%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU772^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:31:16 AM UTC 2026
% Result : Theorem 21.36s 3.51s
% Output : Refutation 21.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU772^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 % Computer : n005.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 14:24:02 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.34 Running higher-order theorem proving
% 0.33/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.33/0.65 % (1741486)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.33/0.65 % (1741496)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=3110098128: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)
% 1.33/0.65 % (1741499)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.33/0.65 % (1741499)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
% 1.33/0.65 % (1741494)lrs+10_16_si=on:nwc=1.5:random_seed=968501436:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.33/0.65 % (1741495)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=737997327:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.33/0.65 % (1741493)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3045962425:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.33/0.65 % (1741497)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1529203384:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.33/0.65 % (1741498)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4127304767:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.33/0.65 % (1741499)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=1994680092:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.33/0.65 % (1741495)Instruction limit reached!
% 1.33/0.65 % (1741495)------------------------------
% 1.33/0.65 % (1741495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.65 % (1741495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.65 % (1741495)CaDiCaL version: 2.1.3
% 1.33/0.65 % (1741495)Termination reason: Instruction limit
% 1.33/0.65 % (1741495)Termination phase: shuffling
% 1.33/0.65 % (1741495)Time elapsed: 0.004 s
% 1.33/0.65 % (1741495)Peak memory usage: 10 MB
% 1.33/0.65 % (1741495)Instructions burned: 4 (million)
% 1.33/0.65 % (1741494)Instruction limit reached!
% 1.33/0.65 % (1741494)------------------------------
% 1.33/0.65 % (1741494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.65 % (1741494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.65 % (1741494)CaDiCaL version: 2.1.3
% 1.33/0.65 % (1741494)Termination reason: Instruction limit
% 1.33/0.65 % (1741494)Termination phase: shuffling
% 1.33/0.65 % (1741494)Time elapsed: 0.016 s
% 1.33/0.65 % (1741494)Peak memory usage: 10 MB
% 1.33/0.65 % (1741494)Instructions burned: 19 (million)
% 1.33/0.65 % (1741497)Instruction limit reached!
% 1.33/0.65 % (1741497)------------------------------
% 1.33/0.65 % (1741497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.65 % (1741497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.65 % (1741497)CaDiCaL version: 2.1.3
% 1.33/0.65 % (1741497)Termination reason: Instruction limit
% 1.33/0.65 % (1741497)Termination phase: shuffling
% 1.33/0.65 % (1741497)Time elapsed: 0.020 s
% 1.33/0.65 % (1741497)Peak memory usage: 10 MB
% 1.33/0.65 % (1741497)Instructions burned: 24 (million)
% 1.33/0.65 % (1741507)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2267886756:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.33/0.65 % (1741507)Instruction limit reached!
% 1.33/0.65 % (1741507)------------------------------
% 1.33/0.65 % (1741507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.33/0.65 % (1741507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.33/0.65 % (1741507)CaDiCaL version: 2.1.3
% 1.33/0.65 % (1741507)Termination reason: Instruction limit
% 1.33/0.65 % (1741507)Termination phase: shuffling
% 1.33/0.65 % (1741507)Time elapsed: 0.002 s
% 1.33/0.65 % (1741507)Peak memory usage: 10 MB
% 1.33/0.65 % (1741507)Instructions burned: 4 (million)
% 1.33/0.65 % (1741509)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.73/0.71 % (1741508)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=520266246:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.73/0.71 % (1741508)Instruction limit reached!
% 1.73/0.71 % (1741508)------------------------------
% 1.73/0.71 % (1741508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.71 % (1741508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.71 % (1741508)CaDiCaL version: 2.1.3
% 1.73/0.71 % (1741508)Termination reason: Instruction limit
% 1.73/0.71 % (1741508)Termination phase: shuffling
% 1.73/0.71 % (1741508)Time elapsed: 0.005 s
% 1.73/0.71 % (1741508)Peak memory usage: 10 MB
% 1.73/0.71 % (1741508)Instructions burned: 6 (million)
% 1.73/0.71 % (1741509)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3625259784:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.73/0.71 % (1741511)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4006910557:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.73/0.71 % (1741498)Instruction limit reached!
% 1.73/0.71 % (1741498)------------------------------
% 1.73/0.71 % (1741498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.71 % (1741498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.71 % (1741498)CaDiCaL version: 2.1.3
% 1.73/0.71 % (1741498)Termination reason: Instruction limit
% 1.73/0.71 % (1741498)Termination phase: Preprocessing 3
% 1.73/0.71 % (1741498)Time elapsed: 0.061 s
% 1.73/0.71 % (1741498)Peak memory usage: 12 MB
% 1.73/0.71 % (1741498)Instructions burned: 75 (million)
% 1.73/0.71 % (1741509)Instruction limit reached!
% 1.73/0.71 % (1741509)------------------------------
% 1.73/0.71 % (1741509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.71 % (1741509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.71 % (1741509)CaDiCaL version: 2.1.3
% 1.73/0.71 % (1741509)Termination reason: Instruction limit
% 1.73/0.71 % (1741509)Termination phase: shuffling
% 1.73/0.71 % (1741509)Time elapsed: 0.007 s
% 1.73/0.71 % (1741509)Peak memory usage: 10 MB
% 1.73/0.71 % (1741509)Instructions burned: 8 (million)
% 1.73/0.71 % (1741511)Instruction limit reached!
% 1.73/0.71 % (1741511)------------------------------
% 1.73/0.71 % (1741511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.71 % (1741511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.71 % (1741511)CaDiCaL version: 2.1.3
% 1.73/0.71 % (1741511)Termination reason: Instruction limit
% 1.73/0.71 % (1741511)Termination phase: shuffling
% 1.73/0.71 % (1741511)Time elapsed: 0.012 s
% 1.73/0.71 % (1741511)Peak memory usage: 10 MB
% 1.73/0.71 % (1741511)Instructions burned: 12 (million)
% 1.73/0.71 % (1741493)Instruction limit reached!
