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ Y1))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1143])).
% 13.85/2.49 thf(f1684,plain,(
% 13.85/2.49 (sF0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ Y1)))))))) => (Y1 = Y2)))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1202])).
% 13.85/2.49 thf(f1685,plain,(
% 13.85/2.49 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0)))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1195])).
% 13.85/2.49 thf(f1686,plain,(
% 13.85/2.49 (setOfPairsIsBReln = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y1 @ Y0) @ (cartprod @ Y2 @ Y1))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1177])).
% 13.85/2.49 thf(f1687,plain,(
% 13.85/2.49 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1192])).
% 13.85/2.49 thf(f1689,plain,(
% 13.85/2.49 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1187])).
% 13.85/2.49 thf(f1692,plain,(
% 13.85/2.49 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => $true))))))))))))),
% 13.85/2.49 inference(boolean_simplification,[],[f895])).
% 13.85/2.49 thf(f1693,plain,(
% 13.85/2.49 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 13.85/2.49 inference(boolean_simplification,[],[f1692])).
% 13.85/2.49 thf(f1694,plain,(
% 13.85/2.49 (emptyset__Cong = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f1127])).
% 13.85/2.49 thf(f1696,plain,(
% 13.85/2.49 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => ((lam @ Y2 @ Y0 @ Y1) = (lam @ Y2 @ Y0 @ Y1)))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1145])).
% 13.85/2.49 thf(f1697,plain,(
% 13.85/2.49 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => $true)))))))))),
% 13.85/2.49 inference(boolean_simplification,[],[f1696])).
% 13.85/2.49 thf(f1698,plain,(
% 13.85/2.49 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ($true)))))))))),
% 13.85/2.49 inference(boolean_simplification,[],[f1697])).
% 13.85/2.49 thf(f1699,plain,(
% 13.85/2.49 (omega__Cong = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f942])).
% 13.85/2.49 thf(f1700,plain,(
% 13.85/2.49 (nonemptyI = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (~ (emptyset = (dsetconstr @ Y2 @ Y0)))))))))))))),
% 13.85/2.49 inference(beta-eta_normalization,[],[f1198])).
% 13.85/2.49 thf(f1701,plain,(
% 13.85/2.49 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.85/2.49 inference(boolean_simplification,[],[f1029])).
% 13.85/2.49 thf(f1702,plain,(
% 13.85/2.49 ($true = ((~ sF290)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1630,f1631])).
% 13.85/2.49 thf(f1704,plain,(
% 13.85/2.49 ($false = sF290) | (((~ $true)) = $true)),
% 13.85/2.49 inference(superposition,[],[f1702,f1172])).
% 13.85/2.49 thf(f1705,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF290)),
% 13.85/2.49 inference(boolean_simplification,[],[f1704])).
% 13.85/2.49 thf(f1706,plain,(
% 13.85/2.49 ($false = sF290)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1705])).
% 13.85/2.49 thf(f1708,plain,(
% 13.85/2.49 ($false = ((setextAx => sF289)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1629,f1706])).
% 13.85/2.49 thf(f1710,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => sF289)))),
% 13.85/2.49 inference(forward_demodulation,[],[f1708,f961])).
% 13.85/2.49 thf(f1711,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => (emptysetAx => sF288))))),
% 13.85/2.49 inference(forward_demodulation,[],[f1710,f1628])).
% 13.85/2.49 thf(f1712,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => sF288))))),
% 13.85/2.49 inference(forward_demodulation,[],[f1711,f1067])).
% 13.85/2.49 thf(f1715,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true)))) | ($false = sF288)),
% 13.85/2.49 inference(superposition,[],[f1712,f1172])).
% 13.85/2.49 thf(f1720,plain,(
% 13.85/2.49 ($false = sF288) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => $true)))),
% 13.85/2.49 inference(boolean_simplification,[],[f1715])).
% 13.85/2.49 thf(f1721,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF288)),
% 13.85/2.49 inference(boolean_simplification,[],[f1720])).
% 13.85/2.49 thf(f1722,plain,(
% 13.85/2.49 ($false = sF288)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1721])).
% 13.85/2.49 thf(f1732,plain,(
% 13.85/2.49 ($false = ((setadjoinAx => sF287)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1626,f1722])).
% 13.85/2.49 thf(f1747,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y2 @ Y1) | (Y2 = Y0)) = (in @ Y2 @ (setadjoin @ Y0 @ Y1))))))))) => sF287)))),
% 13.85/2.49 inference(forward_demodulation,[],[f1732,f1089])).
% 13.85/2.49 thf(f1755,plain,(
% 13.85/2.49 ($false = sF287) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y2 @ Y1) | (Y2 = Y0)) = (in @ Y2 @ (setadjoin @ Y0 @ Y1))))))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f1747,f1172])).
% 13.85/2.49 thf(f1758,plain,(
% 13.85/2.49 ($false = sF287) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f1755])).
% 13.85/2.49 thf(f1759,plain,(
% 13.85/2.49 ($false = sF287)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1758])).
% 13.85/2.49 thf(f1763,plain,(
% 13.85/2.49 ($false = ((powersetAx => sF286)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1624,f1759])).
% 13.85/2.49 thf(f1770,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => sF286)))),
% 13.85/2.49 inference(forward_demodulation,[],[f1763,f998])).
% 13.85/2.49 thf(f1775,plain,(
% 13.85/2.49 ($false = sF286) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f1770,f1172])).
% 13.85/2.49 thf(f1778,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF286)),
% 13.85/2.49 inference(boolean_simplification,[],[f1775])).
% 13.85/2.49 thf(f1779,plain,(
% 13.85/2.49 ($false = sF286)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1778])).
% 13.85/2.49 thf(f1783,plain,(
% 13.85/2.49 ($false = ((setunionAx => sF285)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1622,f1779])).
% 13.85/2.49 thf(f1790,plain,(
% 13.85/2.49 ($false = sF285)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f1783])).
% 13.85/2.49 thf(f1800,plain,(
% 13.85/2.49 ($false = ((omega0Ax => sF284)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1620,f1790])).
% 13.85/2.49 thf(f1805,plain,(
% 13.85/2.49 ($false = (((in @ emptyset @ omega) => sF284)))),
% 13.85/2.49 inference(forward_demodulation,[],[f1800,f1102])).
% 13.85/2.49 thf(f1810,plain,(
% 13.85/2.49 ($false = sF284) | ($false = (((in @ emptyset @ omega) => $true)))),
% 13.85/2.49 inference(superposition,[],[f1805,f1172])).
% 13.85/2.49 thf(f1814,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF284)),
% 13.85/2.49 inference(boolean_simplification,[],[f1810])).
% 13.85/2.49 thf(f1815,plain,(
% 13.85/2.49 ($false = sF284)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1814])).
% 13.85/2.49 thf(f1818,plain,(
% 13.85/2.49 (((omegaSAx => sF283)) = $false)),
% 13.85/2.49 inference(backward_demodulation,[],[f1619,f1815])).
% 13.85/2.49 thf(f1823,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => sF283)))),
% 13.85/2.49 inference(forward_demodulation,[],[f1818,f1153])).
% 13.85/2.49 thf(f1828,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => (omegaIndAx => sF282))))),
% 13.85/2.49 inference(forward_demodulation,[],[f1823,f1617])).
% 13.85/2.49 thf(f1831,plain,(
% 13.85/2.49 ($false = sF282) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => (omegaIndAx => $true))))),
% 13.85/2.49 inference(superposition,[],[f1828,f1172])).
% 13.85/2.49 thf(f1839,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => $true))) | ($false = sF282)),
% 13.85/2.49 inference(boolean_simplification,[],[f1831])).
% 13.85/2.49 thf(f1840,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF282)),
% 13.85/2.49 inference(boolean_simplification,[],[f1839])).
% 13.85/2.49 thf(f1841,plain,(
% 13.85/2.49 ($false = sF282)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1840])).
% 13.85/2.49 thf(f1849,plain,(
% 13.85/2.49 ($false = ((replAx => sF281)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1615,f1841])).
% 13.85/2.49 thf(f1869,plain,(
% 13.85/2.49 ($false = sF281) | ($false = ((replAx => $true)))),
% 13.85/2.49 inference(superposition,[],[f1849,f1172])).
% 13.85/2.49 thf(f1874,plain,(
% 13.85/2.49 ($false = sF281) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f1869])).
% 13.85/2.49 thf(f1875,plain,(
% 13.85/2.49 ($false = sF281)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1874])).
% 13.85/2.49 thf(f1877,plain,(
% 13.85/2.49 ($false = ((foundationAx => sF280)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1614,f1875])).
% 13.85/2.49 thf(f1882,plain,(
% 13.85/2.49 ($false = sF280)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f1877])).
% 13.85/2.49 thf(f1892,plain,(
% 13.85/2.49 ($false = ((wellorderingAx => sF279)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1613,f1882])).
% 13.85/2.49 thf(f1903,plain,(
% 13.85/2.49 (sF279 = $false) | (((wellorderingAx => $true)) = $false)),
% 13.85/2.49 inference(superposition,[],[f1892,f1172])).
% 13.85/2.49 thf(f1906,plain,(
% 13.85/2.49 ($false = $true) | (sF279 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f1903])).
% 13.85/2.49 thf(f1907,plain,(
% 13.85/2.49 (sF279 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1906])).
% 13.85/2.49 thf(f1911,plain,(
% 13.85/2.49 ($false = ((descrp => sF278)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1611,f1907])).
% 13.85/2.49 thf(f1922,plain,(
% 13.85/2.49 ($false = ((descrp => $true))) | ($false = sF278)),
% 13.85/2.49 inference(superposition,[],[f1911,f1172])).
% 13.85/2.49 thf(f1926,plain,(
% 13.85/2.49 ($false = sF278) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f1922])).
% 13.85/2.49 thf(f1927,plain,(
% 13.85/2.49 ($false = sF278)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1926])).
% 13.85/2.49 thf(f1934,plain,(
% 13.85/2.49 ($false = ((dsetconstrI => sF277)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1610,f1927])).
% 13.85/2.49 thf(f1937,plain,(
% 13.85/2.49 ($false = ((dsetconstrI => (dsetconstrEL => sF276))))),
% 13.85/2.49 inference(forward_demodulation,[],[f1934,f1608])).
% 13.85/2.49 thf(f1940,plain,(
% 13.85/2.49 (((dsetconstrI => (dsetconstrEL => $true))) = $false) | ($false = sF276)),
% 13.85/2.49 inference(superposition,[],[f1937,f1172])).
% 13.85/2.49 thf(f1950,plain,(
% 13.85/2.49 ($false = sF276) | ($false = ((dsetconstrI => $true)))),
% 13.85/2.49 inference(boolean_simplification,[],[f1940])).
% 13.85/2.49 thf(f1951,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF276)),
% 13.85/2.49 inference(boolean_simplification,[],[f1950])).
% 13.85/2.49 thf(f1952,plain,(
% 13.85/2.49 ($false = sF276)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f1951])).
% 13.85/2.49 thf(f1958,plain,(
% 13.85/2.49 ($false = ((dsetconstrER => sF275)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1607,f1952])).
% 13.85/2.49 thf(f1970,plain,(
% 13.85/2.49 ($false = sF275)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f1958])).
% 13.85/2.49 thf(f1980,plain,(
% 13.85/2.49 ($false = ((exuE1 => sF274)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1605,f1970])).
% 13.85/2.49 thf(f1985,plain,(
% 13.85/2.49 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))) => sF274)))),
% 13.85/2.49 inference(forward_demodulation,[],[f1980,f1655])).
% 13.85/2.49 thf(f1990,plain,(
% 13.85/2.49 (sF274 = $false)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f1985])).
% 13.85/2.49 thf(f1991,plain,(
% 13.85/2.49 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))))),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f1985])).
% 13.85/2.49 thf(f2000,plain,(
% 13.85/2.49 ($false = ((prop2setE => sF273)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1604,f1990])).
% 13.85/2.49 thf(f2004,plain,(
% 13.85/2.49 (exuI1 = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f1678,f1991])).
% 13.85/2.49 thf(f2008,plain,(
% 13.85/2.49 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))) => sF273)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2000,f987])).
% 13.85/2.49 thf(f2011,plain,(
% 13.85/2.49 ((($true => sF229)) = sF230)),
% 13.85/2.49 inference(backward_demodulation,[],[f1541,f2004])).
% 13.85/2.49 thf(f2012,plain,(
% 13.85/2.49 (sF230 = sF229)),
% 13.85/2.49 inference(boolean_simplification,[],[f2011])).
% 13.85/2.49 thf(f2013,plain,(
% 13.85/2.49 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))) => (emptysetE => sF272))))),
% 13.85/2.49 inference(forward_demodulation,[],[f2008,f1603])).
% 13.85/2.49 thf(f2014,plain,(
% 13.85/2.49 (sF230 = ((exuI3 => sF228)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1540,f2012])).
% 13.85/2.49 thf(f2015,plain,(
% 13.85/2.49 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => sF272))))),
% 13.85/2.49 inference(forward_demodulation,[],[f2013,f937])).
% 13.85/2.49 thf(f2016,plain,(
% 13.85/2.49 (sF230 = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => sF228)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2014,f1689])).
% 13.85/2.49 thf(f2067,plain,(
% 13.85/2.49 ($false = sF272) | ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => $true))))),
% 13.85/2.49 inference(superposition,[],[f2015,f1172])).
% 13.85/2.49 thf(f2074,plain,(
% 13.85/2.49 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))) => $true))) | ($false = sF272)),
% 13.85/2.49 inference(boolean_simplification,[],[f2067])).
% 13.85/2.49 thf(f2075,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF272)),
% 13.85/2.49 inference(boolean_simplification,[],[f2074])).
% 13.85/2.49 thf(f2076,plain,(
% 13.85/2.49 ($false = sF272)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2075])).
% 13.85/2.49 thf(f2088,plain,(
% 13.85/2.49 ($false = ((emptysetimpfalse => sF271)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1601,f2076])).
% 13.85/2.49 thf(f2101,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => sF271)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2088,f1701])).
% 13.85/2.49 thf(f2108,plain,(
% 13.85/2.49 ($true = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2101])).
% 13.85/2.49 thf(f2109,plain,(
% 13.85/2.49 ($false = sF271) | ($false = (((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f2101,f1172])).
% 13.85/2.49 thf(f2112,plain,(
% 13.85/2.49 ($false = sF271) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2109])).
% 13.85/2.49 thf(f2113,plain,(
% 13.85/2.49 ($false = sF271)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2112])).
% 13.85/2.49 thf(f2117,plain,(
% 13.85/2.49 ($false = ((notinemptyset => sF270)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1600,f2113])).
% 13.85/2.49 thf(f2122,plain,(
% 13.85/2.49 (notinemptyset = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f1099,f2108])).
% 13.85/2.49 thf(f2128,plain,(
% 13.85/2.49 ($false = (($true => sF270)))),
% 13.85/2.49 inference(backward_demodulation,[],[f2117,f2122])).
% 13.85/2.49 thf(f2129,plain,(
% 13.85/2.49 ($false = sF270)),
% 13.85/2.49 inference(boolean_simplification,[],[f2128])).
% 13.85/2.49 thf(f2130,plain,(
% 13.85/2.49 ($false = ((exuE3e => sF269)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1598,f2129])).
% 13.85/2.49 thf(f2133,plain,(
% 13.85/2.49 ($false = sF269)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2130])).
% 13.85/2.49 thf(f2143,plain,(
% 13.85/2.49 ($false = ((setext => sF268)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1597,f2133])).
% 13.85/2.49 thf(f2148,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => sF268)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2143,f985])).
% 13.85/2.49 thf(f2176,plain,(
% 13.85/2.49 ($false = sF268) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f2148,f1172])).
% 13.85/2.49 thf(f2180,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF268)),
% 13.85/2.49 inference(boolean_simplification,[],[f2176])).
% 13.85/2.49 thf(f2181,plain,(
% 13.85/2.49 ($false = sF268)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2180])).
% 13.85/2.49 thf(f2184,plain,(
% 13.85/2.49 ($false = ((emptyI => sF267)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1595,f2181])).
% 13.85/2.49 thf(f2189,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => sF267)) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f2184,f1024])).
% 13.85/2.49 thf(f2195,plain,(
% 13.85/2.49 ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2189])).
% 13.85/2.49 thf(f2196,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true))) | ($false = sF267)),
% 13.85/2.49 inference(superposition,[],[f2189,f1172])).
% 13.85/2.49 thf(f2199,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF267)),
% 13.85/2.49 inference(boolean_simplification,[],[f2196])).
% 13.85/2.49 thf(f2200,plain,(
% 13.85/2.49 ($false = sF267)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2199])).
% 13.85/2.49 thf(f2204,plain,(
% 13.85/2.49 ($false = ((noeltsimpempty => sF266)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1593,f2200])).
% 13.85/2.49 thf(f2208,plain,(
% 13.85/2.49 (noeltsimpempty = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f1104,f2195])).
% 13.85/2.49 thf(f2214,plain,(
% 13.85/2.49 ($false = (($true => sF266)))),
% 13.85/2.49 inference(backward_demodulation,[],[f2204,f2208])).
% 13.85/2.49 thf(f2215,plain,(
% 13.85/2.49 ($false = sF266)),
% 13.85/2.49 inference(boolean_simplification,[],[f2214])).
% 13.85/2.49 thf(f2216,plain,(
% 13.85/2.49 ($false = ((setbeta => sF265)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1591,f2215])).
% 13.85/2.49 thf(f2217,plain,(
% 13.85/2.49 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) = (in @ Y1 @ (dsetconstr @ Y2 @ Y0)))))))))) => sF265)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2216,f1632])).
% 13.85/2.49 thf(f2220,plain,(
% 13.85/2.49 ($false = sF265)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2217])).
% 13.85/2.49 thf(f2230,plain,(
% 13.85/2.49 ($false = ((nonemptyE1 => sF264)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1590,f2220])).
% 13.85/2.49 thf(f2235,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => sF264)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2230,f1650])).
% 13.85/2.49 thf(f2239,plain,(
% 13.85/2.49 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2235])).
% 13.85/2.49 thf(f2240,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => $true))) | ($false = sF264)),
% 13.85/2.49 inference(superposition,[],[f2235,f1172])).
% 13.85/2.49 thf(f2244,plain,(
% 13.85/2.49 ($false = sF264) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2240])).
% 13.85/2.49 thf(f2245,plain,(
% 13.85/2.49 ($false = sF264)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2244])).
% 13.85/2.49 thf(f2248,plain,(
% 13.85/2.49 ($false = ((nonemptyI => sF263)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1588,f2245])).
% 13.85/2.49 thf(f2250,plain,(
% 13.85/2.49 (nonemptyImpWitness = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f1668,f2239])).
% 13.85/2.49 thf(f2252,plain,(
% 13.85/2.49 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (~ (emptyset = (dsetconstr @ Y2 @ Y0))))))))))) => sF263)) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f2248,f1700])).
% 13.85/2.49 thf(f2255,plain,(
% 13.85/2.49 ((($true => sF247)) = sF248)),
% 13.85/2.49 inference(backward_demodulation,[],[f1565,f2250])).
% 13.85/2.49 thf(f2256,plain,(
% 13.85/2.49 (sF247 = sF248)),
% 13.85/2.49 inference(boolean_simplification,[],[f2255])).
% 13.85/2.49 thf(f2257,plain,(
% 13.85/2.49 (((exuE2 => sF247)) = sF249)),
% 13.85/2.49 inference(backward_demodulation,[],[f1567,f2256])).
% 13.85/2.49 thf(f2266,plain,(
% 13.85/2.49 ($false = sF247) | (((exuE2 => $true)) = sF249)),
% 13.85/2.49 inference(superposition,[],[f2257,f1172])).
% 13.85/2.49 thf(f2270,plain,(
% 13.85/2.49 ($false = sF247) | ($true = sF249)),
% 13.85/2.49 inference(boolean_simplification,[],[f2266])).
% 13.85/2.49 thf(f2276,plain,(
% 13.85/2.49 (sF263 = $false) | ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (~ (emptyset = (dsetconstr @ Y2 @ Y0))))))))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f2252,f1172])).
% 13.85/2.49 thf(f2281,plain,(
% 13.85/2.49 ($false = $true) | (sF263 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f2276])).
% 13.85/2.49 thf(f2282,plain,(
% 13.85/2.49 (sF263 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2281])).
% 13.85/2.49 thf(f2284,plain,(
% 13.85/2.49 (((nonemptyI1 => sF262)) = $false)),
% 13.85/2.49 inference(backward_demodulation,[],[f1587,f2282])).
% 13.85/2.49 thf(f2289,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => sF262)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2284,f1685])).
% 13.85/2.49 thf(f2290,plain,(
% 13.85/2.49 ($false = sF262)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2289])).