% 1.73/0.71 % (1741493)------------------------------
% 1.73/0.71 % (1741493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.71 % (1741493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.71 % (1741493)CaDiCaL version: 2.1.3
% 1.73/0.71 % (1741493)Termination reason: Instruction limit
% 1.73/0.71 % (1741493)Termination phase: Preprocessing 3
% 1.73/0.71 % (1741493)Time elapsed: 0.073 s
% 1.73/0.71 % (1741493)Peak memory usage: 12 MB
% 1.73/0.71 % (1741493)Instructions burned: 87 (million)
% 1.73/0.71 % (1741514)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
% 1.73/0.71 % (1741514)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.73/0.71 % (1741514)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3594217706:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.73/0.71 % (1741518)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.73/0.71 % (1741518)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=3114990085:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.73/0.77 % (1741518)Instruction limit reached!
% 1.73/0.77 % (1741518)------------------------------
% 1.73/0.77 % (1741518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.77 % (1741518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.77 % (1741518)CaDiCaL version: 2.1.3
% 1.73/0.77 % (1741518)Termination reason: Instruction limit
% 1.73/0.77 % (1741518)Termination phase: shuffling
% 1.73/0.77 % (1741518)Time elapsed: 0.002 s
% 1.73/0.77 % (1741518)Peak memory usage: 10 MB
% 1.73/0.77 % (1741518)Instructions burned: 4 (million)
% 1.73/0.77 % (1741517)lrs+10_1_si=on:cs=on:random_seed=2503669851:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.73/0.77 % (1741516)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=2683479039:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.73/0.77 % (1741517)Instruction limit reached!
% 1.73/0.77 % (1741517)------------------------------
% 1.73/0.77 % (1741517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.77 % (1741517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.77 % (1741517)CaDiCaL version: 2.1.3
% 1.73/0.77 % (1741517)Termination reason: Instruction limit
% 1.73/0.77 % (1741517)Termination phase: shuffling
% 1.73/0.77 % (1741517)Time elapsed: 0.007 s
% 1.73/0.77 % (1741517)Peak memory usage: 10 MB
% 1.73/0.77 % (1741517)Instructions burned: 8 (million)
% 1.73/0.77 % (1741519)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=410387415:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.73/0.77 % (1741514)Instruction limit reached!
% 1.73/0.77 % (1741514)------------------------------
% 1.73/0.77 % (1741514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.77 % (1741514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.77 % (1741514)CaDiCaL version: 2.1.3
% 1.73/0.77 % (1741514)Termination reason: Instruction limit
% 1.73/0.77 % (1741514)Termination phase: shuffling
% 1.73/0.77 % (1741514)Time elapsed: 0.026 s
% 1.73/0.77 % (1741514)Peak memory usage: 11 MB
% 1.73/0.77 % (1741514)Instructions burned: 29 (million)
% 1.73/0.77 % (1741499)Instruction limit reached!
% 1.73/0.77 % (1741499)------------------------------
% 1.73/0.77 % (1741499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.77 % (1741499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.77 % (1741499)CaDiCaL version: 2.1.3
% 1.73/0.77 % (1741499)Termination reason: Instruction limit
% 1.73/0.77 % (1741499)Termination phase: Property scanning
% 1.73/0.77 % (1741499)Time elapsed: 0.125 s
% 1.73/0.77 % (1741499)Peak memory usage: 13 MB
% 1.73/0.77 % (1741499)Instructions burned: 157 (million)
% 1.73/0.77 % (1741522)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=168977477:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.73/0.77 % (1741525)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3460789166:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.73/0.77 % (1741527)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3270762724:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.73/0.77 % (1741519)Instruction limit reached!
% 1.73/0.77 % (1741519)------------------------------
% 1.73/0.77 % (1741519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.77 % (1741519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.77 % (1741519)CaDiCaL version: 2.1.3
% 1.73/0.77 % (1741519)Termination reason: Instruction limit
% 1.73/0.77 % (1741519)Termination phase: Property scanning
% 1.73/0.77 % (1741519)Time elapsed: 0.031 s
% 1.73/0.77 % (1741519)Peak memory usage: 11 MB
% 1.73/0.77 % (1741519)Instructions burned: 38 (million)
% 1.73/0.77 % (1741527)Instruction limit reached!
% 1.73/0.77 % (1741527)------------------------------
% 1.73/0.77 % (1741527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.77 % (1741527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.77 % (1741527)CaDiCaL version: 2.1.3
% 1.73/0.77 % (1741527)Termination reason: Instruction limit
% 1.73/0.77 % (1741527)Termination phase: shuffling
% 1.73/0.77 % (1741527)Time elapsed: 0.010 s
% 2.19/0.84 % (1741527)Peak memory usage: 10 MB
% 2.19/0.84 % (1741527)Instructions burned: 15 (million)
% 2.19/0.84 % (1741525)Instruction limit reached!
% 2.19/0.84 % (1741525)------------------------------
% 2.19/0.84 % (1741525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.84 % (1741525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.84 % (1741525)CaDiCaL version: 2.1.3
% 2.19/0.84 % (1741525)Termination reason: Instruction limit
% 2.19/0.84 % (1741525)Termination phase: shuffling
% 2.19/0.84 % (1741525)Time elapsed: 0.021 s
% 2.19/0.84 % (1741525)Peak memory usage: 10 MB
% 2.19/0.84 % (1741525)Instructions burned: 25 (million)
% 2.19/0.84 % (1741528)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=705109687:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.19/0.84 % (1741533)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1678287453:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 2.19/0.84 % (1741516)Instruction limit reached!
% 2.19/0.84 % (1741516)------------------------------
% 2.19/0.84 % (1741516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.84 % (1741516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.84 % (1741516)CaDiCaL version: 2.1.3
% 2.19/0.84 % (1741516)Termination reason: Instruction limit
% 2.19/0.84 % (1741516)Termination phase: Property scanning
% 2.19/0.84 % (1741516)Time elapsed: 0.070 s
% 2.19/0.84 % (1741516)Peak memory usage: 12 MB
% 2.19/0.84 % (1741516)Instructions burned: 86 (million)
% 2.19/0.84 % (1741533)Instruction limit reached!