% 13.85/2.49 thf(f2300,plain,(
% 13.85/2.49 ($false = ((setadjoinIL => sF261)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1586,f2290])).
% 13.85/2.49 thf(f2307,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => sF261)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2300,f1018])).
% 13.85/2.49 thf(f2310,plain,(
% 13.85/2.49 ($false = sF261)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2307])).
% 13.85/2.49 thf(f2324,plain,(
% 13.85/2.49 ($false = ((emptyinunitempty => sF260)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1584,f2310])).
% 13.85/2.49 thf(f2327,plain,(
% 13.85/2.49 ($false = (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => sF260)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2324,f984])).
% 13.85/2.49 thf(f2328,plain,(
% 13.85/2.49 ($false = sF260)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2327])).
% 13.85/2.49 thf(f2340,plain,(
% 13.85/2.49 ($false = ((setadjoinIR => sF259)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1582,f2328])).
% 13.85/2.49 thf(f2343,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => sF259)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2340,f1035])).
% 13.85/2.49 thf(f2346,plain,(
% 13.85/2.49 ($false = sF259) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f2343,f1172])).
% 13.85/2.49 thf(f2350,plain,(
% 13.85/2.49 ($false = sF259) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2346])).
% 13.85/2.49 thf(f2351,plain,(
% 13.85/2.49 ($false = sF259)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2350])).
% 13.85/2.49 thf(f2358,plain,(
% 13.85/2.49 ($false = ((setadjoinE => sF258)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1580,f2351])).
% 13.85/2.49 thf(f2361,plain,(
% 13.85/2.49 (sF258 = $false)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2358])).
% 13.85/2.49 thf(f2377,plain,(
% 13.85/2.49 ($false = ((setadjoinOr => sF257)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1578,f2361])).
% 13.85/2.49 thf(f2378,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => sF257)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2377,f1023])).
% 13.85/2.49 thf(f2379,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => (setoftrueEq => sF256))))),
% 13.85/2.49 inference(forward_demodulation,[],[f2378,f1577])).
% 13.85/2.49 thf(f2380,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => sF256))))),
% 13.85/2.49 inference(forward_demodulation,[],[f2379,f931])).
% 13.85/2.49 thf(f2394,plain,(
% 13.85/2.49 (sF256 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => $true))))),
% 13.85/2.49 inference(superposition,[],[f2380,f1172])).
% 13.85/2.49 thf(f2399,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => $true))) | (sF256 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f2394])).
% 13.85/2.49 thf(f2400,plain,(
% 13.85/2.49 ($false = $true) | (sF256 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f2399])).
% 13.85/2.49 thf(f2401,plain,(
% 13.85/2.49 (sF256 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2400])).
% 13.85/2.49 thf(f2408,plain,(
% 13.85/2.49 ($false = ((powersetI => sF255)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1576,f2401])).
% 13.85/2.49 thf(f2426,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => sF255)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2408,f1004])).
% 13.85/2.49 thf(f2436,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => $true))) | ($false = sF255)),
% 13.85/2.49 inference(superposition,[],[f2426,f1172])).
% 13.85/2.49 thf(f2440,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF255)),
% 13.85/2.49 inference(boolean_simplification,[],[f2436])).
% 13.85/2.49 thf(f2441,plain,(
% 13.85/2.49 ($false = sF255)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2440])).
% 13.85/2.49 thf(f2444,plain,(
% 13.85/2.49 ($false = ((emptyinPowerset => sF254)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1575,f2441])).
% 13.85/2.49 thf(f2447,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => sF254)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2444,f904])).
% 13.85/2.49 thf(f2452,plain,(
% 13.85/2.49 (sF254 = $false)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2447])).
% 13.85/2.49 thf(f2453,plain,(
% 13.85/2.49 (((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))) = $true)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2447])).
% 13.85/2.49 thf(f2463,plain,(
% 13.85/2.49 (emptyInPowerset = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f1013,f2453])).
% 13.85/2.49 thf(f2467,plain,(
% 13.85/2.49 ($false = ((emptyInPowerset => sF253)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1574,f2452])).
% 13.85/2.49 thf(f2468,plain,(
% 13.85/2.49 ($false = (($true => sF253)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2467,f2463])).
% 13.85/2.49 thf(f2469,plain,(
% 13.85/2.49 ($false = sF253)),
% 13.85/2.49 inference(boolean_simplification,[],[f2468])).
% 13.85/2.49 thf(f2470,plain,(
% 13.85/2.49 ($false = ((powersetE => sF252)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1573,f2469])).
% 13.85/2.49 thf(f2471,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => sF252)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2470,f959])).
% 13.85/2.49 thf(f2474,plain,(
% 13.85/2.49 ($false = sF252)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2471])).
% 13.85/2.49 thf(f2484,plain,(
% 13.85/2.49 ($false = ((setunionI => sF251)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1572,f2474])).
% 13.85/2.49 thf(f2491,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1)))))))))) => sF251)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2484,f1161])).
% 13.85/2.49 thf(f2494,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1)))))))))) => (setunionE => sF250))))),
% 13.85/2.49 inference(forward_demodulation,[],[f2491,f1570])).
% 13.85/2.49 thf(f2495,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => sF250))))),
% 13.85/2.49 inference(forward_demodulation,[],[f2494,f1061])).
% 13.85/2.49 thf(f2498,plain,(
% 13.85/2.49 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => $true)) = sF230) | (sF228 = $false)),
% 13.85/2.49 inference(superposition,[],[f2016,f1172])).
% 13.85/2.49 thf(f2501,plain,(
% 13.85/2.49 (sF228 = $false) | ($true = sF230)),
% 13.85/2.49 inference(boolean_simplification,[],[f2498])).
% 13.85/2.49 thf(f2508,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => $true))) = $false) | ($false = sF250)),
% 13.85/2.49 inference(superposition,[],[f2495,f1172])).
% 13.85/2.49 thf(f2515,plain,(
% 13.85/2.49 ($false = sF250) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1)))))))))) => $true)))),
% 13.85/2.49 inference(boolean_simplification,[],[f2508])).
% 13.85/2.49 thf(f2516,plain,(
% 13.85/2.49 ($false = sF250) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2515])).
% 13.85/2.49 thf(f2517,plain,(
% 13.85/2.49 ($false = sF250)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2516])).
% 13.85/2.49 thf(f2525,plain,(
% 13.85/2.49 ($false = ((subPowSU => sF249)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1569,f2517])).
% 13.85/2.49 thf(f2540,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => sF249)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2525,f992])).
% 13.85/2.49 thf(f2548,plain,(
% 13.85/2.49 ($false = sF249) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f2540,f1172])).
% 13.85/2.49 thf(f2551,plain,(
% 13.85/2.49 ($false = sF249) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2548])).
% 13.85/2.49 thf(f2552,plain,(
% 13.85/2.49 ($false = sF249)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2551])).
% 13.85/2.49 thf(f2558,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF247)),
% 13.85/2.49 inference(backward_demodulation,[],[f2270,f2552])).
% 13.85/2.49 thf(f2561,plain,(
% 13.85/2.49 ($false = sF247)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2558])).
% 13.85/2.49 thf(f2565,plain,(
% 13.85/2.49 ($false = ((uniqinunit => sF246)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1564,f2561])).
% 13.85/2.49 thf(f2568,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => sF246)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2565,f973])).
% 13.85/2.49 thf(f2581,plain,(
% 13.85/2.49 ($false = sF246)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2568])).
% 13.85/2.49 thf(f2595,plain,(
% 13.85/2.49 ($false = ((notinsingleton => sF245)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1562,f2581])).
% 13.85/2.49 thf(f2598,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => sF245)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2595,f894])).
% 13.85/2.49 thf(f2603,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => $true))) | ($false = sF245)),
% 13.85/2.49 inference(superposition,[],[f2598,f1172])).
% 13.85/2.49 thf(f2606,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF245)),
% 13.85/2.49 inference(boolean_simplification,[],[f2603])).
% 13.85/2.49 thf(f2607,plain,(
% 13.85/2.49 ($false = sF245)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2606])).
% 13.85/2.49 thf(f2611,plain,(
% 13.85/2.49 ($false = ((eqinunit => sF244)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1560,f2607])).
% 13.85/2.49 thf(f2618,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => sF244)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2611,f1014])).
% 13.85/2.49 thf(f2621,plain,(
% 13.85/2.49 ($false = sF244)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2618])).
% 13.85/2.49 thf(f2631,plain,(
% 13.85/2.49 ($false = ((singletonsswitch => sF243)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1558,f2621])).
% 13.85/2.49 thf(f2638,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => sF243)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2631,f907])).
% 13.85/2.49 thf(f2643,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true))) | ($false = sF243)),
% 13.85/2.49 inference(superposition,[],[f2638,f1172])).
% 13.85/2.49 thf(f2646,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF243)),
% 13.85/2.49 inference(boolean_simplification,[],[f2643])).
% 13.85/2.49 thf(f2647,plain,(
% 13.85/2.49 ($false = sF243)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2646])).
% 13.85/2.49 thf(f2651,plain,(
% 13.85/2.49 ($false = ((upairsetE => sF242)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1557,f2647])).
% 13.85/2.49 thf(f2658,plain,(
% 13.85/2.49 ($false = sF242)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2651])).
% 13.85/2.49 thf(f2668,plain,(
% 13.85/2.49 ($false = ((upairsetIL => sF241)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1556,f2658])).
% 13.85/2.49 thf(f2673,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => sF241)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2668,f932])).
% 13.85/2.49 thf(f2676,plain,(
% 13.85/2.49 ($false = sF241)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2673])).
% 13.85/2.49 thf(f2688,plain,(
% 13.85/2.49 ($false = ((upairsetIR => sF240)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1555,f2676])).
% 13.85/2.49 thf(f2691,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => sF240)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2688,f923])).
% 13.85/2.49 thf(f2693,plain,(
% 13.85/2.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) = $true)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2691])).
% 13.85/2.49 thf(f2694,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true))) | ($false = sF240)),
% 13.85/2.49 inference(superposition,[],[f2691,f1172])).
% 13.85/2.49 thf(f2697,plain,(
% 13.85/2.49 ($false = sF240) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2694])).
% 13.85/2.49 thf(f2698,plain,(
% 13.85/2.49 ($false = sF240)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2697])).
% 13.85/2.49 thf(f2702,plain,(
% 13.85/2.49 ($false = ((emptyE1 => sF239)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1554,f2698])).
% 13.85/2.49 thf(f2704,plain,(
% 13.85/2.49 (upairset2IR = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f1010,f2693])).
% 13.85/2.49 thf(f2710,plain,(
% 13.85/2.49 (sF191 = (($true => sF190)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1486,f2704])).
% 13.85/2.49 thf(f2711,plain,(
% 13.85/2.49 (sF191 = sF190)),
% 13.85/2.49 inference(boolean_simplification,[],[f2710])).
% 13.85/2.49 thf(f2712,plain,(
% 13.85/2.49 (sF191 = ((binunionIR => sF189)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1485,f2711])).
% 13.85/2.49 thf(f2713,plain,(
% 13.85/2.49 (sF191 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => sF189)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2712,f975])).
% 13.85/2.49 thf(f2714,plain,(
% 13.85/2.49 (sF191 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => (binunionEcases => sF188))))),
% 13.85/2.49 inference(forward_demodulation,[],[f2713,f1484])).
% 13.85/2.49 thf(f2721,plain,(
% 13.85/2.49 ($false = sF239)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2702])).
% 13.85/2.49 thf(f2731,plain,(
% 13.85/2.49 ($false = ((vacuousDall => sF238)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1553,f2721])).
% 13.85/2.49 thf(f2736,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => sF238)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2731,f1065])).
% 13.85/2.49 thf(f2739,plain,(
% 13.85/2.49 ($false = sF238)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2736])).
% 13.85/2.49 thf(f2749,plain,(
% 13.85/2.49 ($false = ((quantDeMorgan1 => sF237)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1552,f2739])).
% 13.85/2.49 thf(f2758,plain,(
% 13.85/2.49 ($false = sF237)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2749])).
% 13.85/2.49 thf(f2772,plain,(
% 13.85/2.49 ($false = ((quantDeMorgan2 => sF236)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1551,f2758])).
% 13.85/2.49 thf(f2775,plain,(
% 13.85/2.49 ($false = ((quantDeMorgan2 => $true))) | ($false = sF236)),
% 13.85/2.49 inference(superposition,[],[f2772,f1172])).
% 13.85/2.49 thf(f2778,plain,(
% 13.85/2.49 ($false = sF236) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2775])).
% 13.85/2.49 thf(f2779,plain,(
% 13.85/2.49 ($false = sF236)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2778])).
% 13.85/2.49 thf(f2783,plain,(
% 13.85/2.49 ($false = ((quantDeMorgan3 => sF235)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1549,f2779])).
% 13.85/2.49 thf(f2790,plain,(
% 13.85/2.49 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => sF235)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2783,f1041])).
% 13.85/2.49 thf(f2793,plain,(
% 13.85/2.49 (sF191 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => (binunionEcases => $true)))) | ($false = sF188)),
% 13.85/2.49 inference(superposition,[],[f2714,f1172])).
% 13.85/2.49 thf(f2799,plain,(
% 13.85/2.49 (sF191 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => $true))) | ($false = sF188)),
% 13.85/2.49 inference(boolean_simplification,[],[f2793])).
% 13.85/2.49 thf(f2800,plain,(
% 13.85/2.49 (sF191 = $true) | ($false = sF188)),
% 13.85/2.49 inference(boolean_simplification,[],[f2799])).
% 13.85/2.49 thf(f2862,plain,(
% 13.85/2.49 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))))))))) = $true)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2790])).
% 13.85/2.49 thf(f2863,plain,(
% 13.85/2.49 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => $true))) | ($false = sF235)),
% 13.85/2.49 inference(superposition,[],[f2790,f1172])).
% 13.85/2.49 thf(f2867,plain,(
% 13.85/2.49 ($false = sF235) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2863])).
% 13.85/2.49 thf(f2868,plain,(
% 13.85/2.49 ($false = sF235)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2867])).
% 13.85/2.49 thf(f2871,plain,(
% 13.85/2.49 ($false = ((quantDeMorgan4 => sF234)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1548,f2868])).
% 13.85/2.49 thf(f2874,plain,(
% 13.85/2.49 (notdexE = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f1082,f2862])).
% 13.85/2.49 thf(f2879,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => sF234)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2871,f972])).
% 13.85/2.49 thf(f2880,plain,(
% 13.85/2.49 (sF232 = (($true => sF231)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1545,f2874])).
% 13.85/2.49 thf(f2881,plain,(
% 13.85/2.49 (sF232 = sF231)),
% 13.85/2.49 inference(boolean_simplification,[],[f2880])).
% 13.85/2.49 thf(f2882,plain,(
% 13.85/2.49 (sF233 = ((prop2set2propI => sF231)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1546,f2881])).
% 13.85/2.49 thf(f2883,plain,(
% 13.85/2.49 (sF234 = ((prop2setI => (prop2set2propI => sF231))))),
% 13.85/2.49 inference(backward_demodulation,[],[f1547,f2882])).
% 13.85/2.49 thf(f2884,plain,(
% 13.85/2.49 (sF234 = (((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => (prop2set2propI => sF231))))),
% 13.85/2.49 inference(forward_demodulation,[],[f2883,f999])).
% 13.85/2.49 thf(f2899,plain,(
% 13.85/2.49 ($false = sF231) | (sF234 = (((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => (prop2set2propI => $true))))),
% 13.85/2.49 inference(superposition,[],[f2884,f1172])).
% 13.85/2.49 thf(f2905,plain,(
% 13.85/2.49 ($false = sF231) | (sF234 = (((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => $true)))),
% 13.85/2.49 inference(boolean_simplification,[],[f2899])).
% 13.85/2.49 thf(f2906,plain,(
% 13.85/2.49 ($false = sF231) | (sF234 = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f2905])).
% 13.85/2.49 thf(f2914,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => $true))) | (sF234 = $false)),
% 13.85/2.49 inference(superposition,[],[f2879,f1172])).
% 13.85/2.49 thf(f2918,plain,(
% 13.85/2.49 ($false = $true) | (sF234 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f2914])).
% 13.85/2.49 thf(f2919,plain,(
% 13.85/2.49 (sF234 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2918])).
% 13.85/2.49 thf(f2924,plain,(
% 13.85/2.49 ($false = sF231) | ($false = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f2906,f2919])).
% 13.85/2.49 thf(f2927,plain,(
% 13.85/2.49 ($false = sF231)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2924])).
% 13.85/2.49 thf(f2933,plain,(
% 13.85/2.49 ($false = ((notdallE => sF230)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1543,f2927])).
% 13.85/2.49 thf(f2958,plain,(
% 13.85/2.49 ($false = sF230) | ($false = ((notdallE => $true)))),
% 13.85/2.49 inference(superposition,[],[f2933,f1172])).
% 13.85/2.49 thf(f2961,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF230)),
% 13.85/2.49 inference(boolean_simplification,[],[f2958])).
% 13.85/2.49 thf(f2962,plain,(
% 13.85/2.49 ($false = sF230)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2961])).
% 13.85/2.49 thf(f2969,plain,(
% 13.85/2.49 ($false = $true) | (sF228 = $false)),
% 13.85/2.49 inference(backward_demodulation,[],[f2501,f2962])).
% 13.85/2.49 thf(f2972,plain,(
% 13.85/2.49 (sF228 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f2969])).
% 13.85/2.49 thf(f2975,plain,(
% 13.85/2.49 ($false = ((exuI2 => sF227)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1539,f2972])).
% 13.85/2.49 thf(f2978,plain,(
% 13.85/2.49 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => sF227)))),
% 13.85/2.49 inference(forward_demodulation,[],[f2975,f1660])).
% 13.85/2.49 thf(f3015,plain,(
% 13.85/2.49 (sF227 = $false)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f2978])).
% 13.85/2.49 thf(f3027,plain,(
% 13.85/2.49 ($false = ((inCongP => sF226)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1538,f3015])).
% 13.85/2.49 thf(f3030,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => sF226)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3027,f885])).
% 13.85/2.49 thf(f3033,plain,(
% 13.85/2.49 ($false = sF226) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f3030,f1172])).
% 13.85/2.49 thf(f3036,plain,(
% 13.85/2.49 ($false = sF226) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3033])).
% 13.85/2.49 thf(f3037,plain,(
% 13.85/2.49 ($false = sF226)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3036])).
% 13.85/2.49 thf(f3041,plain,(
% 13.85/2.49 ($false = ((in__Cong => sF225)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1537,f3037])).
% 13.85/2.49 thf(f3052,plain,(
% 13.85/2.49 ($false = sF225) | ($false = ((in__Cong => $true)))),
% 13.85/2.49 inference(superposition,[],[f3041,f1172])).
% 13.85/2.49 thf(f3056,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF225)),
% 13.85/2.49 inference(boolean_simplification,[],[f3052])).
% 13.85/2.49 thf(f3057,plain,(
% 13.85/2.49 ($false = sF225)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3056])).
% 13.85/2.49 thf(f3060,plain,(
% 13.85/2.49 ($false = ((exuE3u => sF224)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1536,f3057])).
% 13.85/2.49 thf(f3063,plain,(
% 13.85/2.49 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => sF224)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3060,f1687])).
% 13.85/2.49 thf(f3075,plain,(
% 13.85/2.49 ($false = sF224)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3063])).
% 13.85/2.49 thf(f3076,plain,(
% 13.85/2.49 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3063])).
% 13.85/2.49 thf(f3086,plain,(
% 13.85/2.49 (exuEu = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f1658,f3076])).
% 13.85/2.49 thf(f3090,plain,(
% 13.85/2.49 ($false = ((exu__Cong => sF223)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1535,f3075])).
% 13.85/2.49 thf(f3091,plain,(
% 13.85/2.49 (sF218 = (($true => sF217)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1527,f3086])).
% 13.85/2.49 thf(f3092,plain,(
% 13.85/2.49 (sF218 = sF217)),
% 13.85/2.49 inference(boolean_simplification,[],[f3091])).
% 13.85/2.49 thf(f3093,plain,(
% 13.85/2.49 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))))))))) => sF223)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3090,f1659])).
% 13.85/2.49 thf(f3094,plain,(
% 13.85/2.49 (sF218 = ((descr__Cong => sF216)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3092,f1526])).
% 13.85/2.49 thf(f3095,plain,(
% 13.85/2.49 (sF219 = ((omega__Cong => (descr__Cong => sF216))))),
% 13.85/2.49 inference(backward_demodulation,[],[f1528,f3094])).
% 13.85/2.49 thf(f3096,plain,(
% 13.85/2.49 (sF219 = (($true => (descr__Cong => sF216))))),
% 13.85/2.49 inference(forward_demodulation,[],[f3095,f1699])).
% 13.85/2.49 thf(f3097,plain,(
% 13.85/2.49 (((descr__Cong => sF216)) = sF219)),
% 13.85/2.49 inference(boolean_simplification,[],[f3096])).
% 13.85/2.49 thf(f3116,plain,(
% 13.85/2.49 ($false = sF216) | (sF219 = ((descr__Cong => $true)))),
% 13.85/2.49 inference(superposition,[],[f3097,f1172])).
% 13.85/2.49 thf(f3119,plain,(
% 13.85/2.49 ($false = sF216) | (sF219 = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3116])).
% 13.85/2.49 thf(f3157,plain,(
% 13.85/2.49 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))))))))) => $true))) | ($false = sF223)),
% 13.85/2.49 inference(superposition,[],[f3093,f1172])).
% 13.85/2.49 thf(f3160,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF223)),
% 13.85/2.49 inference(boolean_simplification,[],[f3157])).
% 13.85/2.49 thf(f3161,plain,(
% 13.85/2.49 ($false = sF223)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3160])).
% 13.85/2.49 thf(f3167,plain,(
% 13.85/2.49 ($false = ((emptyset__Cong => sF222)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1533,f3161])).
% 13.85/2.49 thf(f3170,plain,(
% 13.85/2.49 ((($true => sF222)) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f3167,f1694])).
% 13.85/2.49 thf(f3171,plain,(
% 13.85/2.49 ($false = sF222)),
% 13.85/2.49 inference(boolean_simplification,[],[f3170])).
% 13.85/2.49 thf(f3172,plain,(
% 13.85/2.49 ($false = ((setadjoin__Cong => sF221)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1531,f3171])).
% 13.85/2.49 thf(f3173,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2)))))))))))) => sF221)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3172,f953])).
% 13.85/2.49 thf(f3176,plain,(
% 13.85/2.49 ($false = sF221)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3173])).
% 13.85/2.49 thf(f3186,plain,(
% 13.85/2.49 ($false = ((powerset__Cong => sF220)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1530,f3176])).
% 13.85/2.49 thf(f3191,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => sF220)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3186,f1112])).
% 13.85/2.49 thf(f3196,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => (setunion__Cong => sF219))))),
% 13.85/2.49 inference(forward_demodulation,[],[f3191,f1529])).
% 13.85/2.49 thf(f3199,plain,(
% 13.85/2.49 ($false = sF219) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => (setunion__Cong => $true))))),
% 13.85/2.49 inference(superposition,[],[f3196,f1172])).
% 13.85/2.49 thf(f3208,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => $true))) | ($false = sF219)),
% 13.85/2.49 inference(boolean_simplification,[],[f3199])).
% 13.85/2.49 thf(f3209,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF219)),
% 13.85/2.49 inference(boolean_simplification,[],[f3208])).
% 13.85/2.49 thf(f3210,plain,(
% 13.85/2.49 ($false = sF219)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3209])).
% 13.85/2.49 thf(f3218,plain,(
% 13.85/2.49 ($false = sF216) | ($false = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f3119,f3210])).
% 13.85/2.49 thf(f3224,plain,(
% 13.85/2.49 ($false = sF216)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3218])).
% 13.85/2.49 thf(f3233,plain,(
% 13.85/2.49 ($false = ((dsetconstr__Cong => sF215)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1524,f3224])).
% 13.85/2.49 thf(f3237,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => sF215)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3233,f1634])).
% 13.85/2.49 thf(f3256,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => $true))) | ($false = sF215)),
% 13.85/2.49 inference(superposition,[],[f3237,f1172])).
% 13.85/2.49 thf(f3259,plain,(
% 13.85/2.49 ($false = sF215) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3256])).
% 13.85/2.49 thf(f3260,plain,(
% 13.85/2.49 ($false = sF215)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3259])).
% 13.85/2.49 thf(f3264,plain,(
% 13.85/2.49 ($false = ((subsetI1 => sF214)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1522,f3260])).
% 13.85/2.49 thf(f3269,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => sF214)) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f3264,f940])).
% 13.85/2.49 thf(f3276,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => $true)) = $false) | (sF214 = $false)),
% 13.85/2.49 inference(superposition,[],[f3269,f1172])).
% 13.85/2.49 thf(f3279,plain,(
% 13.85/2.49 ($false = $true) | (sF214 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f3276])).
% 13.85/2.49 thf(f3280,plain,(
% 13.85/2.49 (sF214 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3279])).
% 13.85/2.49 thf(f3284,plain,(
% 13.85/2.49 ($false = ((eqimpsubset2 => sF213)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1521,f3280])).
% 13.85/2.49 thf(f3291,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => sF213)) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f3284,f1121])).
% 13.85/2.49 thf(f3294,plain,(
% 13.85/2.49 (((eqimpsubset1 => sF213)) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f3291,f933])).
% 13.85/2.49 thf(f3296,plain,(
% 13.85/2.49 (eqimpsubset1 = $true)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3294])).
% 13.85/2.49 thf(f3297,plain,(
% 13.85/2.49 ($false = ((eqimpsubset1 => $true))) | ($false = sF213)),
% 13.85/2.49 inference(superposition,[],[f3294,f1172])).
% 13.85/2.49 thf(f3300,plain,(
% 13.85/2.49 ($false = sF213) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3297])).
% 13.85/2.49 thf(f3301,plain,(
% 13.85/2.49 ($false = sF213)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3300])).
% 13.85/2.49 thf(f3305,plain,(
% 13.85/2.49 ($false = ((eqimpsubset1 => sF212)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1520,f3301])).
% 13.85/2.49 thf(f3310,plain,(
% 13.85/2.49 ($false = (($true => sF212)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3305,f3296])).
% 13.85/2.49 thf(f3311,plain,(
% 13.85/2.49 ($false = sF212)),
% 13.85/2.49 inference(boolean_simplification,[],[f3310])).
% 13.85/2.49 thf(f3317,plain,(
% 13.85/2.49 ($false = ((subsetI2 => sF211)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1518,f3311])).
% 13.85/2.49 thf(f3318,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => sF211)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3317,f889])).
% 13.85/2.49 thf(f3332,plain,(
% 13.85/2.49 ($false = sF211) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f3318,f1172])).
% 13.85/2.49 thf(f3337,plain,(
% 13.85/2.49 ($false = sF211) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3332])).
% 13.85/2.49 thf(f3338,plain,(
% 13.85/2.49 ($false = sF211)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3337])).
% 13.85/2.49 thf(f3346,plain,(
% 13.85/2.49 ($false = ((emptysetsubset => sF210)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1517,f3338])).
% 13.85/2.49 thf(f3347,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (subset @ emptyset)) => sF210)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3346,f1682])).
% 13.85/2.49 thf(f3350,plain,(
% 13.85/2.49 (sF210 = $false) | ($false = (((!! @ $i @ (subset @ emptyset)) => $true)))),
% 13.85/2.49 inference(superposition,[],[f3347,f1172])).
% 13.85/2.49 thf(f3354,plain,(
% 13.85/2.49 ($false = $true) | (sF210 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f3350])).
% 13.85/2.49 thf(f3355,plain,(
% 13.85/2.49 (sF210 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3354])).
% 13.85/2.49 thf(f3358,plain,(
% 13.85/2.49 ($false = ((subsetE => sF209)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1515,f3355])).
% 13.85/2.49 thf(f3363,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => sF209)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3358,f1055])).
% 13.85/2.49 thf(f3368,plain,(
% 13.85/2.49 ($false = sF209)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3363])).
% 13.85/2.49 thf(f3378,plain,(
% 13.85/2.49 (((subsetE2 => sF208)) = $false)),
% 13.85/2.49 inference(backward_demodulation,[],[f1514,f3368])).
% 13.85/2.49 thf(f3387,plain,(
% 13.85/2.49 (((subsetE2 => $true)) = $false) | ($false = sF208)),
% 13.85/2.49 inference(superposition,[],[f3378,f1172])).
% 13.85/2.49 thf(f3391,plain,(
% 13.85/2.49 ($false = sF208) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3387])).
% 13.85/2.49 thf(f3392,plain,(
% 13.85/2.49 ($false = sF208)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3391])).
% 13.85/2.49 thf(f3397,plain,(
% 13.85/2.49 ($false = ((notsubsetI => sF207)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1512,f3392])).
% 13.85/2.49 thf(f3398,plain,(
% 13.85/2.49 (((notsubsetI => (notequalI1 => sF206))) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f3397,f1511])).
% 13.85/2.49 thf(f3399,plain,(
% 13.85/2.49 ($false = ((notsubsetI => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => sF206))))),
% 13.85/2.49 inference(forward_demodulation,[],[f3398,f1007])).
% 13.85/2.49 thf(f3402,plain,(
% 13.85/2.49 ($false = ((notsubsetI => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => $true)))) | ($false = sF206)),
% 13.85/2.49 inference(superposition,[],[f3399,f1172])).
% 13.85/2.49 thf(f3412,plain,(
% 13.85/2.49 ($false = sF206) | ($false = ((notsubsetI => $true)))),
% 13.85/2.49 inference(boolean_simplification,[],[f3402])).
% 13.85/2.49 thf(f3413,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF206)),
% 13.85/2.49 inference(boolean_simplification,[],[f3412])).
% 13.85/2.49 thf(f3414,plain,(
% 13.85/2.49 ($false = sF206)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3413])).
% 13.85/2.49 thf(f3423,plain,(
% 13.85/2.49 ($false = ((notequalI2 => sF205)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1509,f3414])).
% 13.85/2.49 thf(f3431,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (~ (Y2 = Y0)))))))))) => sF205)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3423,f969])).
% 13.85/2.49 thf(f3484,plain,(
% 13.85/2.49 ($false = sF205)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3431])).
% 13.85/2.49 thf(f3494,plain,(
% 13.85/2.49 ($false = ((subsetRefl => sF204)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1508,f3484])).
% 13.85/2.49 thf(f3497,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => sF204)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3494,f1046])).
% 13.85/2.49 thf(f3502,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => $true))) | (sF204 = $false)),
% 13.85/2.49 inference(superposition,[],[f3497,f1172])).
% 13.85/2.49 thf(f3507,plain,(
% 13.85/2.49 ($false = $true) | (sF204 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f3502])).
% 13.85/2.49 thf(f3508,plain,(
% 13.85/2.49 (sF204 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3507])).
% 13.85/2.49 thf(f3514,plain,(
% 13.85/2.49 ($false = ((subsetTrans => sF203)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1506,f3508])).
% 13.85/2.49 thf(f3515,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y1 @ Y0) => (subset @ Y2 @ Y0))))))))) => sF203)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3514,f977])).
% 13.85/2.49 thf(f3516,plain,(
% 13.85/2.49 ($false = sF203)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3515])).
% 13.85/2.49 thf(f3526,plain,(
% 13.85/2.49 (((setadjoinSub => sF202)) = $false)),
% 13.85/2.49 inference(backward_demodulation,[],[f1505,f3516])).
% 13.85/2.49 thf(f3529,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => sF202)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3526,f962])).
% 13.85/2.49 thf(f3534,plain,(
% 13.85/2.49 ($false = sF202) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f3529,f1172])).
% 13.85/2.49 thf(f3537,plain,(
% 13.85/2.49 ($false = sF202) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3534])).
% 13.85/2.49 thf(f3538,plain,(
% 13.85/2.49 ($false = sF202)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3537])).
% 13.85/2.49 thf(f3542,plain,(
% 13.85/2.49 ($false = ((setadjoinSub2 => sF201)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1503,f3538])).
% 13.85/2.49 thf(f3547,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => sF201)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3542,f883])).
% 13.85/2.49 thf(f3552,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => $true))) | ($false = sF201)),
% 13.85/2.49 inference(superposition,[],[f3547,f1172])).
% 13.85/2.49 thf(f3555,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF201)),
% 13.85/2.49 inference(boolean_simplification,[],[f3552])).
% 13.85/2.49 thf(f3556,plain,(
% 13.85/2.49 ($false = sF201)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3555])).
% 13.85/2.49 thf(f3560,plain,(
% 13.85/2.49 ($false = ((subset2powerset => sF200)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1501,f3556])).
% 13.85/2.49 thf(f3565,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => sF200)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3560,f1040])).
% 13.85/2.49 thf(f3570,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => (setextsub => sF199))))),
% 13.85/2.49 inference(forward_demodulation,[],[f3565,f1499])).
% 13.85/2.49 thf(f3571,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => sF199))))),
% 13.85/2.49 inference(forward_demodulation,[],[f3570,f994])).
% 13.85/2.49 thf(f3573,plain,(
% 13.85/2.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))) = $true)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3571])).
% 13.85/2.49 thf(f3574,plain,(
% 13.85/2.49 ($false = sF199) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => $true))))),
% 13.85/2.49 inference(superposition,[],[f3571,f1172])).
% 13.85/2.49 thf(f3579,plain,(
% 13.85/2.49 ($false = sF199) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => $true)))),
% 13.85/2.49 inference(boolean_simplification,[],[f3574])).
% 13.85/2.49 thf(f3580,plain,(
% 13.85/2.49 ($false = sF199) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3579])).
% 13.85/2.49 thf(f3581,plain,(
% 13.85/2.49 ($false = sF199)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3580])).
% 13.85/2.49 thf(f3589,plain,(
% 13.85/2.49 ($false = ((subsetemptysetimpeq => sF198)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1497,f3581])).
% 13.85/2.49 thf(f3603,plain,(
% 13.85/2.49 (powersetI1 = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f935,f3573])).
% 13.85/2.49 thf(f3605,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => sF198)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3589,f944])).
% 13.85/2.49 thf(f3612,plain,(
% 13.85/2.49 (sF198 = (($true => sF197)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1496,f3603])).
% 13.85/2.49 thf(f3613,plain,(
% 13.85/2.49 (sF197 = sF198)),
% 13.85/2.49 inference(boolean_simplification,[],[f3612])).
% 13.85/2.49 thf(f3615,plain,(
% 13.85/2.49 (sF198 = ((powersetE1 => sF196)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1494,f3613])).
% 13.85/2.49 thf(f3616,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => sF196)) = sF198)),
% 13.85/2.49 inference(forward_demodulation,[],[f3615,f1125])).
% 13.85/2.49 thf(f3627,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => $true))) | ($false = sF198)),
% 13.85/2.49 inference(superposition,[],[f3605,f1172])).
% 13.85/2.49 thf(f3630,plain,(
% 13.85/2.49 ($false = sF198) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3627])).
% 13.85/2.49 thf(f3631,plain,(
% 13.85/2.49 ($false = sF198)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3630])).
% 13.85/2.49 thf(f3634,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => sF196)))),
% 13.85/2.49 inference(backward_demodulation,[],[f3616,f3631])).
% 13.85/2.49 thf(f3645,plain,(
% 13.85/2.49 (sF196 = $false)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3634])).
% 13.85/2.49 thf(f3655,plain,(
% 13.85/2.49 ($false = ((inPowerset => sF195)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1493,f3645])).
% 13.85/2.49 thf(f3660,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => sF195)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3655,f1081])).
% 13.85/2.49 thf(f3661,plain,(
% 13.85/2.49 ($false = sF195)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3660])).
% 13.85/2.49 thf(f3671,plain,(
% 13.85/2.49 (((powersetsubset => sF194)) = $false)),
% 13.85/2.49 inference(backward_demodulation,[],[f1492,f3661])).
% 13.85/2.49 thf(f3676,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => sF194)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3671,f1027])).
% 13.85/2.49 thf(f3679,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => $true))) | ($false = sF194)),
% 13.85/2.49 inference(superposition,[],[f3676,f1172])).
% 13.85/2.49 thf(f3683,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF194)),
% 13.85/2.49 inference(boolean_simplification,[],[f3679])).
% 13.85/2.49 thf(f3684,plain,(
% 13.85/2.49 ($false = sF194)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3683])).
% 13.85/2.49 thf(f3687,plain,(
% 13.85/2.49 ($false = ((sepInPowerset => sF193)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1490,f3684])).
% 13.85/2.49 thf(f3692,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => sF193)) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f3687,f1646])).
% 13.85/2.49 thf(f3693,plain,(
% 13.85/2.49 ($false = sF193)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3692])).
% 13.85/2.49 thf(f3703,plain,(
% 13.85/2.49 ($false = ((sepSubset => sF192)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1489,f3693])).
% 13.85/2.49 thf(f3708,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => sF192)) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f3703,f1672])).
% 13.85/2.49 thf(f3711,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => (binunionIL => sF191))))),
% 13.85/2.49 inference(forward_demodulation,[],[f3708,f1487])).
% 13.85/2.49 thf(f3736,plain,(
% 13.85/2.49 (sF191 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => (binunionIL => $true))))),
% 13.85/2.49 inference(superposition,[],[f3711,f1172])).
% 13.85/2.49 thf(f3746,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => $true))) | (sF191 = $false)),
% 13.85/2.49 inference(boolean_simplification,[],[f3736])).
% 13.85/2.49 thf(f3747,plain,(
% 13.85/2.49 (sF191 = $false) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3746])).
% 13.85/2.49 thf(f3748,plain,(
% 13.85/2.49 (sF191 = $false)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3747])).
% 13.85/2.49 thf(f3758,plain,(
% 13.85/2.49 ($false = sF188) | ($false = $true)),
% 13.85/2.49 inference(backward_demodulation,[],[f2800,f3748])).
% 13.85/2.49 thf(f3762,plain,(
% 13.85/2.49 ($false = sF188)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3758])).
% 13.85/2.49 thf(f3767,plain,(
% 13.85/2.49 ($false = ((binunionE => sF187)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1483,f3762])).
% 13.85/2.49 thf(f3787,plain,(
% 13.85/2.49 ($false = sF187)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3767])).
% 13.85/2.49 thf(f3797,plain,(
% 13.85/2.49 ($false = ((binunionLsub => sF186)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1482,f3787])).
% 13.85/2.49 thf(f3802,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => sF186)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3797,f1066])).
% 13.85/2.49 thf(f3809,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => $true))) | ($false = sF186)),
% 13.85/2.49 inference(superposition,[],[f3802,f1172])).
% 13.85/2.49 thf(f3814,plain,(
% 13.85/2.49 ($false = sF186) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3809])).
% 13.85/2.49 thf(f3815,plain,(
% 13.85/2.49 ($false = sF186)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3814])).
% 13.85/2.49 thf(f3823,plain,(
% 13.85/2.49 ($false = ((binunionRsub => sF185)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1481,f3815])).
% 13.85/2.49 thf(f3824,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => sF185)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3823,f1075])).
% 13.85/2.49 thf(f3825,plain,(
% 13.85/2.49 ($false = sF185)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f3824])).
% 13.85/2.49 thf(f3835,plain,(
% 13.85/2.49 ($false = ((binintersectI => sF184)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1480,f3825])).
% 13.85/2.49 thf(f3840,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1)))))))))) => sF184)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3835,f949])).
% 13.85/2.49 thf(f3889,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1)))))))))) => $true)) = $false) | ($false = sF184)),
% 13.85/2.49 inference(superposition,[],[f3840,f1172])).
% 13.85/2.49 thf(f3892,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF184)),
% 13.85/2.49 inference(boolean_simplification,[],[f3889])).
% 13.85/2.49 thf(f3893,plain,(
% 13.85/2.49 ($false = sF184)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3892])).
% 13.85/2.49 thf(f3897,plain,(
% 13.85/2.49 ($false = ((binintersectSubset5 => sF183)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1479,f3893])).
% 13.85/2.49 thf(f3904,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => sF183)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3897,f1069])).
% 13.85/2.49 thf(f3907,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => (binintersectEL => sF182))))),
% 13.85/2.49 inference(forward_demodulation,[],[f3904,f1478])).
% 13.85/2.49 thf(f3908,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => (binintersectEL => (binintersectLsub => sF181)))))),
% 13.85/2.49 inference(forward_demodulation,[],[f3907,f1477])).
% 13.85/2.49 thf(f3909,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => (binintersectEL => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => sF181)))) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f3908,f1155])).
% 13.85/2.49 thf(f3912,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => (binintersectEL => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => $true)))) = $false) | ($false = sF181)),
% 13.85/2.49 inference(superposition,[],[f3909,f1172])).
% 13.85/2.49 thf(f3927,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => (binintersectEL => $true)))) | ($false = sF181)),
% 13.85/2.49 inference(boolean_simplification,[],[f3912])).
% 13.85/2.49 thf(f3928,plain,(
% 13.85/2.49 ($false = sF181) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => $true)))),
% 13.85/2.49 inference(boolean_simplification,[],[f3927])).
% 13.85/2.49 thf(f3929,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF181)),
% 13.85/2.49 inference(boolean_simplification,[],[f3928])).
% 13.85/2.49 thf(f3930,plain,(
% 13.85/2.49 ($false = sF181)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3929])).