% 2.19/0.84 % (1741533)------------------------------
% 2.19/0.84 % (1741533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.84 % (1741533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.84 % (1741533)CaDiCaL version: 2.1.3
% 2.19/0.84 % (1741533)Termination reason: Instruction limit
% 2.19/0.84 % (1741533)Termination phase: shuffling
% 2.19/0.84 % (1741533)Time elapsed: 0.002 s
% 2.19/0.84 % (1741533)Peak memory usage: 10 MB
% 2.19/0.84 % (1741533)Instructions burned: 3 (million)
% 2.19/0.84 % (1741532)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2139344811:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/14Mi)
% 2.19/0.84 % (1741532)Instruction limit reached!
% 2.19/0.84 % (1741532)------------------------------
% 2.19/0.84 % (1741532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.84 % (1741532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.84 % (1741532)CaDiCaL version: 2.1.3
% 2.19/0.84 % (1741532)Termination reason: Instruction limit
% 2.19/0.84 % (1741532)Termination phase: shuffling
% 2.19/0.84 % (1741532)Time elapsed: 0.013 s
% 2.19/0.84 % (1741532)Peak memory usage: 10 MB
% 2.19/0.84 % (1741532)Instructions burned: 14 (million)
% 2.19/0.84 % (1741534)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2311667073:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.19/0.84 % (1741537)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1985127360:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.19/0.84 % (1741538)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2045877467:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.19/0.84 % (1741537)Instruction limit reached!
% 2.19/0.84 % (1741537)------------------------------
% 2.19/0.84 % (1741537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.84 % (1741537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.84 % (1741537)CaDiCaL version: 2.1.3
% 2.19/0.84 % (1741537)Termination reason: Instruction limit
% 2.19/0.84 % (1741537)Termination phase: shuffling
% 2.19/0.84 % (1741537)Time elapsed: 0.015 s
% 2.19/0.84 % (1741537)Peak memory usage: 10 MB
% 2.19/0.84 % (1741537)Instructions burned: 23 (million)
% 2.19/0.84 % (1741534)Instruction limit reached!
% 2.19/0.84 % (1741534)------------------------------
% 2.19/0.84 % (1741534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.84 % (1741534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.84 % (1741534)CaDiCaL version: 2.1.3
% 2.62/0.93 % (1741534)Termination reason: Instruction limit
% 2.62/0.93 % (1741534)Termination phase: shuffling
% 2.62/0.93 % (1741534)Time elapsed: 0.022 s
% 2.62/0.93 % (1741534)Peak memory usage: 11 MB
% 2.62/0.93 % (1741534)Instructions burned: 26 (million)
% 2.62/0.93 % (1741541)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
% 2.62/0.93 % (1741541)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.62/0.93 % (1741541)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=288257149:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.62/0.93 % (1741545)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=382892419:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.62/0.93 % (1741541)Instruction limit reached!
% 2.62/0.93 % (1741541)------------------------------
% 2.62/0.93 % (1741541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.93 % (1741541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.93 % (1741541)CaDiCaL version: 2.1.3
% 2.62/0.93 % (1741541)Termination reason: Instruction limit
% 2.62/0.93 % (1741541)Termination phase: shuffling
% 2.62/0.93 % (1741541)Time elapsed: 0.012 s
% 2.62/0.93 % (1741541)Peak memory usage: 10 MB
% 2.62/0.93 % (1741541)Instructions burned: 14 (million)
% 2.62/0.93 % (1741544)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.62/0.93 % (1741544)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=419624458:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.62/0.93 % (1741544)Instruction limit reached!
% 2.62/0.93 % (1741544)------------------------------
% 2.62/0.93 % (1741544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.93 % (1741544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.93 % (1741544)CaDiCaL version: 2.1.3
% 2.62/0.93 % (1741544)Termination reason: Instruction limit
% 2.62/0.93 % (1741544)Termination phase: shuffling
% 2.62/0.93 % (1741544)Time elapsed: 0.007 s
% 2.62/0.93 % (1741544)Peak memory usage: 10 MB
% 2.62/0.93 % (1741544)Instructions burned: 8 (million)
% 2.62/0.93 % (1741545)Instruction limit reached!
% 2.62/0.93 % (1741545)------------------------------
% 2.62/0.93 % (1741545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.93 % (1741545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.93 % (1741545)CaDiCaL version: 2.1.3
% 2.62/0.93 % (1741545)Termination reason: Instruction limit
% 2.62/0.93 % (1741545)Termination phase: shuffling
% 2.62/0.93 % (1741545)Time elapsed: 0.016 s
% 2.62/0.93 % (1741545)Peak memory usage: 11 MB
% 2.62/0.93 % (1741545)Instructions burned: 32 (million)
% 2.62/0.93 % (1741538)Instruction limit reached!
% 2.62/0.93 % (1741538)------------------------------
% 2.62/0.93 % (1741538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.93 % (1741538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.93 % (1741538)CaDiCaL version: 2.1.3
% 2.62/0.93 % (1741538)Termination reason: Instruction limit
% 2.62/0.93 % (1741538)Termination phase: Preprocessing 3
% 2.62/0.93 % (1741538)Time elapsed: 0.051 s
% 2.62/0.93 % (1741538)Peak memory usage: 12 MB
% 2.62/0.93 % (1741538)Instructions burned: 61 (million)
% 2.62/0.93 % (1741548)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2135951331:i=7:hud=5:bd=preordered:rtra=on:bet=on_2996 on theBenchmark for (2996ds/7Mi)
% 2.62/0.93 % (1741551)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2404603344:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/20Mi)
% 2.62/0.93 % (1741548)Instruction limit reached!