% 13.85/2.49 thf(f3946,plain,(
% 13.85/2.49 (((binintersectSubset2 => sF180)) = $false)),
% 13.85/2.49 inference(backward_demodulation,[],[f1475,f3930])).
% 13.85/2.49 thf(f3960,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => sF180)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3946,f970])).
% 13.85/2.49 thf(f3978,plain,(
% 13.85/2.49 ($false = sF180) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f3960,f1172])).
% 13.85/2.49 thf(f3981,plain,(
% 13.85/2.49 ($false = sF180) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f3978])).
% 13.85/2.49 thf(f3982,plain,(
% 13.85/2.49 ($false = sF180)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3981])).
% 13.85/2.49 thf(f3988,plain,(
% 13.85/2.49 ($false = ((binintersectSubset3 => sF179)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1473,f3982])).
% 13.85/2.49 thf(f3991,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => sF179)))),
% 13.85/2.49 inference(forward_demodulation,[],[f3988,f1101])).
% 13.85/2.49 thf(f3994,plain,(
% 13.85/2.49 ($false = sF179) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => $true)))),
% 13.85/2.49 inference(superposition,[],[f3991,f1172])).
% 13.85/2.49 thf(f3998,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF179)),
% 13.85/2.49 inference(boolean_simplification,[],[f3994])).
% 13.85/2.49 thf(f3999,plain,(
% 13.85/2.49 ($false = sF179)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f3998])).
% 13.85/2.49 thf(f4002,plain,(
% 13.85/2.49 ($false = ((binintersectER => sF178)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1471,f3999])).
% 13.85/2.49 thf(f4009,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => sF178)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4002,f1122])).
% 13.85/2.49 thf(f4012,plain,(
% 13.85/2.49 ($false = sF178)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f4009])).
% 13.85/2.49 thf(f4022,plain,(
% 13.85/2.49 ($false = ((disjointsetsI1 => sF177)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1469,f4012])).
% 13.85/2.49 thf(f4027,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => sF177)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4022,f886])).
% 13.85/2.49 thf(f4028,plain,(
% 13.85/2.49 ($false = sF177)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f4027])).
% 13.85/2.49 thf(f4038,plain,(
% 13.85/2.49 ($false = ((binintersectRsub => sF176)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1468,f4028])).
% 13.85/2.49 thf(f4043,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y0))))) => sF176)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4038,f1120])).
% 13.85/2.49 thf(f4046,plain,(
% 13.85/2.49 ($false = sF176)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f4043])).
% 13.85/2.49 thf(f4058,plain,(
% 13.85/2.49 ($false = ((binintersectSubset4 => sF175)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1466,f4046])).
% 13.85/2.49 thf(f4059,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => sF175)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4058,f909])).
% 13.85/2.49 thf(f4060,plain,(
% 13.85/2.49 (sF175 = $false)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f4059])).
% 13.85/2.49 thf(f4070,plain,(
% 13.85/2.49 ($false = ((binintersectSubset1 => sF174)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1464,f4060])).
% 13.85/2.49 thf(f4077,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => sF174)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4070,f950])).
% 13.85/2.49 thf(f4080,plain,(
% 13.85/2.49 ($false = sF174)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f4077])).
% 13.85/2.49 thf(f4094,plain,(
% 13.85/2.49 ($false = ((bs114d => sF173)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1463,f4080])).
% 13.85/2.49 thf(f4097,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y0 @ Y1)) = (binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1))))))))) => sF173)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4094,f910])).
% 13.85/2.49 thf(f4098,plain,(
% 13.85/2.49 ($false = sF173)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f4097])).
% 13.85/2.49 thf(f4114,plain,(
% 13.85/2.49 ($false = ((setminusI => sF172)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1461,f4098])).
% 13.85/2.49 thf(f4115,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => sF172)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4114,f1057])).
% 13.85/2.49 thf(f4116,plain,(
% 13.85/2.49 ($false = sF172)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f4115])).
% 13.85/2.49 thf(f4128,plain,(
% 13.85/2.49 ($false = ((setminusEL => sF171)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1460,f4116])).
% 13.85/2.49 thf(f4131,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => sF171)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4128,f1157])).
% 13.85/2.49 thf(f4132,plain,(
% 13.85/2.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => (setminusER => sF170))) = $false)),
% 13.85/2.49 inference(forward_demodulation,[],[f4131,f1458])).
% 13.85/2.49 thf(f4133,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => sF170))))),
% 13.85/2.49 inference(forward_demodulation,[],[f4132,f908])).
% 13.85/2.49 thf(f4136,plain,(
% 13.85/2.49 ($false = sF170) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => $true))))),
% 13.85/2.49 inference(superposition,[],[f4133,f1172])).
% 13.85/2.49 thf(f4142,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => $true))) | ($false = sF170)),
% 13.85/2.49 inference(boolean_simplification,[],[f4136])).
% 13.85/2.49 thf(f4143,plain,(
% 13.85/2.49 ($false = sF170) | ($false = $true)),
% 13.85/2.49 inference(boolean_simplification,[],[f4142])).
% 13.85/2.49 thf(f4144,plain,(
% 13.85/2.49 ($false = sF170)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f4143])).
% 13.85/2.49 thf(f4151,plain,(
% 13.85/2.49 (((setminusSubset2 => sF169)) = $false)),
% 13.85/2.49 inference(backward_demodulation,[],[f1456,f4144])).
% 13.85/2.49 thf(f4179,plain,(
% 13.85/2.49 ($false = sF169) | ($false = ((setminusSubset2 => $true)))),
% 13.85/2.49 inference(superposition,[],[f4151,f1172])).
% 13.85/2.49 thf(f4183,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF169)),
% 13.85/2.49 inference(boolean_simplification,[],[f4179])).
% 13.85/2.49 thf(f4184,plain,(
% 13.85/2.49 ($false = sF169)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f4183])).
% 13.85/2.49 thf(f4191,plain,(
% 13.85/2.49 ($false = ((setminusERneg => sF168)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1454,f4184])).
% 13.85/2.49 thf(f4192,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => sF168)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4191,f1030])).
% 13.85/2.49 thf(f4202,plain,(
% 13.85/2.49 ($false = sF168)),
% 13.85/2.49 inference(imp_proxy_clausification,[],[f4192])).
% 13.85/2.49 thf(f4212,plain,(
% 13.85/2.49 ($false = ((setminusELneg => sF167)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1452,f4202])).
% 13.85/2.49 thf(f4217,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => sF167)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4212,f1044])).
% 13.85/2.49 thf(f4222,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => $true))) | ($false = sF167)),
% 13.85/2.49 inference(superposition,[],[f4217,f1172])).
% 13.85/2.49 thf(f4225,plain,(
% 13.85/2.49 ($false = $true) | ($false = sF167)),
% 13.85/2.49 inference(boolean_simplification,[],[f4222])).
% 13.85/2.49 thf(f4226,plain,(
% 13.85/2.49 ($false = sF167)),
% 13.85/2.49 inference(trivial_inequality_removal,[],[f4225])).
% 13.85/2.49 thf(f4230,plain,(
% 13.85/2.49 ($false = ((setminusILneg => sF166)))),
% 13.85/2.49 inference(backward_demodulation,[],[f1451,f4226])).
% 13.85/2.49 thf(f4235,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => sF166)))),
% 13.85/2.49 inference(forward_demodulation,[],[f4230,f925])).
% 13.85/2.49 thf(f4240,plain,(
% 13.85/2.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => (setminusIRneg => sF165))))),
% 13.85/2.49 inference(forward_demodulation,[],[f4235,f1450])).
% 13.85/2.49 thf(f4245,plain,(
% 13.85/2.49 ($false = sF165) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => (setminusIRneg => $true))))),
% 13.85/2.49 inference(superposition,[],[f4240,f1172])).
% 13.85/2.49 thf(f4251,plain,(
% 13.85/2.49 ($false = sF165) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => $true)))),
% 13.85/2.50 inference(boolean_simplification,[],[f4245])).
% 13.85/2.50 thf(f4252,plain,(
% 13.85/2.50 ($false = sF165) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f4251])).
% 13.85/2.50 thf(f4253,plain,(
% 13.85/2.50 ($false = sF165)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4252])).
% 13.85/2.50 thf(f4262,plain,(
% 13.85/2.50 ($false = ((setminusLsub => sF164)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1449,f4253])).
% 13.85/2.50 thf(f4273,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => sF164)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4262,f900])).
% 13.85/2.50 thf(f4282,plain,(
% 13.85/2.50 ($false = sF164) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => $true)))),
% 13.85/2.50 inference(superposition,[],[f4273,f1172])).
% 13.85/2.50 thf(f4287,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF164)),
% 13.85/2.50 inference(boolean_simplification,[],[f4282])).
% 13.85/2.50 thf(f4288,plain,(
% 13.85/2.50 ($false = sF164)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4287])).
% 13.85/2.50 thf(f4290,plain,(
% 13.85/2.50 ($false = ((setminusSubset1 => sF163)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1447,f4288])).
% 13.85/2.50 thf(f4293,plain,(
% 13.85/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => sF163)) = $false)),
% 13.85/2.50 inference(forward_demodulation,[],[f4290,f905])).
% 13.85/2.50 thf(f4298,plain,(
% 13.85/2.50 ($false = sF163) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => $true)))),
% 13.85/2.50 inference(superposition,[],[f4293,f1172])).
% 13.85/2.50 thf(f4301,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF163)),
% 13.85/2.50 inference(boolean_simplification,[],[f4298])).
% 13.85/2.50 thf(f4302,plain,(
% 13.85/2.50 ($false = sF163)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4301])).
% 13.85/2.50 thf(f4306,plain,(
% 13.85/2.50 ($false = ((symdiffE => sF162)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1446,f4302])).
% 13.85/2.50 thf(f4315,plain,(
% 13.85/2.50 ($false = sF162) | ($false = ((symdiffE => $true)))),
% 13.85/2.50 inference(superposition,[],[f4306,f1172])).
% 13.85/2.50 thf(f4318,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF162)),
% 13.85/2.50 inference(boolean_simplification,[],[f4315])).
% 13.85/2.50 thf(f4319,plain,(
% 13.85/2.50 ($false = sF162)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4318])).
% 13.85/2.50 thf(f4323,plain,(
% 13.85/2.50 ($false = ((symdiffI1 => sF161)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1444,f4319])).
% 13.85/2.50 thf(f4334,plain,(
% 13.85/2.50 ($false = sF161)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4323])).
% 13.85/2.50 thf(f4344,plain,(
% 13.85/2.50 ($false = ((symdiffI2 => sF160)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1442,f4334])).
% 13.85/2.50 thf(f4349,plain,(
% 13.85/2.50 ($false = ((symdiffI2 => (symdiffIneg1 => sF159))))),
% 13.85/2.50 inference(forward_demodulation,[],[f4344,f1441])).
% 13.85/2.50 thf(f4354,plain,(
% 13.85/2.50 ($false = sF159) | ($false = ((symdiffI2 => (symdiffIneg1 => $true))))),
% 13.85/2.50 inference(superposition,[],[f4349,f1172])).
% 13.85/2.50 thf(f4362,plain,(
% 13.85/2.50 ($false = ((symdiffI2 => $true))) | ($false = sF159)),
% 13.85/2.50 inference(boolean_simplification,[],[f4354])).
% 13.85/2.50 thf(f4363,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF159)),
% 13.85/2.50 inference(boolean_simplification,[],[f4362])).
% 13.85/2.50 thf(f4364,plain,(
% 13.85/2.50 ($false = sF159)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4363])).
% 13.85/2.50 thf(f4374,plain,(
% 13.85/2.50 ($false = ((symdiffIneg2 => sF158)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1439,f4364])).
% 13.85/2.50 thf(f4386,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => sF158)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4374,f1170])).
% 13.85/2.50 thf(f4445,plain,(
% 13.85/2.50 (sF158 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => $true)))),
% 13.85/2.50 inference(superposition,[],[f4386,f1172])).
% 13.85/2.50 thf(f4448,plain,(
% 13.85/2.50 (sF158 = $false) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f4445])).
% 13.85/2.50 thf(f4449,plain,(
% 13.85/2.50 (sF158 = $false)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4448])).
% 13.85/2.50 thf(f4453,plain,(
% 13.85/2.50 (((secondinupair => sF157)) = $false)),
% 13.85/2.50 inference(backward_demodulation,[],[f1438,f4449])).
% 13.85/2.50 thf(f4458,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => sF157)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4453,f1151])).
% 13.85/2.50 thf(f4463,plain,(
% 13.85/2.50 ($false = sF157) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))),
% 13.85/2.50 inference(superposition,[],[f4458,f1172])).
% 13.85/2.50 thf(f4466,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF157)),
% 13.85/2.50 inference(boolean_simplification,[],[f4463])).
% 13.85/2.50 thf(f4467,plain,(
% 13.85/2.50 ($false = sF157)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4466])).
% 13.85/2.50 thf(f4473,plain,(
% 13.85/2.50 ($false = ((setukpairIL => sF156)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1437,f4467])).
% 13.85/2.50 thf(f4476,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => sF156)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4473,f1136])).
% 13.85/2.50 thf(f4477,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => (setukpairIR => sF155))))),
% 13.85/2.50 inference(forward_demodulation,[],[f4476,f1436])).
% 13.85/2.50 thf(f4480,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => (setukpairIR => $true)))) | ($false = sF155)),
% 13.85/2.50 inference(superposition,[],[f4477,f1172])).
% 13.85/2.50 thf(f4490,plain,(
% 13.85/2.50 ($false = sF155) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => $true)) = $false)),
% 13.85/2.50 inference(boolean_simplification,[],[f4480])).
% 13.85/2.50 thf(f4491,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF155)),
% 13.85/2.50 inference(boolean_simplification,[],[f4490])).
% 13.85/2.50 thf(f4492,plain,(
% 13.85/2.50 ($false = sF155)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4491])).
% 13.85/2.50 thf(f4502,plain,(
% 13.85/2.50 ($false = ((kpairiskpair => sF154)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1434,f4492])).
% 13.85/2.50 thf(f4512,plain,(
% 13.85/2.50 ($false = ((kpairiskpair => $true))) | ($false = sF154)),
% 13.85/2.50 inference(superposition,[],[f4502,f1172])).
% 13.85/2.50 thf(f4515,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF154)),
% 13.85/2.50 inference(boolean_simplification,[],[f4512])).
% 13.85/2.50 thf(f4516,plain,(
% 13.85/2.50 ($false = sF154)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4515])).
% 13.85/2.50 thf(f4520,plain,(
% 13.85/2.50 ($false = ((kpairp => sF153)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1433,f4516])).
% 13.85/2.50 thf(f4527,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => sF153)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4520,f1128])).
% 13.85/2.50 thf(f4528,plain,(
% 13.85/2.50 ($false = sF153)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4527])).
% 13.85/2.50 thf(f4538,plain,(
% 13.85/2.50 ($false = ((singletonsubset => sF152)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1432,f4528])).
% 13.85/2.50 thf(f4543,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => sF152)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4538,f1100])).
% 13.85/2.50 thf(f4548,plain,(
% 13.85/2.50 ($false = sF152)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4543])).
% 13.85/2.50 thf(f4558,plain,(
% 13.85/2.50 ($false = ((singletoninpowerset => sF151)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1431,f4548])).
% 13.85/2.50 thf(f4567,plain,(
% 13.85/2.50 ($false = sF151)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4558])).
% 13.85/2.50 thf(f4577,plain,(
% 13.85/2.50 ($false = ((singletoninpowunion => sF150)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1430,f4567])).
% 13.85/2.50 thf(f4580,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y1 @ Y2)))))))))) => sF150)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4577,f958])).
% 13.85/2.50 thf(f4604,plain,(
% 13.85/2.50 ($false = sF150)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4580])).
% 13.85/2.50 thf(f4614,plain,(
% 13.85/2.50 ($false = ((upairset2E => sF149)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1428,f4604])).
% 13.85/2.50 thf(f4621,plain,(
% 13.85/2.50 ($false = sF149)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4614])).
% 13.85/2.50 thf(f4631,plain,(
% 13.85/2.50 ($false = ((upairsubunion => sF148)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1427,f4621])).
% 13.85/2.50 thf(f4636,plain,(
% 13.85/2.50 ($false = sF148)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4631])).
% 13.85/2.50 thf(f4646,plain,(
% 13.85/2.50 ($false = ((upairinpowunion => sF147)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1425,f4636])).
% 13.85/2.50 thf(f4651,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => sF147)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4646,f916])).
% 13.85/2.50 thf(f4686,plain,(
% 13.85/2.50 ($false = sF147)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4651])).
% 13.85/2.50 thf(f4696,plain,(
% 13.85/2.50 ($false = ((ubforcartprodlem1 => sF146)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1423,f4686])).
% 13.85/2.50 thf(f4707,plain,(
% 13.85/2.50 ($false = sF146) | ($false = ((ubforcartprodlem1 => $true)))),
% 13.85/2.50 inference(superposition,[],[f4696,f1172])).
% 13.85/2.50 thf(f4710,plain,(
% 13.85/2.50 ($false = sF146) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f4707])).
% 13.85/2.50 thf(f4711,plain,(
% 13.85/2.50 ($false = sF146)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4710])).
% 13.85/2.50 thf(f4715,plain,(
% 13.85/2.50 ($false = ((ubforcartprodlem2 => sF145)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1421,f4711])).
% 13.85/2.50 thf(f4720,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => sF145)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4715,f1028])).
% 13.85/2.50 thf(f4742,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => $true))) | ($false = sF145)),
% 13.85/2.50 inference(superposition,[],[f4720,f1172])).
% 13.85/2.50 thf(f4745,plain,(
% 13.85/2.50 ($false = sF145) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f4742])).
% 13.85/2.50 thf(f4746,plain,(
% 13.85/2.50 ($false = sF145)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4745])).
% 13.85/2.50 thf(f4750,plain,(
% 13.85/2.50 ($false = ((ubforcartprodlem3 => sF144)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1420,f4746])).
% 13.85/2.50 thf(f4755,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => sF144)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4750,f1095])).
% 13.85/2.50 thf(f4758,plain,(
% 13.85/2.50 (sF144 = $false)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4755])).
% 13.85/2.50 thf(f4768,plain,(
% 13.85/2.50 ($false = ((cartprodpairin => sF143)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1418,f4758])).
% 13.85/2.50 thf(f4773,plain,(
% 13.85/2.50 ($false = ((cartprodpairin => (cartprodmempair1 => sF142))))),
% 13.85/2.50 inference(forward_demodulation,[],[f4768,f1417])).
% 13.85/2.50 thf(f4780,plain,(
% 13.85/2.50 ($false = ((cartprodpairin => (cartprodmempair1 => $true)))) | ($false = sF142)),
% 13.85/2.50 inference(superposition,[],[f4773,f1172])).
% 13.85/2.50 thf(f4786,plain,(
% 13.85/2.50 ($false = sF142) | ($false = ((cartprodpairin => $true)))),
% 13.85/2.50 inference(boolean_simplification,[],[f4780])).
% 13.85/2.50 thf(f4787,plain,(
% 13.85/2.50 ($false = sF142) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f4786])).
% 13.85/2.50 thf(f4788,plain,(
% 13.85/2.50 ($false = sF142)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4787])).
% 13.85/2.50 thf(f4796,plain,(
% 13.85/2.50 ($false = ((cartprodmempair => sF141)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1415,f4788])).
% 13.85/2.50 thf(f4814,plain,(
% 13.85/2.50 ($false = sF141)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4796])).
% 13.85/2.50 thf(f4824,plain,(
% 13.85/2.50 ($false = ((setunionE2 => sF140)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1414,f4814])).
% 13.85/2.50 thf(f4829,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => sF140)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4824,f983])).
% 13.85/2.50 thf(f4849,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => $true))) | ($false = sF140)),
% 13.85/2.50 inference(superposition,[],[f4829,f1172])).
% 13.85/2.50 thf(f4853,plain,(
% 13.85/2.50 ($false = sF140) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f4849])).
% 13.85/2.50 thf(f4854,plain,(
% 13.85/2.50 ($false = sF140)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4853])).
% 13.85/2.50 thf(f4857,plain,(
% 13.85/2.50 ($false = ((setunionsingleton1 => sF139)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1413,f4854])).
% 13.85/2.50 thf(f4862,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => sF139)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4857,f924])).
% 13.85/2.50 thf(f4863,plain,(
% 13.85/2.50 ((((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => (setunionsingleton2 => sF138))) = $false)),
% 13.85/2.50 inference(forward_demodulation,[],[f4862,f1411])).
% 13.85/2.50 thf(f4864,plain,(
% 13.85/2.50 ((((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => sF138))) = $false)),
% 13.85/2.50 inference(forward_demodulation,[],[f4863,f1048])).
% 13.85/2.50 thf(f4867,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => $true)))) | ($false = sF138)),
% 13.85/2.50 inference(superposition,[],[f4864,f1172])).
% 13.85/2.50 thf(f4873,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => $true))) | ($false = sF138)),
% 13.85/2.50 inference(boolean_simplification,[],[f4867])).
% 13.85/2.50 thf(f4874,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF138)),
% 13.85/2.50 inference(boolean_simplification,[],[f4873])).
% 13.85/2.50 thf(f4875,plain,(
% 13.85/2.50 ($false = sF138)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4874])).
% 13.85/2.50 thf(f4881,plain,(
% 13.85/2.50 ($false = ((setunionsingleton => sF137)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1409,f4875])).
% 13.85/2.50 thf(f4894,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => sF137)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4881,f891])).
% 13.85/2.50 thf(f4905,plain,(
% 13.85/2.50 ($false = sF137)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4894])).
% 13.85/2.50 thf(f4915,plain,(
% 13.85/2.50 ($false = ((singletonprop => sF136)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1408,f4905])).
% 13.85/2.50 thf(f4920,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ Y1)))))))) => sF136)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4915,f1683])).
% 13.85/2.50 thf(f4951,plain,(
% 13.85/2.50 ($false = sF136) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ Y1)))))))) => $true)))),
% 13.85/2.50 inference(superposition,[],[f4920,f1172])).
% 13.85/2.50 thf(f4955,plain,(
% 13.85/2.50 ($false = sF136) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f4951])).
% 13.85/2.50 thf(f4956,plain,(
% 13.85/2.50 ($false = sF136)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4955])).
% 13.85/2.50 thf(f4959,plain,(
% 13.85/2.50 ($false = ((ex1E1 => sF135)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1406,f4956])).
% 13.85/2.50 thf(f4964,plain,(
% 13.85/2.50 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => sF135)))),
% 13.85/2.50 inference(forward_demodulation,[],[f4959,f1642])).
% 13.85/2.50 thf(f4967,plain,(
% 13.85/2.50 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => (ex1I => sF134))))),
% 13.85/2.50 inference(forward_demodulation,[],[f4964,f1405])).
% 13.85/2.50 thf(f4970,plain,(
% 13.85/2.50 ($false = sF134) | ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => (ex1I => $true))))),
% 13.85/2.50 inference(superposition,[],[f4967,f1172])).
% 13.85/2.50 thf(f4977,plain,(
% 13.85/2.50 ($false = sF134) | ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => $true)))),
% 13.85/2.50 inference(boolean_simplification,[],[f4970])).
% 13.85/2.50 thf(f4978,plain,(
% 13.85/2.50 ($false = sF134) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f4977])).
% 13.85/2.50 thf(f4979,plain,(
% 13.85/2.50 ($false = sF134)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f4978])).
% 13.85/2.50 thf(f4988,plain,(
% 13.85/2.50 ($false = ((ex1I2 => sF133)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1404,f4979])).
% 13.85/2.50 thf(f5004,plain,(
% 13.85/2.50 ($false = sF133)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f4988])).
% 13.85/2.50 thf(f5018,plain,(
% 13.85/2.50 ($false = ((singletonsuniq => sF132)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1403,f5004])).
% 13.85/2.50 thf(f5021,plain,(
% 13.85/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => sF132)) = $false)),
% 13.85/2.50 inference(forward_demodulation,[],[f5018,f1074])).
% 13.85/2.50 thf(f5024,plain,(
% 13.85/2.50 ($false = sF132)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f5021])).
% 13.85/2.50 thf(f5034,plain,(
% 13.85/2.50 (((setukpairinjL1 => sF131)) = $false)),
% 13.85/2.50 inference(backward_demodulation,[],[f1402,f5024])).
% 13.85/2.50 thf(f5041,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => sF131)))),
% 13.85/2.50 inference(forward_demodulation,[],[f5034,f1159])).
% 13.85/2.50 thf(f5042,plain,(
% 13.85/2.50 ($false = sF131)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f5041])).
% 13.85/2.50 thf(f5052,plain,(
% 13.85/2.50 ($false = ((kfstsingleton => sF130)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1400,f5042])).
% 13.85/2.50 thf(f5063,plain,(
% 13.85/2.50 ($false = ((kfstsingleton => $true))) | ($false = sF130)),
% 13.85/2.50 inference(superposition,[],[f5052,f1172])).
% 13.85/2.50 thf(f5066,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF130)),
% 13.85/2.50 inference(boolean_simplification,[],[f5063])).
% 13.85/2.50 thf(f5067,plain,(
% 13.85/2.50 ($false = sF130)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f5066])).
% 13.85/2.50 thf(f5071,plain,(
% 13.85/2.50 ($false = ((theprop => sF129)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1398,f5067])).
% 13.85/2.50 thf(f5078,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))) => sF129)))),
% 13.85/2.50 inference(forward_demodulation,[],[f5071,f1053])).
% 13.85/2.50 thf(f5081,plain,(
% 13.85/2.50 ((((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))) => (kfstpairEq => sF128))) = $false)),
% 13.85/2.50 inference(forward_demodulation,[],[f5078,f1396])).
% 13.85/2.50 thf(f5082,plain,(
% 13.85/2.50 ((((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))) => sF128))) = $false)),
% 13.85/2.50 inference(forward_demodulation,[],[f5081,f1130])).
% 13.85/2.50 thf(f5094,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))) => $true)))) | ($false = sF128)),
% 13.85/2.50 inference(superposition,[],[f5082,f1172])).
% 13.85/2.50 thf(f5099,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))) => $true))) | ($false = sF128)),
% 13.85/2.50 inference(boolean_simplification,[],[f5094])).
% 13.85/2.50 thf(f5100,plain,(
% 13.85/2.50 ($false = sF128) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f5099])).
% 13.85/2.50 thf(f5101,plain,(
% 13.85/2.50 ($false = sF128)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f5100])).
% 13.85/2.50 thf(f5109,plain,(
% 13.85/2.50 ($false = ((cartprodfstin => sF127)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1395,f5101])).
% 13.85/2.50 thf(f5126,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (kfst @ Y1) @ Y2)))))))) => sF127)))),
% 13.85/2.50 inference(forward_demodulation,[],[f5109,f1093])).
% 13.85/2.50 thf(f5136,plain,(
% 13.85/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (kfst @ Y1) @ Y2)))))))) => $true)) = $false) | (sF127 = $false)),
% 13.85/2.50 inference(superposition,[],[f5126,f1172])).
% 13.85/2.50 thf(f5141,plain,(
% 13.85/2.50 ($false = $true) | (sF127 = $false)),
% 13.85/2.50 inference(boolean_simplification,[],[f5136])).
% 13.85/2.50 thf(f5142,plain,(
% 13.85/2.50 (sF127 = $false)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f5141])).
% 13.85/2.50 thf(f5144,plain,(
% 13.85/2.50 ($false = ((setukpairinjL2 => sF126)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1394,f5142])).
% 13.85/2.50 thf(f5149,plain,(
% 13.85/2.50 ($false = sF126)),
% 13.85/2.50 inference(imp_proxy_clausification,[],[f5144])).
% 13.85/2.50 thf(f5165,plain,(
% 13.85/2.50 ($false = ((setukpairinjL => sF125)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1393,f5149])).
% 13.85/2.50 thf(f5166,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y2 @ Y0)) => (Y3 = Y2)))))))))) => sF125)))),
% 13.85/2.50 inference(forward_demodulation,[],[f5165,f878])).
% 13.85/2.50 thf(f5169,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y2 @ Y0)) => (Y3 = Y2)))))))))) => $true))) | ($false = sF125)),
% 13.85/2.50 inference(superposition,[],[f5166,f1172])).
% 13.85/2.50 thf(f5172,plain,(
% 13.85/2.50 ($false = sF125) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f5169])).
% 13.85/2.50 thf(f5173,plain,(
% 13.85/2.50 ($false = sF125)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f5172])).
% 13.85/2.50 thf(f5177,plain,(
% 13.85/2.50 ($false = ((setukpairinjR11 => sF124)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1391,f5173])).
% 13.85/2.50 thf(f5182,plain,(
% 13.85/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => sF124)) = $false)),
% 13.85/2.50 inference(forward_demodulation,[],[f5177,f1096])).
% 13.85/2.50 thf(f5189,plain,(
% 13.85/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => $true))) | ($false = sF124)),
% 13.85/2.50 inference(superposition,[],[f5182,f1172])).
% 13.85/2.50 thf(f5194,plain,(
% 13.85/2.50 ($false = $true) | ($false = sF124)),
% 13.85/2.50 inference(boolean_simplification,[],[f5189])).
% 13.85/2.50 thf(f5195,plain,(
% 13.85/2.50 ($false = sF124)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f5194])).
% 13.85/2.50 thf(f5203,plain,(
% 13.85/2.50 ($false = ((setukpairinjR12 => sF123)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1390,f5195])).
% 13.85/2.50 thf(f5208,plain,(
% 13.85/2.50 ($false = ((setukpairinjR12 => $true))) | ($false = sF123)),
% 13.85/2.50 inference(superposition,[],[f5203,f1172])).
% 13.85/2.50 thf(f5212,plain,(
% 13.85/2.50 ($false = sF123) | ($false = $true)),
% 13.85/2.50 inference(boolean_simplification,[],[f5208])).
% 13.85/2.50 thf(f5213,plain,(
% 13.85/2.50 ($false = sF123)),
% 13.85/2.50 inference(trivial_inequality_removal,[],[f5212])).
% 13.85/2.50 thf(f5220,plain,(
% 13.85/2.50 ($false = ((setukpairinjR1 => sF122)))),
% 13.85/2.50 inference(backward_demodulation,[],[f1389,f5213])).
% 13.85/2.50 thf(f5223,plain,(
% 13.85/2.50 ($false = sF122) | ($false = ((setukpairinjR1 => $true)))),
% 13.85/2.50 inference(superposition,[],[f5220,f1172])).
% 14.67/2.50 thf(f5226,plain,(
% 14.67/2.50 ($false = sF122) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5223])).
% 14.67/2.50 thf(f5227,plain,(
% 14.67/2.50 ($false = sF122)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5226])).
% 14.67/2.50 thf(f5231,plain,(
% 14.67/2.50 ($false = ((upairequniteq => sF121)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1388,f5227])).
% 14.67/2.50 thf(f5236,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => sF121)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5231,f920])).
% 14.67/2.50 thf(f5243,plain,(
% 14.67/2.50 ($false = sF121) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f5236,f1172])).
% 14.67/2.50 thf(f5246,plain,(
% 14.67/2.50 ($false = sF121) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5243])).
% 14.67/2.50 thf(f5247,plain,(
% 14.67/2.50 ($false = sF121)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5246])).
% 14.67/2.50 thf(f5253,plain,(
% 14.67/2.50 ($false = ((setukpairinjR2 => sF120)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1386,f5247])).
% 14.67/2.50 thf(f5256,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => sF120)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5253,f903])).
% 14.67/2.50 thf(f5281,plain,(
% 14.67/2.50 ($false = sF120)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5256])).
% 14.67/2.50 thf(f5291,plain,(
% 14.67/2.50 ($false = ((setukpairinjR => sF119)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1384,f5281])).
% 14.67/2.50 thf(f5298,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y3) = (kpair @ Y0 @ Y1)) => (Y3 = Y1)))))))))) => sF119)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5291,f1144])).
% 14.67/2.50 thf(f5301,plain,(
% 14.67/2.50 ($false = sF119) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y3) = (kpair @ Y0 @ Y1)) => (Y3 = Y1)))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f5298,f1172])).
% 14.67/2.50 thf(f5305,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF119)),
% 14.67/2.50 inference(boolean_simplification,[],[f5301])).
% 14.67/2.50 thf(f5306,plain,(
% 14.67/2.50 ($false = sF119)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5305])).
% 14.67/2.50 thf(f5313,plain,(
% 14.67/2.50 ($false = ((ksndsingleton => sF118)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1382,f5306])).
% 14.67/2.50 thf(f5316,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))) => sF118)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5313,f1086])).
% 14.67/2.50 thf(f5319,plain,(
% 14.67/2.50 ($false = sF118)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5316])).
% 14.67/2.50 thf(f5329,plain,(
% 14.67/2.50 ($false = ((ksndpairEq => sF117)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1380,f5319])).
% 14.67/2.50 thf(f5334,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1))))) => sF117)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5329,f1097])).
% 14.67/2.50 thf(f5335,plain,(
% 14.67/2.50 ($false = sF117)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5334])).
% 14.67/2.50 thf(f5345,plain,(
% 14.67/2.50 ($false = ((kpairsurjEq => sF116)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1379,f5335])).
% 14.67/2.50 thf(f5350,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => sF116)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5345,f1131])).
% 14.67/2.50 thf(f5353,plain,(
% 14.67/2.50 ($false = sF116) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f5350,f1172])).
% 14.67/2.50 thf(f5356,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF116)),
% 14.67/2.50 inference(boolean_simplification,[],[f5353])).
% 14.67/2.50 thf(f5357,plain,(
% 14.67/2.50 ($false = sF116)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5356])).
% 14.67/2.50 thf(f5363,plain,(
% 14.67/2.50 ($false = ((cartprodsndin => sF115)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1378,f5357])).
% 14.67/2.50 thf(f5366,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (ksnd @ Y0) @ Y2)))))))) => sF115)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5363,f1106])).
% 14.67/2.50 thf(f5369,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (ksnd @ Y0) @ Y2)))))))) => $true))) | ($false = sF115)),
% 14.67/2.50 inference(superposition,[],[f5366,f1172])).
% 14.67/2.50 thf(f5374,plain,(
% 14.67/2.50 ($false = sF115) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5369])).
% 14.67/2.50 thf(f5375,plain,(
% 14.67/2.50 ($false = sF115)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5374])).
% 14.67/2.50 thf(f5381,plain,(
% 14.67/2.50 ($false = ((cartprodpairmemEL => sF114)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1376,f5375])).
% 14.67/2.50 thf(f5382,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))) => sF114)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5381,f918])).
% 14.67/2.50 thf(f5383,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))) => (cartprodpairmemER => sF113))))),
% 14.67/2.50 inference(forward_demodulation,[],[f5382,f1375])).
% 14.67/2.50 thf(f5384,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))) => (cartprodpairmemER => (cartprodmempaircEq => sF112)))))),
% 14.67/2.50 inference(forward_demodulation,[],[f5383,f1373])).
% 14.67/2.50 thf(f5385,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))) => (cartprodpairmemER => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF112)))))),
% 14.67/2.50 inference(forward_demodulation,[],[f5384,f1666])).
% 14.67/2.50 thf(f5390,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))) => (cartprodpairmemER => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => $true))))) | ($false = sF112)),
% 14.67/2.50 inference(superposition,[],[f5385,f1172])).
% 14.67/2.50 thf(f5402,plain,(
% 14.67/2.50 ($false = sF112) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))) => (cartprodpairmemER => $true))))),
% 14.67/2.50 inference(boolean_simplification,[],[f5390])).
% 14.67/2.50 thf(f5403,plain,(
% 14.67/2.50 ($false = sF112) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))) => $true)))),
% 14.67/2.50 inference(boolean_simplification,[],[f5402])).
% 14.67/2.50 thf(f5404,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF112)),
% 14.67/2.50 inference(boolean_simplification,[],[f5403])).
% 14.67/2.50 thf(f5405,plain,(
% 14.67/2.50 ($false = sF112)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5404])).
% 14.67/2.50 thf(f5415,plain,(
% 14.67/2.50 (((cartprodfstpairEq => sF111)) = $false)),
% 14.67/2.50 inference(backward_demodulation,[],[f1371,f5405])).
% 14.67/2.50 thf(f5429,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => sF111)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5415,f1042])).
% 14.67/2.50 thf(f5450,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => $true))) | ($false = sF111)),
% 14.67/2.50 inference(superposition,[],[f5429,f1172])).
% 14.67/2.50 thf(f5454,plain,(
% 14.67/2.50 ($false = sF111) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5450])).
% 14.67/2.50 thf(f5455,plain,(
% 14.67/2.50 ($false = sF111)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5454])).
% 14.67/2.50 thf(f5458,plain,(
% 14.67/2.50 ($false = ((cartprodsndpairEq => sF110)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1369,f5455])).
% 14.67/2.50 thf(f5463,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))) => sF110)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5458,f902])).
% 14.67/2.50 thf(f5466,plain,(
% 14.67/2.50 ($false = sF110) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f5463,f1172])).
% 14.67/2.50 thf(f5470,plain,(
% 14.67/2.50 ($false = sF110) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5466])).
% 14.67/2.50 thf(f5471,plain,(
% 14.67/2.50 ($false = sF110)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5470])).
% 14.67/2.50 thf(f5474,plain,(
% 14.67/2.50 (((cartprodpairsurjEq => sF109)) = $false)),
% 14.67/2.50 inference(backward_demodulation,[],[f1367,f5471])).
% 14.67/2.50 thf(f5477,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => sF109)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5474,f1091])).
% 14.67/2.50 thf(f5482,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => $true))) | ($false = sF109)),
% 14.67/2.50 inference(superposition,[],[f5477,f1172])).
% 14.67/2.50 thf(f5486,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF109)),
% 14.67/2.50 inference(boolean_simplification,[],[f5482])).
% 14.67/2.50 thf(f5487,plain,(
% 14.67/2.50 ($false = sF109)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5486])).
% 14.67/2.50 thf(f5490,plain,(
% 14.67/2.50 ($false = ((dpsetconstrI => sF108)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1365,f5487])).
% 14.67/2.50 thf(f5493,plain,(
% 14.67/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3))))))))))))))) => sF108)) = $false)),
% 14.67/2.50 inference(forward_demodulation,[],[f5490,f1651])).
% 14.67/2.50 thf(f5498,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3))))))))))))))) => $true))) | ($false = sF108)),
% 14.67/2.50 inference(superposition,[],[f5493,f1172])).
% 14.67/2.50 thf(f5503,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF108)),
% 14.67/2.50 inference(boolean_simplification,[],[f5498])).
% 14.67/2.50 thf(f5504,plain,(
% 14.67/2.50 ($false = sF108)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5503])).
% 14.67/2.50 thf(f5506,plain,(
% 14.67/2.50 ($false = ((dpsetconstrSub => sF107)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1363,f5504])).
% 14.67/2.50 thf(f5511,plain,(
% 14.67/2.50 ($false = sF107)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5506])).
% 14.67/2.50 thf(f5525,plain,(
% 14.67/2.50 (((setOfPairsIsBReln => sF106)) = $false)),
% 14.67/2.50 inference(backward_demodulation,[],[f1361,f5511])).
% 14.67/2.50 thf(f5528,plain,(
% 14.67/2.50 ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y1 @ Y0) @ (cartprod @ Y2 @ Y1)))))))) => sF106)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5525,f1686])).
% 14.67/2.50 thf(f5551,plain,(
% 14.67/2.50 ($false = sF106)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5528])).
% 14.67/2.50 thf(f5561,plain,(
% 14.67/2.50 ($false = ((dpsetconstrERa => sF105)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1359,f5551])).
% 14.67/2.50 thf(f5566,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ Y2)) => (Y2 @ Y3 @ Y4)))))))))))))) => sF105)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5561,f1645])).
% 14.67/2.50 thf(f5571,plain,(
% 14.67/2.50 ($false = sF105) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ Y2)) => (Y2 @ Y3 @ Y4)))))))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f5566,f1172])).
% 14.67/2.50 thf(f5575,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF105)),
% 14.67/2.50 inference(boolean_simplification,[],[f5571])).
% 14.67/2.50 thf(f5576,plain,(
% 14.67/2.50 ($false = sF105)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5575])).
% 14.67/2.50 thf(f5579,plain,(
% 14.67/2.50 ($false = ((dpsetconstrEL1 => sF104)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1358,f5576])).
% 14.67/2.50 thf(f5586,plain,(
% 14.67/2.50 ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y4 @ Y2 @ Y0)) => (in @ Y1 @ Y4)))))))))))) => sF104)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5579,f1648])).
% 14.67/2.50 thf(f5589,plain,(
% 14.67/2.50 (sF104 = $false)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5586])).
% 14.67/2.50 thf(f5599,plain,(
% 14.67/2.50 ($false = ((dpsetconstrEL2 => sF103)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1356,f5589])).
% 14.67/2.50 thf(f5604,plain,(
% 14.67/2.50 ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ Y0)) => (in @ Y4 @ Y3)))))))))))) => sF103)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5599,f1662])).
% 14.67/2.50 thf(f5611,plain,(
% 14.67/2.50 ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ Y0)) => (in @ Y4 @ Y3)))))))))))) => $true))) | ($false = sF103)),
% 14.67/2.50 inference(superposition,[],[f5604,f1172])).
% 14.67/2.50 thf(f5616,plain,(
% 14.67/2.50 ($false = sF103) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5611])).