% 2.62/0.93 % (1741548)------------------------------
% 2.62/0.93 % (1741548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.93 % (1741548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.93 % (1741548)CaDiCaL version: 2.1.3
% 2.62/1.00 % (1741548)Termination reason: Instruction limit
% 2.62/1.00 % (1741548)Termination phase: shuffling
% 2.62/1.00 % (1741548)Time elapsed: 0.007 s
% 2.62/1.00 % (1741548)Peak memory usage: 10 MB
% 2.62/1.00 % (1741548)Instructions burned: 8 (million)
% 2.62/1.00 % (1741551)Instruction limit reached!
% 2.62/1.00 % (1741551)------------------------------
% 2.62/1.00 % (1741551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/1.00 % (1741551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.00 % (1741551)CaDiCaL version: 2.1.3
% 2.62/1.00 % (1741551)Termination reason: Instruction limit
% 2.62/1.00 % (1741551)Termination phase: shuffling
% 2.62/1.00 % (1741551)Time elapsed: 0.010 s
% 2.62/1.00 % (1741551)Peak memory usage: 10 MB
% 2.62/1.00 % (1741551)Instructions burned: 20 (million)
% 2.62/1.00 % (1741550)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=714446827:i=23:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/23Mi)
% 2.62/1.00 % (1741496)Instruction limit reached!
% 2.62/1.00 % (1741496)------------------------------
% 2.62/1.00 % (1741496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/1.00 % (1741496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.00 % (1741496)CaDiCaL version: 2.1.3
% 2.62/1.00 % (1741496)Termination reason: Instruction limit
% 2.62/1.00 % (1741496)Termination phase: Saturation
% 2.62/1.00 % (1741496)Time elapsed: 0.299 s
% 2.62/1.00 % (1741496)Peak memory usage: 21 MB
% 2.62/1.00 % (1741496)Instructions burned: 636 (million)
% 2.62/1.00 % (1741552)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1343688334:i=1240:rtra=on:ixr=off_2996 on theBenchmark for (2996ds/1240Mi)
% 2.62/1.00 % (1741550)Instruction limit reached!
% 2.62/1.00 % (1741550)------------------------------
% 2.62/1.00 % (1741550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/1.00 % (1741550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.00 % (1741550)CaDiCaL version: 2.1.3
% 2.62/1.00 % (1741550)Termination reason: Instruction limit
% 2.62/1.00 % (1741550)Termination phase: shuffling
% 2.62/1.00 % (1741550)Time elapsed: 0.020 s
% 2.62/1.00 % (1741550)Peak memory usage: 10 MB
% 2.62/1.00 % (1741550)Instructions burned: 24 (million)
% 2.62/1.00 % (1741557)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1583729816:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/193Mi)
% 2.62/1.00 % (1741555)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1694675102:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2996 on theBenchmark for (2996ds/143Mi)
% 2.62/1.00 % (1741561)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.62/1.00 % (1741558)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1543500525:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 2.62/1.00 % (1741561)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2119439293:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 2.62/1.00 % (1741561)Instruction limit reached!
% 2.62/1.00 % (1741561)------------------------------
% 2.62/1.00 % (1741561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/1.00 % (1741561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.00 % (1741561)CaDiCaL version: 2.1.3
% 2.62/1.00 % (1741561)Termination reason: Instruction limit
% 2.62/1.00 % (1741561)Termination phase: shuffling
% 2.62/1.00 % (1741561)Time elapsed: 0.004 s
% 2.62/1.00 % (1741561)Peak memory usage: 10 MB
% 2.62/1.00 % (1741561)Instructions burned: 9 (million)
% 2.62/1.00 % (1741522)Instruction limit reached!
% 2.62/1.00 % (1741522)------------------------------
% 2.62/1.00 % (1741522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/1.00 % (1741522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.00 % (1741522)CaDiCaL version: 2.1.3
% 2.62/1.00 % (1741522)Termination reason: Instruction limit
% 2.62/1.00 % (1741522)Termination phase: Saturation
% 2.62/1.00 % (1741522)Time elapsed: 0.199 s
% 2.62/1.00 % (1741522)Peak memory usage: 15 MB
% 2.62/1.00 % (1741522)Instructions burned: 249 (million)
% 2.62/1.00 % (1741565)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3166385395:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 4.29/1.14 % (1741567)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=3378086665:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 4.29/1.14 % (1741558)Instruction limit reached!
% 4.29/1.14 % (1741558)------------------------------
% 4.29/1.14 % (1741558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.14 % (1741558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.14 % (1741558)CaDiCaL version: 2.1.3
% 4.29/1.14 % (1741558)Termination reason: Instruction limit
% 4.29/1.14 % (1741558)Termination phase: shuffling
% 4.29/1.14 % (1741558)Time elapsed: 0.036 s
% 4.29/1.14 % (1741558)Peak memory usage: 11 MB
% 4.29/1.14 % (1741558)Instructions burned: 42 (million)
% 4.29/1.14 % (1741570)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 4.29/1.14 % (1741570)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1902292943:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2995 on theBenchmark for (2995ds/6Mi)
% 4.29/1.14 % (1741570)Instruction limit reached!
% 4.29/1.14 % (1741570)------------------------------
% 4.29/1.14 % (1741570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.14 % (1741570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.14 % (1741570)CaDiCaL version: 2.1.3
% 4.29/1.14 % (1741570)Termination reason: Instruction limit
% 4.29/1.14 % (1741570)Termination phase: shuffling
% 4.29/1.14 % (1741570)Time elapsed: 0.006 s
% 4.29/1.14 % (1741570)Peak memory usage: 10 MB
% 4.29/1.14 % (1741570)Instructions burned: 7 (million)
% 4.29/1.14 % (1741555)Instruction limit reached!
% 4.29/1.14 % (1741555)------------------------------
% 4.29/1.14 % (1741555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.14 % (1741555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.14 % (1741555)CaDiCaL version: 2.1.3
% 4.29/1.14 % (1741555)Termination reason: Instruction limit
% 4.29/1.14 % (1741555)Termination phase: Twee Goal Transformation
% 4.29/1.14 % (1741555)Time elapsed: 0.114 s
% 4.29/1.14 % (1741555)Peak memory usage: 12 MB
% 4.29/1.14 % (1741555)Instructions burned: 143 (million)
% 4.29/1.14 % (1741565)Instruction limit reached!
% 4.29/1.14 % (1741565)------------------------------
% 4.29/1.14 % (1741565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.14 % (1741565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.14 % (1741565)CaDiCaL version: 2.1.3
% 4.29/1.14 % (1741565)Termination reason: Instruction limit
% 4.29/1.14 % (1741565)Termination phase: Saturation
% 4.29/1.14 % (1741565)Time elapsed: 0.075 s
% 4.29/1.14 % (1741565)Peak memory usage: 14 MB
% 4.29/1.14 % (1741565)Instructions burned: 183 (million)
% 4.29/1.14 % (1741528)Instruction limit reached!
% 4.29/1.14 % (1741528)------------------------------
% 4.29/1.14 % (1741528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.14 % (1741528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.14 % (1741528)CaDiCaL version: 2.1.3
% 4.29/1.14 % (1741528)Termination reason: Instruction limit
% 4.29/1.14 % (1741528)Termination phase: Saturation
% 4.29/1.14 % (1741528)Time elapsed: 0.265 s
% 4.29/1.14 % (1741528)Peak memory usage: 16 MB
% 4.29/1.14 % (1741528)Instructions burned: 328 (million)
% 4.29/1.14 % (1741557)Instruction limit reached!
% 4.29/1.14 % (1741557)------------------------------
% 4.29/1.14 % (1741557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.14 % (1741557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.14 % (1741557)CaDiCaL version: 2.1.3
% 4.29/1.14 % (1741557)Termination reason: Instruction limit
% 4.29/1.14 % (1741557)Termination phase: Saturation
% 4.29/1.14 % (1741557)Time elapsed: 0.127 s
% 4.29/1.14 % (1741557)Peak memory usage: 12 MB
% 4.29/1.14 % (1741557)Instructions burned: 193 (million)
% 4.29/1.14 % (1741567)Instruction limit reached!
% 4.29/1.14 % (1741567)------------------------------
% 4.29/1.14 % (1741567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.14 % (1741567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.34 % (1741567)CaDiCaL version: 2.1.3
% 5.77/1.34 % (1741567)Termination reason: Instruction limit
% 5.77/1.34 % (1741567)Termination phase: Property scanning
% 5.77/1.34 % (1741567)Time elapsed: 0.078 s
% 5.77/1.34 % (1741567)Peak memory usage: 12 MB
% 5.77/1.34 % (1741567)Instructions burned: 170 (million)
% 5.77/1.34 % (1741573)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1956501381:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2995 on theBenchmark for (2995ds/22Mi)
% 5.77/1.34 % (1741575)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=3555280547:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 5.77/1.34 % (1741576)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=1323953046:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 5.77/1.34 % (1741574)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2890052851:i=19:add=on:rtra=on_2995 on theBenchmark for (2995ds/19Mi)
% 5.77/1.34 % (1741573)Instruction limit reached!
% 5.77/1.34 % (1741573)------------------------------
% 5.77/1.34 % (1741573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.34 % (1741573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.34 % (1741573)CaDiCaL version: 2.1.3
% 5.77/1.34 % (1741573)Termination reason: Instruction limit
% 5.77/1.34 % (1741573)Termination phase: shuffling
% 5.77/1.34 % (1741573)Time elapsed: 0.019 s
% 5.77/1.34 % (1741573)Peak memory usage: 11 MB
% 5.77/1.34 % (1741573)Instructions burned: 22 (million)
% 5.77/1.34 % (1741577)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=2163156253:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 5.77/1.34 % (1741578)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2650481187:i=480:rtra=on_2994 on theBenchmark for (2994ds/480Mi)
% 5.77/1.34 % (1741574)Instruction limit reached!
% 5.77/1.34 % (1741574)------------------------------
% 5.77/1.34 % (1741574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.34 % (1741574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.34 % (1741574)CaDiCaL version: 2.1.3
% 5.77/1.34 % (1741574)Termination reason: Instruction limit
% 5.77/1.34 % (1741574)Termination phase: shuffling
% 5.77/1.34 % (1741574)Time elapsed: 0.016 s
% 5.77/1.34 % (1741574)Peak memory usage: 10 MB
% 5.77/1.34 % (1741574)Instructions burned: 19 (million)
% 5.77/1.34 % (1741583)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=860722935:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2994 on theBenchmark for (2994ds/21Mi)
% 5.77/1.34 % (1741586)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 5.77/1.34 % (1741586)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3606446524:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/200Mi)
% 5.77/1.34 % (1741583)Instruction limit reached!
% 5.77/1.34 % (1741583)------------------------------
% 5.77/1.34 % (1741583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.34 % (1741583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.34 % (1741583)CaDiCaL version: 2.1.3
% 5.77/1.34 % (1741583)Termination reason: Instruction limit
% 5.77/1.34 % (1741583)Termination phase: shuffling
% 5.77/1.34 % (1741583)Time elapsed: 0.019 s
% 5.77/1.34 % (1741583)Peak memory usage: 10 MB
% 5.77/1.34 % (1741583)Instructions burned: 22 (million)
% 5.77/1.34 % (1741577)Instruction limit reached!
% 5.77/1.34 % (1741577)------------------------------
% 5.77/1.34 % (1741577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.34 % (1741577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.34 % (1741577)CaDiCaL version: 2.1.3
% 5.77/1.34 % (1741577)Termination reason: Instruction limit
% 5.77/1.34 % (1741577)Termination phase: shuffling
% 6.73/1.58 % (1741577)Time elapsed: 0.037 s
% 6.73/1.58 % (1741577)Peak memory usage: 11 MB
% 6.73/1.58 % (1741577)Instructions burned: 45 (million)
% 6.73/1.58 % (1741590)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=3791026818:i=66:s2at=3:nm=2:rtra=on:rawr=on_2994 on theBenchmark for (2994ds/66Mi)
% 6.73/1.58 % (1741589)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=685492671:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2994 on theBenchmark for (2994ds/13Mi)
% 6.73/1.58 % (1741589)Instruction limit reached!