% 14.67/2.50 thf(f5617,plain,(
% 14.67/2.50 ($false = sF103)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5616])).
% 14.67/2.50 thf(f5619,plain,(
% 14.67/2.50 ($false = ((dpsetconstrER => sF102)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1355,f5617])).
% 14.67/2.50 thf(f5626,plain,(
% 14.67/2.50 ($false = ((dpsetconstrER => $true))) | ($false = sF102)),
% 14.67/2.50 inference(superposition,[],[f5619,f1172])).
% 14.67/2.50 thf(f5630,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF102)),
% 14.67/2.50 inference(boolean_simplification,[],[f5626])).
% 14.67/2.50 thf(f5631,plain,(
% 14.67/2.50 ($false = sF102)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5630])).
% 14.67/2.50 thf(f5638,plain,(
% 14.67/2.50 ($false = ((funcImageSingleton => sF101)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1353,f5631])).
% 14.67/2.50 thf(f5641,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))))))))))))) => sF101)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5638,f1064])).
% 14.67/2.50 thf(f5663,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))))))))))))) => $true))) | ($false = sF101)),
% 14.67/2.50 inference(superposition,[],[f5641,f1172])).
% 14.67/2.50 thf(f5666,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF101)),
% 14.67/2.50 inference(boolean_simplification,[],[f5663])).
% 14.67/2.50 thf(f5667,plain,(
% 14.67/2.50 ($false = sF101)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5666])).
% 14.67/2.50 thf(f5671,plain,(
% 14.67/2.50 ($false = ((apProp => sF100)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1351,f5667])).
% 14.67/2.50 thf(f5678,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2))))))))))) => sF100)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5671,f876])).
% 14.67/2.50 thf(f5681,plain,(
% 14.67/2.50 ($false = sF100)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5678])).
% 14.67/2.50 thf(f5691,plain,(
% 14.67/2.50 ($false = ((app => sF99)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1349,f5681])).
% 14.67/2.50 thf(f5696,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y1 @ Y0 @ Y3) @ Y1))))))))))) => sF99)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5691,f1025])).
% 14.67/2.50 thf(f5697,plain,(
% 14.67/2.50 ($false = sF99)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5696])).
% 14.67/2.50 thf(f5709,plain,(
% 14.67/2.50 ($false = ((infuncsetfunc => sF98)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1347,f5697])).
% 14.67/2.50 thf(f5714,plain,(
% 14.67/2.50 ($false = ((infuncsetfunc => $true))) | ($false = sF98)),
% 14.67/2.50 inference(superposition,[],[f5709,f1172])).
% 14.67/2.50 thf(f5717,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF98)),
% 14.67/2.50 inference(boolean_simplification,[],[f5714])).
% 14.67/2.50 thf(f5718,plain,(
% 14.67/2.50 ($false = sF98)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5717])).
% 14.67/2.50 thf(f5724,plain,(
% 14.67/2.50 ($false = ((ap2p => sF97)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1345,f5718])).
% 14.67/2.50 thf(f5727,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ Y1 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (ap @ Y1 @ Y0 @ Y2 @ Y3) @ Y0))))))))))) => sF97)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5724,f1085])).
% 14.67/2.50 thf(f5743,plain,(
% 14.67/2.50 ($false = sF97) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ Y1 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (ap @ Y1 @ Y0 @ Y2 @ Y3) @ Y0))))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f5727,f1172])).
% 14.67/2.50 thf(f5747,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF97)),
% 14.67/2.50 inference(boolean_simplification,[],[f5743])).
% 14.67/2.50 thf(f5748,plain,(
% 14.67/2.50 ($false = sF97)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5747])).
% 14.67/2.50 thf(f5751,plain,(
% 14.67/2.50 ($false = ((funcinfuncset => sF96)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1344,f5748])).
% 14.67/2.50 thf(f5756,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (in @ Y2 @ (funcSet @ Y0 @ Y1))))))))) => sF96)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5751,f963])).
% 14.67/2.50 thf(f5759,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (in @ Y2 @ (funcSet @ Y0 @ Y1))))))))) => $true))) | ($false = sF96)),
% 14.67/2.50 inference(superposition,[],[f5756,f1172])).
% 14.67/2.50 thf(f5762,plain,(
% 14.67/2.50 ($false = sF96) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5759])).
% 14.67/2.50 thf(f5763,plain,(
% 14.67/2.50 ($false = sF96)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5762])).
% 14.67/2.50 thf(f5767,plain,(
% 14.67/2.50 ($false = ((lamProp => sF95)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1343,f5763])).
% 14.67/2.50 thf(f5774,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (func @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))))))))))) => sF95)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5767,f1653])).
% 14.67/2.50 thf(f5777,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (func @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))))))))))) => $true))) | ($false = sF95)),
% 14.67/2.50 inference(superposition,[],[f5774,f1172])).
% 14.67/2.50 thf(f5780,plain,(
% 14.67/2.50 ($false = sF95) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5777])).
% 14.67/2.50 thf(f5781,plain,(
% 14.67/2.50 ($false = sF95)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5780])).
% 14.67/2.50 thf(f5785,plain,(
% 14.67/2.50 ($false = ((lamp => sF94)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1341,f5781])).
% 14.67/2.50 thf(f5790,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (func @ Y2 @ Y0 @ (lam @ Y2 @ Y0 @ Y1))))))))) => sF94)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5785,f1680])).
% 14.67/2.50 thf(f5797,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (func @ Y2 @ Y0 @ (lam @ Y2 @ Y0 @ Y1))))))))) => $true))) | ($false = sF94)),
% 14.67/2.50 inference(superposition,[],[f5790,f1172])).
% 14.67/2.50 thf(f5801,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF94)),
% 14.67/2.50 inference(boolean_simplification,[],[f5797])).
% 14.67/2.50 thf(f5802,plain,(
% 14.67/2.50 ($false = sF94)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5801])).
% 14.67/2.50 thf(f5805,plain,(
% 14.67/2.50 ($false = ((lam2p => sF93)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1339,f5802])).
% 14.67/2.50 thf(f5810,plain,(
% 14.67/2.50 ($false = (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (in @ (lam @ Y1 @ Y2 @ Y0) @ (funcSet @ Y1 @ Y2))))))))) => sF93)))),
% 14.67/2.50 inference(forward_demodulation,[],[f5805,f1669])).
% 14.67/2.50 thf(f5866,plain,(
% 14.67/2.50 ($false = sF93)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5810])).
% 14.67/2.50 thf(f5882,plain,(
% 14.67/2.50 ($false = ((brelnall1 => sF92)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1337,f5866])).
% 14.67/2.50 thf(f5885,plain,(
% 14.67/2.50 ($false = sF92) | (((brelnall1 => $true)) = $false)),
% 14.67/2.50 inference(superposition,[],[f5882,f1172])).
% 14.67/2.50 thf(f5889,plain,(
% 14.67/2.50 ($false = sF92) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5885])).
% 14.67/2.50 thf(f5890,plain,(
% 14.67/2.50 ($false = sF92)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5889])).
% 14.67/2.50 thf(f5893,plain,(
% 14.67/2.50 ($false = ((brelnall2 => sF91)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1335,f5890])).
% 14.67/2.50 thf(f5896,plain,(
% 14.67/2.50 ($false = ((brelnall2 => (ex1E2 => sF90))))),
% 14.67/2.50 inference(forward_demodulation,[],[f5893,f1334])).
% 14.67/2.50 thf(f5901,plain,(
% 14.67/2.50 ($false = ((brelnall2 => (ex1E2 => $true)))) | ($false = sF90)),
% 14.67/2.50 inference(superposition,[],[f5896,f1172])).
% 14.67/2.50 thf(f5907,plain,(
% 14.67/2.50 ($false = sF90) | ($false = ((brelnall2 => $true)))),
% 14.67/2.50 inference(boolean_simplification,[],[f5901])).
% 14.67/2.50 thf(f5908,plain,(
% 14.67/2.50 ($false = sF90) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5907])).
% 14.67/2.50 thf(f5909,plain,(
% 14.67/2.50 ($false = sF90)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5908])).
% 14.67/2.50 thf(f5918,plain,(
% 14.67/2.50 ($false = ((funcGraphProp1 => sF89)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1332,f5909])).
% 14.67/2.50 thf(f5933,plain,(
% 14.67/2.50 ($false = sF89) | ($false = ((funcGraphProp1 => $true)))),
% 14.67/2.50 inference(superposition,[],[f5918,f1172])).
% 14.67/2.50 thf(f5936,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF89)),
% 14.67/2.50 inference(boolean_simplification,[],[f5933])).
% 14.67/2.50 thf(f5937,plain,(
% 14.67/2.50 ($false = sF89)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5936])).
% 14.67/2.50 thf(f5941,plain,(
% 14.67/2.50 ($false = ((funcGraphProp3 => sF88)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1331,f5937])).
% 14.67/2.50 thf(f5946,plain,(
% 14.67/2.50 ($false = ((funcGraphProp3 => (funcGraphProp2 => sF87))))),
% 14.67/2.50 inference(forward_demodulation,[],[f5941,f1330])).
% 14.67/2.50 thf(f5953,plain,(
% 14.67/2.50 ($false = sF87) | ($false = ((funcGraphProp3 => (funcGraphProp2 => $true))))),
% 14.67/2.50 inference(superposition,[],[f5946,f1172])).
% 14.67/2.50 thf(f5963,plain,(
% 14.67/2.50 ($false = sF87) | ($false = ((funcGraphProp3 => $true)))),
% 14.67/2.50 inference(boolean_simplification,[],[f5953])).
% 14.67/2.50 thf(f5964,plain,(
% 14.67/2.50 ($false = sF87) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f5963])).
% 14.67/2.50 thf(f5965,plain,(
% 14.67/2.50 ($false = sF87)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f5964])).
% 14.67/2.50 thf(f5975,plain,(
% 14.67/2.50 ($false = ((funcextLem => sF86)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1328,f5965])).
% 14.67/2.50 thf(f5983,plain,(
% 14.67/2.50 ($false = sF86)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5975])).
% 14.67/2.50 thf(f5997,plain,(
% 14.67/2.50 ($false = ((funcGraphProp4 => sF85)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1327,f5983])).
% 14.67/2.50 thf(f5998,plain,(
% 14.67/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))) => sF85)) = $false)),
% 14.67/2.50 inference(forward_demodulation,[],[f5997,f1092])).
% 14.67/2.50 thf(f6050,plain,(
% 14.67/2.50 ($false = sF85)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f5998])).
% 14.67/2.50 thf(f6060,plain,(
% 14.67/2.50 ($false = ((subbreln => sF84)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1325,f6050])).
% 14.67/2.50 thf(f6071,plain,(
% 14.67/2.50 ($false = sF84)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6060])).
% 14.67/2.50 thf(f6083,plain,(
% 14.67/2.50 ($false = ((eqbreln => sF83)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1323,f6071])).
% 14.67/2.50 thf(f6086,plain,(
% 14.67/2.50 ($false = sF83)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6083])).
% 14.67/2.50 thf(f6087,plain,(
% 14.67/2.50 (eqbreln = $true)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6083])).
% 14.67/2.50 thf(f6096,plain,(
% 14.67/2.50 ($false = ((funcext => sF82)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1321,f6086])).
% 14.67/2.50 thf(f6098,plain,(
% 14.67/2.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3)))))))))))))))),
% 14.67/2.50 inference(backward_demodulation,[],[f1649,f6087])).
% 14.67/2.50 thf(f6103,plain,(
% 14.67/2.50 ($false = sF82)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6096])).
% 14.67/2.50 thf(f6113,plain,(
% 14.67/2.50 ($false = ((funcext2 => sF81)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1320,f6103])).
% 14.67/2.50 thf(f6120,plain,(
% 14.67/2.50 ($false = ((funcext2 => (ap2apEq1 => sF80))))),
% 14.67/2.50 inference(forward_demodulation,[],[f6113,f1318])).
% 14.67/2.50 thf(f6123,plain,(
% 14.67/2.50 ($false = ((funcext2 => (ap2apEq1 => $true)))) | ($false = sF80)),
% 14.67/2.50 inference(superposition,[],[f6120,f1172])).
% 14.67/2.50 thf(f6132,plain,(
% 14.67/2.50 ($false = ((funcext2 => $true))) | ($false = sF80)),
% 14.67/2.50 inference(boolean_simplification,[],[f6123])).
% 14.67/2.50 thf(f6133,plain,(
% 14.67/2.50 ($false = sF80) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6132])).
% 14.67/2.50 thf(f6134,plain,(
% 14.67/2.50 ($false = sF80)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6133])).
% 14.67/2.50 thf(f6145,plain,(
% 14.67/2.50 ($false = ((ap2apEq2 => sF79)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1317,f6134])).
% 14.67/2.50 thf(f6153,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF79)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6145,f1693])).
% 14.67/2.50 thf(f6158,plain,(
% 14.67/2.50 ($false = sF79) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f6153,f1172])).
% 14.67/2.50 thf(f6161,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF79)),
% 14.67/2.50 inference(boolean_simplification,[],[f6158])).
% 14.67/2.50 thf(f6162,plain,(
% 14.67/2.50 ($false = sF79)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6161])).
% 14.67/2.50 thf(f6166,plain,(
% 14.67/2.50 ($false = ((beta1 => sF78)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1315,f6162])).
% 14.67/2.50 thf(f6175,plain,(
% 14.67/2.50 (((beta1 => $true)) = $false) | ($false = sF78)),
% 14.67/2.50 inference(superposition,[],[f6166,f1172])).
% 14.67/2.50 thf(f6180,plain,(
% 14.67/2.50 ($false = sF78) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6175])).
% 14.67/2.50 thf(f6181,plain,(
% 14.67/2.50 ($false = sF78)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6180])).
% 14.67/2.50 thf(f6183,plain,(
% 14.67/2.50 ($false = ((eta1 => sF77)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1314,f6181])).
% 14.67/2.50 thf(f6190,plain,(
% 14.67/2.50 ($false = sF77)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6183])).
% 14.67/2.50 thf(f6200,plain,(
% 14.67/2.50 ($false = ((lam2lamEq => sF76)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1313,f6190])).
% 14.67/2.50 thf(f6207,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ($true))))))) => sF76)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6200,f1698])).
% 14.67/2.50 thf(f6210,plain,(
% 14.67/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ($true))))))) => $true)) = $false) | ($false = sF76)),
% 14.67/2.50 inference(superposition,[],[f6207,f1172])).
% 14.67/2.50 thf(f6213,plain,(
% 14.67/2.50 ($false = sF76) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6210])).
% 14.67/2.50 thf(f6214,plain,(
% 14.67/2.50 ($false = sF76)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6213])).
% 14.67/2.50 thf(f6218,plain,(
% 14.67/2.50 ($false = ((beta2 => sF75)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1311,f6214])).
% 14.67/2.50 thf(f6227,plain,(
% 14.67/2.50 (sF75 = $false)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6218])).
% 14.67/2.50 thf(f6237,plain,(
% 14.67/2.50 ($false = ((eta2 => sF74)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1310,f6227])).
% 14.67/2.50 thf(f6244,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => ((lam @ Y0 @ Y2 @ (ap @ Y0 @ Y2 @ Y1)) = Y1)))))))) => sF74)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6237,f1636])).
% 14.67/2.50 thf(f6260,plain,(
% 14.67/2.50 ($false = sF74)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6244])).
% 14.67/2.50 thf(f6272,plain,(
% 14.67/2.50 ($false = ((iffalseProp1 => sF73)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1309,f6260])).
% 14.67/2.50 thf(f6275,plain,(
% 14.67/2.50 ($false = sF73)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6272])).
% 14.67/2.50 thf(f6287,plain,(
% 14.67/2.50 ($false = ((iffalseProp2 => sF72)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1308,f6275])).
% 14.67/2.50 thf(f6292,plain,(
% 14.67/2.50 ($false = sF72) | ($false = ((iffalseProp2 => $true)))),
% 14.67/2.50 inference(superposition,[],[f6287,f1172])).
% 14.67/2.50 thf(f6296,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF72)),
% 14.67/2.50 inference(boolean_simplification,[],[f6292])).
% 14.67/2.50 thf(f6297,plain,(
% 14.67/2.50 ($false = sF72)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6296])).
% 14.67/2.50 thf(f6300,plain,(
% 14.67/2.50 ($false = ((iftrueProp1 => sF71)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1307,f6297])).
% 14.67/2.50 thf(f6307,plain,(
% 14.67/2.50 ($false = sF71) | ($false = ((iftrueProp1 => $true)))),
% 14.67/2.50 inference(superposition,[],[f6300,f1172])).
% 14.67/2.50 thf(f6310,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF71)),
% 14.67/2.50 inference(boolean_simplification,[],[f6307])).
% 14.67/2.50 thf(f6311,plain,(
% 14.67/2.50 ($false = sF71)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6310])).
% 14.67/2.50 thf(f6315,plain,(
% 14.67/2.50 ($false = ((iftrueProp2 => sF70)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1305,f6311])).
% 14.67/2.50 thf(f6322,plain,(
% 14.67/2.50 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (Y0 => ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y0 & (Y1 = Y4)) | ((Y3 = Y4) & (~ Y0))))))))))))))))) => sF70)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6315,f1150])).
% 14.67/2.50 thf(f6366,plain,(
% 14.67/2.50 ($false = sF70)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6322])).
% 14.67/2.50 thf(f6376,plain,(
% 14.67/2.50 (((ifSingleton => sF69)) = $false)),
% 14.67/2.50 inference(backward_demodulation,[],[f1303,f6366])).
% 14.67/2.50 thf(f6387,plain,(
% 14.67/2.50 ($false = ((ifSingleton => $true))) | ($false = sF69)),
% 14.67/2.50 inference(superposition,[],[f6376,f1172])).
% 14.67/2.50 thf(f6391,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF69)),
% 14.67/2.50 inference(boolean_simplification,[],[f6387])).
% 14.67/2.50 thf(f6392,plain,(
% 14.67/2.50 ($false = sF69)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6391])).
% 14.67/2.50 thf(f6399,plain,(
% 14.67/2.50 ($false = ((ifp => sF68)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1301,f6392])).
% 14.67/2.50 thf(f6402,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (if @ Y2 @ Y1 @ Y0 @ Y3) @ Y2))))))))))) => sF68)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6399,f988])).
% 14.67/2.50 thf(f6405,plain,(
% 14.67/2.50 ($false = sF68) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (if @ Y2 @ Y1 @ Y0 @ Y3) @ Y2))))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f6402,f1172])).
% 14.67/2.50 thf(f6410,plain,(
% 14.67/2.50 ($false = sF68) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6405])).
% 14.67/2.50 thf(f6411,plain,(
% 14.67/2.50 ($false = sF68)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6410])).
% 14.67/2.50 thf(f6419,plain,(
% 14.67/2.50 ($false = ((theeq => sF67)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1299,f6411])).
% 14.67/2.50 thf(f6420,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1))))))) => sF67)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6419,f1109])).
% 14.67/2.50 thf(f6423,plain,(
% 14.67/2.50 ($false = sF67) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f6420,f1172])).
% 14.67/2.50 thf(f6427,plain,(
% 14.67/2.50 ($false = sF67) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6423])).
% 14.67/2.50 thf(f6428,plain,(
% 14.67/2.50 ($false = sF67)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6427])).
% 14.67/2.50 thf(f6435,plain,(
% 14.67/2.50 ($false = ((iftrue => sF66)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1297,f6428])).
% 14.67/2.50 thf(f6436,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((if @ Y0 @ Y2 @ Y1 @ Y3) = Y1)))))))))))) => sF66)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6435,f951])).
% 14.67/2.50 thf(f6437,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((if @ Y0 @ Y2 @ Y1 @ Y3) = Y1)))))))))))) => (iffalse => sF65))))),
% 14.67/2.50 inference(forward_demodulation,[],[f6436,f1295])).
% 14.67/2.50 thf(f6442,plain,(
% 14.67/2.50 ($false = sF65) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((if @ Y0 @ Y2 @ Y1 @ Y3) = Y1)))))))))))) => (iffalse => $true))))),
% 14.67/2.50 inference(superposition,[],[f6437,f1172])).
% 14.67/2.50 thf(f6451,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 => ((if @ Y0 @ Y2 @ Y1 @ Y3) = Y1)))))))))))) => $true))) | ($false = sF65)),
% 14.67/2.50 inference(boolean_simplification,[],[f6442])).
% 14.67/2.50 thf(f6452,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF65)),
% 14.67/2.50 inference(boolean_simplification,[],[f6451])).
% 14.67/2.50 thf(f6453,plain,(
% 14.67/2.50 ($false = sF65)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6452])).
% 14.67/2.50 thf(f6460,plain,(
% 14.67/2.50 ($false = ((iftrueorfalse => sF64)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1294,f6453])).
% 14.67/2.50 thf(f6470,plain,(
% 14.67/2.50 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (if @ Y1 @ Y0 @ Y2 @ Y3) @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset))))))))))))) => sF64)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6460,f890])).