% 6.73/1.58 % (1741589)------------------------------
% 6.73/1.58 % (1741589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.58 % (1741589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.58 % (1741589)CaDiCaL version: 2.1.3
% 6.73/1.58 % (1741589)Termination reason: Instruction limit
% 6.73/1.58 % (1741589)Termination phase: shuffling
% 6.73/1.58 % (1741589)Time elapsed: 0.013 s
% 6.73/1.58 % (1741589)Peak memory usage: 10 MB
% 6.73/1.58 % (1741589)Instructions burned: 13 (million)
% 6.73/1.58 % (1741593)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1472811581:i=51:fsr=off:rtra=on_2993 on theBenchmark for (2993ds/51Mi)
% 6.73/1.58 % (1741575)Instruction limit reached!
% 6.73/1.58 % (1741575)------------------------------
% 6.73/1.58 % (1741575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.58 % (1741575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.58 % (1741575)CaDiCaL version: 2.1.3
% 6.73/1.58 % (1741575)Termination reason: Instruction limit
% 6.73/1.58 % (1741575)Termination phase: Saturation
% 6.73/1.58 % (1741575)Time elapsed: 0.136 s
% 6.73/1.58 % (1741575)Peak memory usage: 16 MB
% 6.73/1.58 % (1741575)Instructions burned: 317 (million)
% 6.73/1.58 % (1741590)Instruction limit reached!
% 6.73/1.58 % (1741590)------------------------------
% 6.73/1.58 % (1741590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.58 % (1741590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.58 % (1741590)CaDiCaL version: 2.1.3
% 6.73/1.58 % (1741590)Termination reason: Instruction limit
% 6.73/1.58 % (1741590)Termination phase: Property scanning
% 6.73/1.58 % (1741590)Time elapsed: 0.055 s
% 6.73/1.58 % (1741590)Peak memory usage: 11 MB
% 6.73/1.58 % (1741590)Instructions burned: 67 (million)
% 6.73/1.58 % (1741593)Instruction limit reached!
% 6.73/1.58 % (1741593)------------------------------
% 6.73/1.58 % (1741593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.58 % (1741593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.58 % (1741593)CaDiCaL version: 2.1.3
% 6.73/1.58 % (1741593)Termination reason: Instruction limit
% 6.73/1.58 % (1741593)Termination phase: Property scanning
% 6.73/1.58 % (1741593)Time elapsed: 0.025 s
% 6.73/1.58 % (1741593)Peak memory usage: 11 MB
% 6.73/1.58 % (1741593)Instructions burned: 51 (million)
% 6.73/1.58 % (1741596)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2338945303:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2993 on theBenchmark for (2993ds/137Mi)
% 6.73/1.58 % (1741595)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1418744658:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/31Mi)
% 6.73/1.58 % (1741597)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=3119153416:cond=on:i=34:hud=10:nm=10:rtra=on_2993 on theBenchmark for (2993ds/34Mi)
% 6.73/1.58 % (1741597)Instruction limit reached!
% 6.73/1.58 % (1741597)------------------------------
% 6.73/1.58 % (1741597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.58 % (1741597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.58 % (1741597)CaDiCaL version: 2.1.3
% 6.73/1.58 % (1741597)Termination reason: Instruction limit
% 6.73/1.58 % (1741597)Termination phase: shuffling
% 6.73/1.58 % (1741597)Time elapsed: 0.017 s
% 6.73/1.58 % (1741597)Peak memory usage: 11 MB
% 6.73/1.58 % (1741597)Instructions burned: 35 (million)
% 6.73/1.58 % (1741595)Instruction limit reached!
% 6.73/1.58 % (1741595)------------------------------
% 6.73/1.58 % (1741595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.58 % (1741595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/1.86 % (1741595)CaDiCaL version: 2.1.3
% 8.20/1.86 % (1741595)Termination reason: Instruction limit
% 8.20/1.86 % (1741595)Termination phase: shuffling
% 8.20/1.86 % (1741595)Time elapsed: 0.030 s
% 8.20/1.86 % (1741595)Peak memory usage: 11 MB
% 8.20/1.86 % (1741595)Instructions burned: 32 (million)
% 8.20/1.86 % (1741586)Instruction limit reached!
% 8.20/1.86 % (1741586)------------------------------
% 8.20/1.86 % (1741586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.20/1.86 % (1741586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/1.86 % (1741586)CaDiCaL version: 2.1.3
% 8.20/1.86 % (1741586)Termination reason: Instruction limit
% 8.20/1.86 % (1741586)Termination phase: Saturation
% 8.20/1.86 % (1741586)Time elapsed: 0.157 s
% 8.20/1.86 % (1741586)Peak memory usage: 13 MB
% 8.20/1.86 % (1741586)Instructions burned: 202 (million)
% 8.20/1.86 % (1741601)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1711005182:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2992 on theBenchmark for (2992ds/67Mi)
% 8.20/1.86 % (1741596)Instruction limit reached!
% 8.20/1.86 % (1741596)------------------------------
% 8.20/1.86 % (1741596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.20/1.86 % (1741596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/1.86 % (1741596)CaDiCaL version: 2.1.3
% 8.20/1.86 % (1741596)Termination reason: Instruction limit
% 8.20/1.86 % (1741596)Termination phase: Twee Goal Transformation
% 8.20/1.86 % (1741596)Time elapsed: 0.058 s
% 8.20/1.86 % (1741596)Peak memory usage: 12 MB
% 8.20/1.86 % (1741596)Instructions burned: 138 (million)
% 8.20/1.86 % (1741602)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 8.20/1.86 % (1741602)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=2703017829:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2992 on theBenchmark for (2992ds/180Mi)
% 8.20/1.86 % (1741603)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1101012593:st=2:i=246:sd=3:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/246Mi)
% 8.20/1.86 % (1741605)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3029392686:cond=on:i=96:bd=all:rtra=on_2992 on theBenchmark for (2992ds/96Mi)
% 8.20/1.86 % (1741601)Instruction limit reached!