% 14.67/2.50 thf(f6477,plain,(
% 14.67/2.50 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (if @ Y1 @ Y0 @ Y2 @ Y3) @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset))))))))))))) => $true))) | ($false = sF64)),
% 14.67/2.50 inference(superposition,[],[f6470,f1172])).
% 14.67/2.50 thf(f6480,plain,(
% 14.67/2.50 ($false = sF64) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6477])).
% 14.67/2.50 thf(f6481,plain,(
% 14.67/2.50 ($false = sF64)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6480])).
% 14.67/2.50 thf(f6485,plain,(
% 14.67/2.50 ($false = ((binintersectT_lem => sF63)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1292,f6481])).
% 14.67/2.50 thf(f6492,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ Y0)))))))))) => sF63)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6485,f993])).
% 14.67/2.50 thf(f6495,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ Y0)))))))))) => $true))) | ($false = sF63)),
% 14.67/2.50 inference(superposition,[],[f6492,f1172])).
% 14.67/2.50 thf(f6498,plain,(
% 14.67/2.50 ($false = sF63) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6495])).
% 14.67/2.50 thf(f6499,plain,(
% 14.67/2.50 ($false = sF63)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6498])).
% 14.67/2.50 thf(f6503,plain,(
% 14.67/2.50 ($false = ((binunionT_lem => sF62)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1291,f6499])).
% 14.67/2.50 thf(f6510,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binunion @ Y0 @ Y2) @ (powerset @ Y1)))))))))) => sF62)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6503,f1158])).
% 14.67/2.50 thf(f6513,plain,(
% 14.67/2.50 (sF62 = $false)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6510])).
% 14.67/2.50 thf(f6523,plain,(
% 14.67/2.50 ($false = ((powersetT_lem => sF61)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1289,f6513])).
% 14.67/2.50 thf(f6528,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (powerset @ Y0) @ (powerset @ (powerset @ Y1)))))))) => sF61)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6523,f960])).
% 14.67/2.50 thf(f6531,plain,(
% 14.67/2.50 ($false = sF61)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6528])).
% 14.67/2.50 thf(f6541,plain,(
% 14.67/2.50 ($false = ((setminusT_lem => sF60)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1288,f6531])).
% 14.67/2.50 thf(f6546,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y0 @ Y2) @ (powerset @ Y1)))))))))) => sF60)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6541,f990])).
% 14.67/2.50 thf(f6549,plain,(
% 14.67/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y0 @ Y2) @ (powerset @ Y1)))))))))) => $true)) = $false) | ($false = sF60)),
% 14.67/2.50 inference(superposition,[],[f6546,f1172])).
% 14.67/2.50 thf(f6553,plain,(
% 14.67/2.50 ($false = sF60) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6549])).
% 14.67/2.50 thf(f6554,plain,(
% 14.67/2.50 ($false = sF60)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6553])).
% 14.67/2.50 thf(f6557,plain,(
% 14.67/2.50 ($false = ((complementT_lem => sF59)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1286,f6554])).
% 14.67/2.50 thf(f6562,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))) => sF59)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6557,f884])).
% 14.67/2.50 thf(f6565,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))) => (setextT => sF58))))),
% 14.67/2.50 inference(forward_demodulation,[],[f6562,f1285])).
% 14.67/2.50 thf(f6568,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))) => (setextT => $true)))) | ($false = sF58)),
% 14.67/2.50 inference(superposition,[],[f6565,f1172])).
% 14.67/2.50 thf(f6578,plain,(
% 14.67/2.50 ($false = sF58) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))) => $true)))),
% 14.67/2.50 inference(boolean_simplification,[],[f6568])).
% 14.67/2.50 thf(f6579,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF58)),
% 14.67/2.50 inference(boolean_simplification,[],[f6578])).
% 14.67/2.50 thf(f6580,plain,(
% 14.67/2.50 ($false = sF58)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6579])).
% 14.67/2.50 thf(f6590,plain,(
% 14.67/2.50 ($false = ((subsetTI => sF57)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1284,f6580])).
% 14.67/2.50 thf(f6598,plain,(
% 14.67/2.50 ($false = sF57)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6590])).
% 14.67/2.50 thf(f6608,plain,(
% 14.67/2.50 ($false = ((powersetTI1 => sF56)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1283,f6598])).
% 14.67/2.50 thf(f6613,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2))))))))))) => sF56)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6608,f1111])).
% 14.67/2.50 thf(f6640,plain,(
% 14.67/2.50 ($false = sF56)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6613])).
% 14.67/2.50 thf(f6650,plain,(
% 14.67/2.50 ($false = ((powersetTE1 => sF55)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1281,f6640])).
% 14.67/2.50 thf(f6657,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2)))))))))))))) => sF55)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6650,f879])).
% 14.67/2.50 thf(f6660,plain,(
% 14.67/2.50 ($false = sF55)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6657])).
% 14.67/2.50 thf(f6670,plain,(
% 14.67/2.50 ($false = ((complementTI1 => sF54)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1280,f6660])).
% 14.67/2.50 thf(f6677,plain,(
% 14.67/2.50 ($false = sF54)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6670])).
% 14.67/2.50 thf(f6687,plain,(
% 14.67/2.50 ($false = ((complementTE1 => sF53)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1278,f6677])).
% 14.67/2.50 thf(f6694,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => sF53)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6687,f974])).
% 14.67/2.50 thf(f6708,plain,(
% 14.67/2.50 ($false = sF53) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0)))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f6694,f1172])).
% 14.67/2.50 thf(f6712,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF53)),
% 14.67/2.50 inference(boolean_simplification,[],[f6708])).
% 14.67/2.50 thf(f6713,plain,(
% 14.67/2.50 ($false = sF53)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6712])).
% 14.67/2.50 thf(f6720,plain,(
% 14.67/2.50 ($false = ((binintersectTELcontra => sF52)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1276,f6713])).
% 14.67/2.50 thf(f6725,plain,(
% 14.67/2.50 ($false = ((binintersectTELcontra => $true))) | ($false = sF52)),
% 14.67/2.50 inference(superposition,[],[f6720,f1172])).
% 14.67/2.50 thf(f6728,plain,(
% 14.67/2.50 ($false = sF52) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6725])).
% 14.67/2.50 thf(f6729,plain,(
% 14.67/2.50 ($false = sF52)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6728])).
% 14.67/2.50 thf(f6733,plain,(
% 14.67/2.50 (((binintersectTERcontra => sF51)) = $false)),
% 14.67/2.50 inference(backward_demodulation,[],[f1274,f6729])).
% 14.67/2.50 thf(f6742,plain,(
% 14.67/2.50 ($false = sF51) | (((binintersectTERcontra => $true)) = $false)),
% 14.67/2.50 inference(superposition,[],[f6733,f1172])).
% 14.67/2.50 thf(f6745,plain,(
% 14.67/2.50 ($false = sF51) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6742])).
% 14.67/2.50 thf(f6746,plain,(
% 14.67/2.50 ($false = sF51)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6745])).
% 14.67/2.50 thf(f6750,plain,(
% 14.67/2.50 ($false = ((contrasubsetT => sF50)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1272,f6746])).
% 14.67/2.50 thf(f6757,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((subset @ Y1 @ (setminus @ Y0 @ Y2)) => ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y1))))))))))))))) => sF50)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6750,f1068])).
% 14.67/2.50 thf(f6780,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((subset @ Y1 @ (setminus @ Y0 @ Y2)) => ((in @ Y3 @ Y2) => (~ (in @ Y3 @ Y1))))))))))))))) => $true))) | ($false = sF50)),
% 14.67/2.50 inference(superposition,[],[f6757,f1172])).
% 14.67/2.50 thf(f6784,plain,(
% 14.67/2.50 ($false = sF50) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6780])).
% 14.67/2.50 thf(f6785,plain,(
% 14.67/2.50 ($false = sF50)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6784])).
% 14.67/2.50 thf(f6792,plain,(
% 14.67/2.50 ($false = ((contrasubsetT1 => sF49)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1271,f6785])).
% 14.67/2.50 thf(f6795,plain,(
% 14.67/2.50 ($false = sF49)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6792])).
% 14.67/2.50 thf(f6805,plain,(
% 14.67/2.50 ($false = ((contrasubsetT2 => sF48)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1270,f6795])).
% 14.67/2.50 thf(f6810,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => (subset @ (setminus @ Y0 @ Y2) @ (setminus @ Y0 @ Y1))))))))))) => sF48)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6805,f965])).
% 14.67/2.50 thf(f6815,plain,(
% 14.67/2.50 (sF48 = $false)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6810])).
% 14.67/2.50 thf(f6825,plain,(
% 14.67/2.50 ($false = ((contrasubsetT3 => sF47)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1269,f6815])).
% 14.67/2.50 thf(f6836,plain,(
% 14.67/2.50 ($false = sF47) | ($false = ((contrasubsetT3 => $true)))),
% 14.67/2.50 inference(superposition,[],[f6825,f1172])).
% 14.67/2.50 thf(f6839,plain,(
% 14.67/2.50 ($false = sF47) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f6836])).
% 14.67/2.50 thf(f6840,plain,(
% 14.67/2.50 ($false = sF47)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6839])).
% 14.67/2.50 thf(f6844,plain,(
% 14.67/2.50 ($false = ((doubleComplementI1 => sF46)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1268,f6840])).
% 14.67/2.50 thf(f6849,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1)))))))))))) => sF46)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6844,f1090])).
% 14.67/2.50 thf(f6861,plain,(
% 14.67/2.50 ($false = sF46)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6849])).
% 14.67/2.50 thf(f6871,plain,(
% 14.67/2.50 ($false = ((doubleComplementE1 => sF45)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1267,f6861])).
% 14.67/2.50 thf(f6880,plain,(
% 14.67/2.50 ($false = sF45)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6871])).
% 14.67/2.50 thf(f6894,plain,(
% 14.67/2.50 ($false = ((doubleComplementSub1 => sF44)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1266,f6880])).
% 14.67/2.50 thf(f6895,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1)))))))) => sF44)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6894,f1063])).
% 14.67/2.50 thf(f6896,plain,(
% 14.67/2.50 ($false = sF44)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6895])).
% 14.67/2.50 thf(f6908,plain,(
% 14.67/2.50 ($false = ((doubleComplementSub2 => sF43)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1265,f6896])).
% 14.67/2.50 thf(f6911,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ (setminus @ Y0 @ Y1)) @ Y1)))))) => sF43)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6908,f1017])).
% 14.67/2.50 thf(f6912,plain,(
% 14.67/2.50 ($false = sF43)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6911])).
% 14.67/2.50 thf(f6924,plain,(
% 14.67/2.50 ($false = ((doubleComplementEq => sF42)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1264,f6912])).
% 14.67/2.50 thf(f6925,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))) => sF42)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6924,f1072])).
% 14.67/2.50 thf(f6930,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))) => $true))) | ($false = sF42)),
% 14.67/2.50 inference(superposition,[],[f6925,f1172])).
% 14.67/2.50 thf(f6934,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF42)),
% 14.67/2.50 inference(boolean_simplification,[],[f6930])).
% 14.67/2.50 thf(f6935,plain,(
% 14.67/2.50 ($false = sF42)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f6934])).
% 14.67/2.50 thf(f6938,plain,(
% 14.67/2.50 ($false = ((complementTnotintersectT => sF41)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1262,f6935])).
% 14.67/2.50 thf(f6943,plain,(
% 14.67/2.50 ($false = sF41)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f6938])).
% 14.67/2.50 thf(f6953,plain,(
% 14.67/2.50 ($false = ((complementImpComplementIntersect => sF40)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1261,f6943])).
% 14.67/2.50 thf(f6958,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))))) => sF40)))),
% 14.67/2.50 inference(forward_demodulation,[],[f6953,f1132])).
% 14.67/2.50 thf(f6963,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))))) => (complementSubsetComplementIntersect => sF39))))),
% 14.67/2.50 inference(forward_demodulation,[],[f6958,f1259])).
% 14.67/2.50 thf(f6995,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))))) => (complementSubsetComplementIntersect => $true)))) | ($false = sF39)),
% 14.67/2.50 inference(superposition,[],[f6963,f1172])).
% 14.67/2.50 thf(f7000,plain,(
% 14.67/2.50 ($false = sF39) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))))) => $true)))),
% 14.67/2.50 inference(boolean_simplification,[],[f6995])).
% 14.67/2.50 thf(f7001,plain,(
% 14.67/2.50 ($false = sF39) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7000])).
% 14.67/2.50 thf(f7002,plain,(
% 14.67/2.50 ($false = sF39)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7001])).
% 14.67/2.50 thf(f7013,plain,(
% 14.67/2.50 ($false = ((complementInPowersetComplementIntersect => sF38)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1258,f7002])).
% 14.67/2.50 thf(f7025,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2)))))))))))) => sF38)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7013,f922])).
% 14.67/2.50 thf(f7033,plain,(
% 14.67/2.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))))))),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7025])).
% 14.67/2.50 thf(f7034,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2)))))))))))) => $true))) | ($false = sF38)),
% 14.67/2.50 inference(superposition,[],[f7025,f1172])).
% 14.67/2.50 thf(f7039,plain,(
% 14.67/2.50 ($false = sF38) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7034])).
% 14.67/2.50 thf(f7040,plain,(
% 14.67/2.50 ($false = sF38)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7039])).
% 14.67/2.50 thf(f7042,plain,(
% 14.67/2.50 ($false = ((contraSubsetComplement => sF37)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1257,f7040])).
% 14.67/2.50 thf(f7045,plain,(
% 14.67/2.50 (woz1_1 = $true)),
% 14.67/2.50 inference(backward_demodulation,[],[f941,f7033])).
% 14.67/2.50 thf(f7048,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))))) => sF37)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7042,f1009])).
% 14.67/2.50 thf(f7049,plain,(
% 14.67/2.50 (sF11 = (($true => sF10)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1218,f7045])).
% 14.67/2.50 thf(f7050,plain,(
% 14.67/2.50 (sF11 = sF10)),
% 14.67/2.50 inference(boolean_simplification,[],[f7049])).
% 14.67/2.50 thf(f7051,plain,(
% 14.67/2.50 (sF11 = ((woz1_2 => sF9)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1217,f7050])).
% 14.67/2.50 thf(f7052,plain,(
% 14.67/2.50 (sF11 = ((woz1_2 => (woz1_3 => sF8))))),
% 14.67/2.50 inference(forward_demodulation,[],[f7051,f1215])).
% 14.67/2.50 thf(f7061,plain,(
% 14.67/2.50 ($false = sF8) | (sF11 = ((woz1_2 => (woz1_3 => $true))))),
% 14.67/2.50 inference(superposition,[],[f7052,f1172])).
% 14.67/2.50 thf(f7069,plain,(
% 14.67/2.50 ($false = sF8) | (sF11 = ((woz1_2 => $true)))),
% 14.67/2.50 inference(boolean_simplification,[],[f7061])).
% 14.67/2.50 thf(f7070,plain,(
% 14.67/2.50 ($false = sF8) | (sF11 = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7069])).
% 14.67/2.50 thf(f7074,plain,(
% 14.67/2.50 ($false = sF37)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7048])).
% 14.67/2.50 thf(f7084,plain,(
% 14.67/2.50 ($false = ((complementTcontraSubset => sF36)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1256,f7074])).
% 14.67/2.50 thf(f7089,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (subset @ Y2 @ (setminus @ Y1 @ Y0))))))))))) => sF36)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7084,f1129])).
% 14.67/2.50 thf(f7090,plain,(
% 14.67/2.50 ($false = ((woz1_4 => sF36)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7089,f1149])).
% 14.67/2.50 thf(f7092,plain,(
% 14.67/2.50 (woz1_4 = $true)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7090])).
% 14.67/2.50 thf(f7093,plain,(
% 14.67/2.50 ($false = ((woz1_4 => $true))) | (sF36 = $false)),
% 14.67/2.50 inference(superposition,[],[f7090,f1172])).
% 14.67/2.50 thf(f7097,plain,(
% 14.67/2.50 ($false = $true) | (sF36 = $false)),
% 14.67/2.50 inference(boolean_simplification,[],[f7093])).
% 14.67/2.50 thf(f7098,plain,(
% 14.67/2.50 (sF36 = $false)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7097])).
% 14.67/2.50 thf(f7102,plain,(
% 14.67/2.50 (sF8 = (($true => sF7)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1214,f7092])).
% 14.67/2.50 thf(f7104,plain,(
% 14.67/2.50 (sF8 = sF7)),
% 14.67/2.50 inference(boolean_simplification,[],[f7102])).
% 14.67/2.50 thf(f7107,plain,(
% 14.67/2.50 ($false = ((binunionTILcontra => sF35)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1255,f7098])).
% 14.67/2.50 thf(f7108,plain,(
% 14.67/2.50 (sF8 = ((woz1_5 => sF6)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1213,f7104])).
% 14.67/2.50 thf(f7110,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1)))))))))))))) => sF35)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7107,f1052])).
% 14.67/2.50 thf(f7121,plain,(
% 14.67/2.50 (sF8 = ((woz1_5 => $true))) | ($false = sF6)),
% 14.67/2.50 inference(superposition,[],[f7108,f1172])).
% 14.67/2.50 thf(f7124,plain,(
% 14.67/2.50 (sF8 = $true) | ($false = sF6)),
% 14.67/2.50 inference(boolean_simplification,[],[f7121])).
% 14.67/2.50 thf(f7140,plain,(
% 14.67/2.50 ($false = sF35) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1)))))))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f7110,f1172])).
% 14.67/2.50 thf(f7144,plain,(
% 14.67/2.50 ($false = sF35) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7140])).
% 14.67/2.50 thf(f7145,plain,(
% 14.67/2.50 ($false = sF35)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7144])).
% 14.67/2.50 thf(f7148,plain,(
% 14.67/2.50 ($false = ((binunionTIRcontra => sF34)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1254,f7145])).
% 14.67/2.50 thf(f7153,plain,(
% 14.67/2.50 ($false = ((binunionTIRcontra => (inIntersectImpInUnion => sF33))))),
% 14.67/2.50 inference(forward_demodulation,[],[f7148,f1253])).
% 14.67/2.50 thf(f7158,plain,(
% 14.67/2.50 ($false = sF33) | ($false = ((binunionTIRcontra => (inIntersectImpInUnion => $true))))),
% 14.67/2.50 inference(superposition,[],[f7153,f1172])).
% 14.67/2.50 thf(f7166,plain,(
% 14.67/2.50 ($false = ((binunionTIRcontra => $true))) | ($false = sF33)),
% 14.67/2.50 inference(boolean_simplification,[],[f7158])).
% 14.67/2.50 thf(f7167,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF33)),
% 14.67/2.50 inference(boolean_simplification,[],[f7166])).
% 14.67/2.50 thf(f7168,plain,(
% 14.67/2.50 ($false = sF33)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7167])).
% 14.67/2.50 thf(f7177,plain,(
% 14.67/2.50 ($false = ((inIntersectImpInUnion2 => sF32)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1252,f7168])).
% 14.67/2.50 thf(f7192,plain,(
% 14.67/2.50 ($false = sF32)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7177])).
% 14.67/2.50 thf(f7202,plain,(
% 14.67/2.50 ($false = ((inIntersectImpInIntersectUnions => sF31)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1250,f7192])).
% 14.67/2.50 thf(f7211,plain,(
% 14.67/2.50 ($false = sF31) | ($false = ((inIntersectImpInIntersectUnions => $true)))),
% 14.67/2.50 inference(superposition,[],[f7202,f1172])).
% 14.67/2.50 thf(f7214,plain,(
% 14.67/2.50 ($false = sF31) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7211])).
% 14.67/2.50 thf(f7215,plain,(
% 14.67/2.50 ($false = sF31)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7214])).
% 14.67/2.50 thf(f7221,plain,(
% 14.67/2.50 ($false = ((intersectInPowersetIntersectUnions => sF30)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1248,f7215])).
% 14.67/2.50 thf(f7224,plain,(
% 14.67/2.50 ($false = ((intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => sF29))))),
% 14.67/2.50 inference(forward_demodulation,[],[f7221,f1246])).
% 14.67/2.50 thf(f7227,plain,(
% 14.67/2.50 ($false = ((intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => $true)))) | ($false = sF29)),
% 14.67/2.50 inference(superposition,[],[f7224,f1172])).
% 14.67/2.50 thf(f7237,plain,(
% 14.67/2.50 ($false = sF29) | ($false = ((intersectInPowersetIntersectUnions => $true)))),
% 14.67/2.50 inference(boolean_simplification,[],[f7227])).
% 14.67/2.50 thf(f7238,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF29)),
% 14.67/2.50 inference(boolean_simplification,[],[f7237])).
% 14.67/2.50 thf(f7239,plain,(
% 14.67/2.50 ($false = sF29)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7238])).