% 8.20/1.86 % (1741601)------------------------------
% 8.20/1.86 % (1741601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.20/1.86 % (1741601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/1.86 % (1741601)CaDiCaL version: 2.1.3
% 8.20/1.86 % (1741601)Termination reason: Instruction limit
% 8.20/1.86 % (1741601)Termination phase: Property scanning
% 8.20/1.86 % (1741601)Time elapsed: 0.056 s
% 8.20/1.86 % (1741601)Peak memory usage: 11 MB
% 8.20/1.86 % (1741601)Instructions burned: 68 (million)
% 8.20/1.86 % (1741605)Instruction limit reached!
% 8.20/1.86 % (1741605)------------------------------
% 8.20/1.86 % (1741605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.20/1.86 % (1741605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/1.86 % (1741605)CaDiCaL version: 2.1.3
% 8.20/1.86 % (1741605)Termination reason: Instruction limit
% 8.20/1.86 % (1741605)Termination phase: Property scanning
% 8.20/1.86 % (1741605)Time elapsed: 0.041 s
% 8.20/1.86 % (1741605)Peak memory usage: 12 MB
% 8.20/1.86 % (1741605)Instructions burned: 96 (million)
% 8.20/1.86 % (1741609)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2256137472:i=427:sd=1:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/427Mi)
% 8.20/1.86 % (1741610)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3288610376:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/874Mi)
% 8.20/1.86 % (1741602)Instruction limit reached!
% 8.20/1.86 % (1741602)------------------------------
% 8.20/1.86 % (1741602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.20/1.86 % (1741602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/1.86 % (1741602)CaDiCaL version: 2.1.3
% 8.20/1.86 % (1741602)Termination reason: Instruction limit
% 8.20/1.86 % (1741602)Termination phase: Saturation
% 8.20/1.86 % (1741602)Time elapsed: 0.141 s
% 8.20/1.86 % (1741602)Peak memory usage: 13 MB
% 8.20/1.86 % (1741602)Instructions burned: 181 (million)
% 8.20/1.86 % (1741613)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=832844512:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/515Mi)
% 8.85/1.96 % (1741603)Instruction limit reached!
% 8.85/1.96 % (1741603)------------------------------
% 8.85/1.96 % (1741603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.85/1.96 % (1741603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/1.96 % (1741603)CaDiCaL version: 2.1.3
% 8.85/1.96 % (1741603)Termination reason: Instruction limit
% 8.85/1.96 % (1741603)Termination phase: Saturation
% 8.85/1.96 % (1741603)Time elapsed: 0.194 s
% 8.85/1.96 % (1741603)Peak memory usage: 14 MB
% 8.85/1.96 % (1741603)Instructions burned: 247 (million)
% 8.85/1.96 % (1741578)Instruction limit reached!
% 8.85/1.96 % (1741578)------------------------------
% 8.85/1.96 % (1741578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.85/1.96 % (1741578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/1.96 % (1741578)CaDiCaL version: 2.1.3
% 8.85/1.96 % (1741578)Termination reason: Instruction limit
% 8.85/1.96 % (1741578)Termination phase: Saturation
% 8.85/1.96 % (1741578)Time elapsed: 0.414 s
% 8.85/1.96 % (1741578)Peak memory usage: 18 MB
% 8.85/1.96 % (1741578)Instructions burned: 480 (million)
% 8.85/1.96 % (1741616)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3170604580:i=44:ep=R:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/44Mi)
% 8.85/1.96 % (1741615)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=4251038822:st=1.5:i=130:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/130Mi)
% 8.85/1.96 % (1741616)Instruction limit reached!
% 8.85/1.96 % (1741616)------------------------------
% 8.85/1.96 % (1741616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.85/1.96 % (1741616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/1.96 % (1741616)CaDiCaL version: 2.1.3
% 8.85/1.96 % (1741616)Termination reason: Instruction limit
% 8.85/1.96 % (1741616)Termination phase: Property scanning
% 8.85/1.96 % (1741616)Time elapsed: 0.039 s
% 8.85/1.96 % (1741616)Peak memory usage: 11 MB
% 8.85/1.96 % (1741616)Instructions burned: 45 (million)
% 8.85/1.96 % (1741619)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=3590972753:s2a=on:i=571:nm=16:rtra=on_2989 on theBenchmark for (2989ds/571Mi)
% 8.85/1.96 % (1741615)Instruction limit reached!
% 8.85/1.96 % (1741615)------------------------------
% 8.85/1.96 % (1741615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.85/1.96 % (1741615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/1.96 % (1741615)CaDiCaL version: 2.1.3
% 8.85/1.96 % (1741615)Termination reason: Instruction limit
% 8.85/1.96 % (1741615)Termination phase: Property scanning
% 8.85/1.96 % (1741615)Time elapsed: 0.101 s
% 8.85/1.96 % (1741615)Peak memory usage: 12 MB
% 8.85/1.96 % (1741615)Instructions burned: 130 (million)
% 8.85/1.96 % (1741621)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=699937717:i=450:rtra=on:ixr=off:ntd=on_2989 on theBenchmark for (2989ds/450Mi)
% 8.85/1.96 % (1741609)Instruction limit reached!
% 8.85/1.96 % (1741609)------------------------------
% 8.85/1.96 % (1741609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.85/1.96 % (1741609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/1.96 % (1741609)CaDiCaL version: 2.1.3
% 8.85/1.96 % (1741609)Termination reason: Instruction limit
% 8.85/1.96 % (1741609)Termination phase: Saturation
% 8.85/1.96 % (1741609)Time elapsed: 0.311 s
% 8.85/1.96 % (1741609)Peak memory usage: 16 MB
% 8.85/1.96 % (1741609)Instructions burned: 428 (million)
% 8.85/1.96 % (1741613)Instruction limit reached!