% 14.67/2.50 thf(f7251,plain,(
% 14.67/2.50 ($false = ((inComplementUnionImpInComplement1 => sF28)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1244,f7239])).
% 14.67/2.50 thf(f7263,plain,(
% 14.67/2.50 ($false = sF28)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7251])).
% 14.67/2.50 thf(f7264,plain,(
% 14.67/2.50 (inComplementUnionImpInComplement1 = $true)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7251])).
% 14.67/2.50 thf(f7273,plain,(
% 14.67/2.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))))),
% 14.67/2.50 inference(backward_demodulation,[],[f929,f7264])).
% 14.67/2.50 thf(f7277,plain,(
% 14.67/2.50 ($false = ((binunionTE => sF27)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1243,f7263])).
% 14.67/2.50 thf(f7280,plain,(
% 14.67/2.50 (demorgan2a1 = $true)),
% 14.67/2.50 inference(backward_demodulation,[],[f1045,f7273])).
% 14.67/2.50 thf(f7281,plain,(
% 14.67/2.50 (sF26 = (($true => sF25)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1239,f7280])).
% 14.67/2.50 thf(f7282,plain,(
% 14.67/2.50 (sF26 = sF25)),
% 14.67/2.50 inference(boolean_simplification,[],[f7281])).
% 14.67/2.50 thf(f7283,plain,(
% 14.67/2.50 (sF26 = ((complementUnionInPowersetComplement => sF24)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7282,f1238])).
% 14.67/2.50 thf(f7284,plain,(
% 14.67/2.50 (((binunionTEcontra => (complementUnionInPowersetComplement => sF24))) = sF27)),
% 14.67/2.50 inference(backward_demodulation,[],[f1241,f7283])).
% 14.67/2.50 thf(f7287,plain,(
% 14.67/2.50 ($false = sF27) | ($false = ((binunionTE => $true)))),
% 14.67/2.50 inference(superposition,[],[f7277,f1172])).
% 14.67/2.50 thf(f7290,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF27)),
% 14.67/2.50 inference(boolean_simplification,[],[f7287])).
% 14.67/2.50 thf(f7291,plain,(
% 14.67/2.50 ($false = sF27)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7290])).
% 14.67/2.50 thf(f7294,plain,(
% 14.67/2.50 ($false = ((binunionTEcontra => (complementUnionInPowersetComplement => sF24))))),
% 14.67/2.50 inference(backward_demodulation,[],[f7284,f7291])).
% 14.67/2.50 thf(f7314,plain,(
% 14.67/2.50 ($false = sF24) | ($false = ((binunionTEcontra => (complementUnionInPowersetComplement => $true))))),
% 14.67/2.50 inference(superposition,[],[f7294,f1172])).
% 14.67/2.50 thf(f7320,plain,(
% 14.67/2.50 ($false = ((binunionTEcontra => $true))) | ($false = sF24)),
% 14.67/2.50 inference(boolean_simplification,[],[f7314])).
% 14.67/2.50 thf(f7321,plain,(
% 14.67/2.50 ($false = sF24) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7320])).
% 14.67/2.50 thf(f7322,plain,(
% 14.67/2.50 ($false = sF24)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7321])).
% 14.67/2.50 thf(f7333,plain,(
% 14.67/2.50 ($false = ((demorgan2a2 => sF23)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1237,f7322])).
% 14.67/2.50 thf(f7359,plain,(
% 14.67/2.50 ($false = ((demorgan2a2 => $true))) | ($false = sF23)),
% 14.67/2.50 inference(superposition,[],[f7333,f1172])).
% 14.67/2.50 thf(f7364,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF23)),
% 14.67/2.50 inference(boolean_simplification,[],[f7359])).
% 14.67/2.50 thf(f7365,plain,(
% 14.67/2.50 ($false = sF23)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7364])).
% 14.67/2.50 thf(f7371,plain,(
% 14.67/2.50 ($false = ((demorgan1a => sF22)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1235,f7365])).
% 14.67/2.50 thf(f7372,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))) => (in @ Y3 @ (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))))))) => sF22)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7371,f952])).
% 14.67/2.50 thf(f7448,plain,(
% 14.67/2.50 ($false = sF22) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))) => (in @ Y3 @ (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f7372,f1172])).
% 14.67/2.50 thf(f7451,plain,(
% 14.67/2.50 ($false = sF22) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7448])).
% 14.67/2.50 thf(f7452,plain,(
% 14.67/2.50 ($false = sF22)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7451])).
% 14.67/2.50 thf(f7458,plain,(
% 14.67/2.50 (((demorgan1b => sF21)) = $false)),
% 14.67/2.50 inference(backward_demodulation,[],[f1233,f7452])).
% 14.67/2.50 thf(f7463,plain,(
% 14.67/2.50 ($false = ((demorgan1b => $true))) | ($false = sF21)),
% 14.67/2.50 inference(superposition,[],[f7458,f1172])).
% 14.67/2.50 thf(f7466,plain,(
% 14.67/2.50 ($false = sF21) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7463])).
% 14.67/2.50 thf(f7467,plain,(
% 14.67/2.50 ($false = sF21)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7466])).
% 14.67/2.50 thf(f7471,plain,(
% 14.67/2.50 ($false = ((demorgan1 => sF20)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1231,f7467])).
% 14.67/2.50 thf(f7484,plain,(
% 14.67/2.50 ($false = sF20) | ($false = ((demorgan1 => $true)))),
% 14.67/2.50 inference(superposition,[],[f7471,f1172])).
% 14.67/2.50 thf(f7488,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF20)),
% 14.67/2.50 inference(boolean_simplification,[],[f7484])).
% 14.67/2.50 thf(f7489,plain,(
% 14.67/2.50 ($false = sF20)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7488])).
% 14.67/2.50 thf(f7492,plain,(
% 14.67/2.50 ($false = ((demorgan2a => sF19)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1230,f7489])).
% 14.67/2.50 thf(f7499,plain,(
% 14.67/2.50 (sF19 = $false)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7492])).
% 14.67/2.50 thf(f7509,plain,(
% 14.67/2.50 ($false = ((demorgan2b2 => sF18)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1228,f7499])).
% 14.67/2.50 thf(f7518,plain,(
% 14.67/2.50 ($false = ((demorgan2b2 => $true))) | ($false = sF18)),
% 14.67/2.50 inference(superposition,[],[f7509,f1172])).
% 14.67/2.50 thf(f7521,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF18)),
% 14.67/2.50 inference(boolean_simplification,[],[f7518])).
% 14.67/2.50 thf(f7522,plain,(
% 14.67/2.50 ($false = sF18)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7521])).
% 14.67/2.50 thf(f7526,plain,(
% 14.67/2.50 ($false = ((demorgan2b => sF17)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1227,f7522])).
% 14.67/2.50 thf(f7531,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (binintersect @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))))))))))))))) => sF17)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7526,f976])).
% 14.67/2.50 thf(f7565,plain,(
% 14.67/2.50 ($false = sF17)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7531])).
% 14.67/2.50 thf(f7575,plain,(
% 14.67/2.50 ($false = ((demorgan2 => sF16)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1226,f7565])).
% 14.67/2.50 thf(f7580,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((setminus @ Y1 @ (binunion @ Y0 @ Y2)) = (binintersect @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ Y2))))))))))) => sF16)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7575,f989])).
% 14.67/2.50 thf(f7583,plain,(
% 14.67/2.50 ($false = sF16) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((setminus @ Y1 @ (binunion @ Y0 @ Y2)) = (binintersect @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ Y2))))))))))) => $true)))),
% 14.67/2.50 inference(superposition,[],[f7580,f1172])).
% 14.67/2.50 thf(f7586,plain,(
% 14.67/2.50 ($false = sF16) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7583])).
% 14.67/2.50 thf(f7587,plain,(
% 14.67/2.50 ($false = sF16)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7586])).
% 14.67/2.50 thf(f7591,plain,(
% 14.67/2.50 ($false = ((woz13rule0 => sF15)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1225,f7587])).
% 14.67/2.50 thf(f7596,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y0 @ Y2)) => (in @ Y3 @ Y1)))))))))))) => sF15)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7591,f1169])).
% 14.67/2.50 thf(f7603,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y0 @ Y2)) => (in @ Y3 @ Y1)))))))))))) => $true))) | ($false = sF15)),
% 14.67/2.50 inference(superposition,[],[f7596,f1172])).
% 14.67/2.50 thf(f7606,plain,(
% 14.67/2.50 ($false = sF15) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7603])).
% 14.67/2.50 thf(f7607,plain,(
% 14.67/2.50 ($false = sF15)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7606])).
% 14.67/2.50 thf(f7611,plain,(
% 14.67/2.50 ($false = ((woz13rule1 => sF14)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1224,f7607])).
% 14.67/2.50 thf(f7616,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3))))))))))))) => sF14)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7611,f1080])).
% 14.67/2.50 thf(f7621,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y0 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3))))))))))))) => $true))) | ($false = sF14)),
% 14.67/2.50 inference(superposition,[],[f7616,f1172])).
% 14.67/2.50 thf(f7626,plain,(
% 14.67/2.50 ($false = sF14) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7621])).
% 14.67/2.50 thf(f7627,plain,(
% 14.67/2.50 ($false = sF14)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7626])).
% 14.67/2.50 thf(f7635,plain,(
% 14.67/2.50 ($false = ((woz13rule2 => sF13)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1223,f7627])).
% 14.67/2.50 thf(f7636,plain,(
% 14.67/2.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y0 @ Y2) @ Y3))))))))))))) => sF13)) = $false)),
% 14.67/2.50 inference(forward_demodulation,[],[f7635,f1105])).
% 14.67/2.50 thf(f7637,plain,(
% 14.67/2.50 (sF13 = $false)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7636])).
% 14.67/2.50 thf(f7651,plain,(
% 14.67/2.50 ($false = ((woz13rule3 => sF12)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1221,f7637])).
% 14.67/2.50 thf(f7654,plain,(
% 14.67/2.50 ($false = sF12) | ($false = ((woz13rule3 => $true)))),
% 14.67/2.50 inference(superposition,[],[f7651,f1172])).
% 14.67/2.50 thf(f7659,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF12)),
% 14.67/2.50 inference(boolean_simplification,[],[f7654])).
% 14.67/2.50 thf(f7660,plain,(
% 14.67/2.50 ($false = sF12)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7659])).
% 14.67/2.50 thf(f7668,plain,(
% 14.67/2.50 (((woz13rule4 => sF11)) = $false)),
% 14.67/2.50 inference(backward_demodulation,[],[f1220,f7660])).
% 14.67/2.50 thf(f7671,plain,(
% 14.67/2.50 ($false = sF11) | ($false = ((woz13rule4 => $true)))),
% 14.67/2.50 inference(superposition,[],[f7668,f1172])).
% 14.67/2.50 thf(f7674,plain,(
% 14.67/2.50 ($false = sF11) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7671])).
% 14.67/2.50 thf(f7675,plain,(
% 14.67/2.50 ($false = sF11)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7674])).
% 14.67/2.50 thf(f7683,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF8)),
% 14.67/2.50 inference(backward_demodulation,[],[f7070,f7675])).
% 14.67/2.50 thf(f7685,plain,(
% 14.67/2.50 ($false = sF8)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7683])).
% 14.67/2.50 thf(f7694,plain,(
% 14.67/2.50 ($false = sF6) | ($false = $true)),
% 14.67/2.50 inference(backward_demodulation,[],[f7124,f7685])).
% 14.67/2.50 thf(f7699,plain,(
% 14.67/2.50 ($false = sF6)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7694])).
% 14.67/2.50 thf(f7711,plain,(
% 14.67/2.50 ($false = ((breln1all2 => sF5)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1211,f7699])).
% 14.67/2.50 thf(f7716,plain,(
% 14.67/2.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y1)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3)))))))))))) => sF5)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7711,f1643])).
% 14.67/2.50 thf(f7717,plain,(
% 14.67/2.50 ($false = ((breln1all1 => sF5)))),
% 14.67/2.50 inference(forward_demodulation,[],[f7716,f1647])).
% 14.67/2.50 thf(f7718,plain,(
% 14.67/2.50 ($false = ((breln1all1 => (breln1SetBreln1 => sF4))))),
% 14.67/2.50 inference(forward_demodulation,[],[f7717,f1209])).
% 14.67/2.50 thf(f7747,plain,(
% 14.67/2.50 (breln1all1 = $true)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7718])).
% 14.67/2.50 thf(f7748,plain,(
% 14.67/2.50 (((breln1all1 => (breln1SetBreln1 => $true))) = $false) | ($false = sF4)),
% 14.67/2.50 inference(superposition,[],[f7718,f1172])).
% 14.67/2.50 thf(f7754,plain,(
% 14.67/2.50 ($false = sF4) | ($false = ((breln1all1 => $true)))),
% 14.67/2.50 inference(boolean_simplification,[],[f7748])).
% 14.67/2.50 thf(f7755,plain,(
% 14.67/2.50 ($false = sF4) | ($false = $true)),
% 14.67/2.50 inference(boolean_simplification,[],[f7754])).
% 14.67/2.50 thf(f7756,plain,(
% 14.67/2.50 ($false = sF4)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7755])).
% 14.67/2.50 thf(f7763,plain,(
% 14.67/2.50 ($false = ((choice2fnsingleton => sF3)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1207,f7756])).
% 14.67/2.50 thf(f7774,plain,(
% 14.67/2.50 (sF2 = (($true => sF1)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1204,f7747])).
% 14.67/2.50 thf(f7776,plain,(
% 14.67/2.50 (sF2 = sF1)),
% 14.67/2.50 inference(boolean_simplification,[],[f7774])).
% 14.67/2.50 thf(f7784,plain,(
% 14.67/2.50 (sF3 = ((setOfPairsIsBReln1 => sF1)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1205,f7776])).
% 14.67/2.50 thf(f7788,plain,(
% 14.67/2.50 ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ Y1 @ Y0) @ (cartprod @ Y1 @ Y1)))))) => sF1)) = sF3)),
% 14.67/2.50 inference(forward_demodulation,[],[f7784,f1661])).
% 14.67/2.50 thf(f7797,plain,(
% 14.67/2.50 ($false = sF3)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7763])).
% 14.67/2.50 thf(f7806,plain,(
% 14.67/2.50 ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ Y1 @ Y1 @ Y0) @ (cartprod @ Y1 @ Y1)))))) => sF1)))),
% 14.67/2.50 inference(backward_demodulation,[],[f7788,f7797])).
% 14.67/2.50 thf(f7833,plain,(
% 14.67/2.50 ($false = sF1)),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f7806])).
% 14.67/2.50 thf(f7844,plain,(
% 14.67/2.50 ($false = ((subbreln1 => sF0)))),
% 14.67/2.50 inference(backward_demodulation,[],[f1203,f7833])).
% 14.67/2.50 thf(f7857,plain,(
% 14.67/2.50 ($false = ((subbreln1 => $true))) | ($false = sF0)),
% 14.67/2.50 inference(superposition,[],[f7844,f1172])).
% 14.67/2.50 thf(f7861,plain,(
% 14.67/2.50 ($false = $true) | ($false = sF0)),
% 14.67/2.50 inference(boolean_simplification,[],[f7857])).
% 14.67/2.50 thf(f7862,plain,(
% 14.67/2.50 ($false = sF0)),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f7861])).
% 14.67/2.50 thf(f7867,plain,(
% 14.67/2.50 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ Y1)))))))) => (Y1 = Y2)))))))))))))),
% 14.67/2.50 inference(backward_demodulation,[],[f1684,f7862])).
% 14.67/2.50 thf(f8085,plain,(
% 14.67/2.50 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ Y1)))))))) => (Y1 = Y2)))))))))) @ sK292)))),
% 14.67/2.50 inference(sigma_proxy_clausification,[],[f7867])).
% 14.67/2.50 thf(f8088,plain,(
% 14.67/2.50 ($false = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK292 @ sK292)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ sK292 @ sK292)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK292) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK292) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => (in @ (kpair @ Y2 @ Y3) @ Y0)))))))) => (Y0 = Y1)))))))))))),
% 14.67/2.50 inference(beta-eta_normalization,[],[f8085])).
% 14.67/2.50 thf(f8089,plain,(
% 14.67/2.50 ($false = (((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK292 @ sK292)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ sK292 @ sK292)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK292) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK292) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => (in @ (kpair @ Y2 @ Y3) @ Y0)))))))) => (Y0 = Y1)))))))) @ sK293)))),
% 14.67/2.50 inference(sigma_proxy_clausification,[],[f8088])).
% 14.67/2.50 thf(f8091,plain,(
% 14.67/2.50 ($false = (((subset @ sK293 @ (cartprod @ sK292 @ sK292)) => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK292 @ sK292)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK292) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => ((in @ (kpair @ Y1 @ Y2) @ sK293) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK292) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ sK293)))))))) => (sK293 = Y0)))))))))),
% 14.67/2.50 inference(beta-eta_normalization,[],[f8089])).
% 14.67/2.50 thf(f8093,plain,(
% 14.67/2.50 ($false = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK292 @ sK292)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK292) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => ((in @ (kpair @ Y1 @ Y2) @ sK293) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK292) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ sK293)))))))) => (sK293 = Y0))))))))),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f8091])).
% 14.67/2.50 thf(f8094,plain,(
% 14.67/2.50 ($true = ((subset @ sK293 @ (cartprod @ sK292 @ sK292))))),
% 14.67/2.50 inference(imp_proxy_clausification,[],[f8091])).
% 14.67/2.50 thf(f8112,plain,(
% 14.67/2.50 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3)))))))))))) @ X1)))) )),
% 14.67/2.50 inference(pi_proxy_clausification,[],[f6098])).
% 14.67/2.50 thf(f8113,plain,(
% 14.67/2.50 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ X1)))))))) => (X1 = Y2)))))))))))) = $true)) )),
% 14.67/2.50 inference(beta-eta_normalization,[],[f8112])).
% 14.67/2.50 thf(f8114,plain,(
% 14.67/2.50 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ X1)))))))) => (X1 = Y2)))))))))) @ X2)))) )),
% 14.67/2.50 inference(pi_proxy_clausification,[],[f8113])).
% 14.67/2.50 thf(f8115,plain,(
% 14.67/2.50 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ (cartprod @ X2 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X2 @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => (in @ (kpair @ Y2 @ Y3) @ X1)))))))) => (X1 = Y1)))))))))) = $true)) )),
% 14.67/2.50 inference(beta-eta_normalization,[],[f8114])).
% 14.67/2.50 thf(f8118,plain,(
% 14.67/2.50 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((subset @ X1 @ (cartprod @ X2 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X2 @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => (in @ (kpair @ Y2 @ Y3) @ X1)))))))) => (X1 = Y1)))))))) @ X3)))) )),
% 14.67/2.50 inference(pi_proxy_clausification,[],[f8115])).
% 14.67/2.50 thf(f8119,plain,(
% 14.67/2.50 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((subset @ X1 @ (cartprod @ X2 @ X3)) => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X2 @ X3)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X3) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X3) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ X1)))))))) => (X1 = Y0)))))))))) )),
% 14.67/2.50 inference(beta-eta_normalization,[],[f8118])).
% 14.67/2.50 thf(f9743,plain,(
% 14.67/2.50 ($true = (($true => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK292 @ sK292)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK292) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => ((in @ (kpair @ Y1 @ Y2) @ sK293) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK292) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ sK293)))))))) => (sK293 = Y0)))))))))),
% 14.67/2.50 inference(superposition,[],[f8119,f8094])).
% 14.67/2.50 thf(f9762,plain,(
% 14.67/2.50 ($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK292 @ sK292)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK292) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => ((in @ (kpair @ Y1 @ Y2) @ sK293) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK292) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK292) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ sK293)))))))) => (sK293 = Y0))))))))),
% 14.67/2.50 inference(boolean_simplification,[],[f9743])).
% 14.67/2.50 thf(f9771,plain,(
% 14.67/2.50 ($false = $true)),
% 14.67/2.50 inference(forward_demodulation,[],[f9762,f8093])).
% 14.67/2.50 thf(f9772,plain,(
% 14.67/2.50 $false),
% 14.67/2.50 inference(trivial_inequality_removal,[],[f9771])).
% 14.67/2.50 % SZS output end Proof for theBenchmark
% 14.67/2.50 % (4075915)------------------------------
% 14.67/2.50 % (4075915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.67/2.50 % (4075915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.67/2.50 % (4075915)CaDiCaL version: 2.1.3
% 14.67/2.50 % (4075915)Termination reason: Refutation
% 14.67/2.50 % (4075915)Time elapsed: 0.734 s
% 14.67/2.50 % (4075915)Peak memory usage: 23 MB
% 14.67/2.50 % (4075915)Instructions burned: 1375 (million)
% 14.67/2.50 % (4075570)Success in time 2.075 s
% 14.67/2.50 % Vampire exiting
%------------------------------------------------------------------------------