% 8.85/1.96 % (1741613)------------------------------
% 8.85/1.96 % (1741613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.85/1.96 % (1741613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.85/1.96 % (1741613)CaDiCaL version: 2.1.3
% 8.85/1.96 % (1741613)Termination reason: Instruction limit
% 8.85/1.96 % (1741613)Termination phase: Saturation
% 8.85/1.96 % (1741613)Time elapsed: 0.224 s
% 8.85/1.96 % (1741613)Peak memory usage: 17 MB
% 8.85/1.96 % (1741613)Instructions burned: 517 (million)
% 8.85/1.96 % (1741624)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=1537387230:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2988 on theBenchmark for (2988ds/65Mi)
% 11.38/2.12 % (1741623)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3969467466:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/95Mi)
% 11.38/2.12 % (1741624)Instruction limit reached!
% 11.38/2.12 % (1741624)------------------------------
% 11.38/2.12 % (1741624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.38/2.12 % (1741624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.38/2.12 % (1741624)CaDiCaL version: 2.1.3
% 11.38/2.12 % (1741624)Termination reason: Instruction limit
% 11.38/2.12 % (1741624)Termination phase: Property scanning
% 11.38/2.12 % (1741624)Time elapsed: 0.029 s
% 11.38/2.12 % (1741624)Peak memory usage: 11 MB
% 11.38/2.12 % (1741624)Instructions burned: 66 (million)
% 11.38/2.12 % (1741627)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=2291591326: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_2988 on theBenchmark for (2988ds/105Mi)
% 11.38/2.12 % (1741623)Instruction limit reached!
% 11.38/2.12 % (1741623)------------------------------
% 11.38/2.12 % (1741623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.38/2.12 % (1741623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.38/2.12 % (1741623)CaDiCaL version: 2.1.3
% 11.38/2.12 % (1741623)Termination reason: Instruction limit
% 11.38/2.12 % (1741623)Termination phase: Property scanning
% 11.38/2.12 % (1741623)Time elapsed: 0.077 s
% 11.38/2.12 % (1741623)Peak memory usage: 12 MB
% 11.38/2.12 % (1741623)Instructions burned: 96 (million)
% 11.38/2.12 % (1741627)Instruction limit reached!
% 11.38/2.12 % (1741627)------------------------------
% 11.38/2.12 % (1741627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.38/2.12 % (1741627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.38/2.12 % (1741627)CaDiCaL version: 2.1.3
% 11.38/2.12 % (1741627)Termination reason: Instruction limit
% 11.38/2.12 % (1741627)Termination phase: Property scanning
% 11.38/2.12 % (1741627)Time elapsed: 0.049 s
% 11.38/2.12 % (1741627)Peak memory usage: 12 MB
% 11.38/2.12 % (1741627)Instructions burned: 107 (million)
% 11.38/2.12 % (1741576)Instruction limit reached!
% 11.38/2.12 % (1741576)------------------------------
% 11.38/2.12 % (1741576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.38/2.12 % (1741576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.38/2.12 % (1741576)CaDiCaL version: 2.1.3
% 11.38/2.12 % (1741576)Termination reason: Instruction limit
% 11.38/2.12 % (1741576)Termination phase: Saturation
% 11.38/2.12 % (1741576)Time elapsed: 0.748 s
% 11.38/2.12 % (1741576)Peak memory usage: 23 MB
% 11.38/2.12 % (1741576)Instructions burned: 853 (million)
% 11.38/2.12 % (1741629)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=426945953:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2987 on theBenchmark for (2987ds/5755Mi)
% 11.38/2.12 % (1741630)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2226517334:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/375Mi)
% 11.38/2.12 % (1741631)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1715967451:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2987 on theBenchmark for (2987ds/495Mi)
% 11.38/2.12 % (1741552)Instruction limit reached!
% 11.38/2.12 % (1741552)------------------------------
% 11.38/2.12 % (1741552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.38/2.12 % (1741552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.38/2.12 % (1741552)CaDiCaL version: 2.1.3
% 11.38/2.12 % (1741552)Termination reason: Instruction limit
% 11.38/2.12 % (1741552)Termination phase: Saturation
% 11.38/2.12 % (1741552)Time elapsed: 1.037 s
% 11.38/2.12 % (1741552)Peak memory usage: 20 MB
% 11.38/2.12 % (1741552)Instructions burned: 1241 (million)
% 11.38/2.12 % (1741621)Instruction limit reached!
% 11.38/2.12 % (1741621)------------------------------
% 11.38/2.12 % (1741621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.38/2.12 % (1741621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.36 % (1741621)CaDiCaL version: 2.1.3
% 12.62/2.36 % (1741621)Termination reason: Instruction limit
% 12.62/2.36 % (1741621)Termination phase: Saturation
% 12.62/2.36 % (1741621)Time elapsed: 0.328 s
% 12.62/2.36 % (1741621)Peak memory usage: 19 MB
% 12.62/2.36 % (1741621)Instructions burned: 452 (million)
% 12.62/2.36 % (1741635)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=255816876:cond=on:i=34:hud=10:nm=10:rtra=on_2985 on theBenchmark for (2985ds/34Mi)
% 12.62/2.36 % (1741630)Instruction limit reached!
% 12.62/2.36 % (1741630)------------------------------
% 12.62/2.36 % (1741630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.62/2.36 % (1741630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.36 % (1741630)CaDiCaL version: 2.1.3
% 12.62/2.36 % (1741630)Termination reason: Instruction limit
% 12.62/2.36 % (1741630)Termination phase: Saturation
% 12.62/2.36 % (1741630)Time elapsed: 0.164 s
% 12.62/2.36 % (1741630)Peak memory usage: 16 MB
% 12.62/2.36 % (1741630)Instructions burned: 376 (million)
% 12.62/2.36 % (1741636)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=3577253581:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2985 on theBenchmark for (2985ds/91Mi)
% 12.62/2.36 % (1741635)Instruction limit reached!
% 12.62/2.36 % (1741635)------------------------------
% 12.62/2.36 % (1741635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.62/2.36 % (1741635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.36 % (1741635)CaDiCaL version: 2.1.3
% 12.62/2.36 % (1741635)Termination reason: Instruction limit
% 12.62/2.36 % (1741635)Termination phase: shuffling
% 12.62/2.36 % (1741635)Time elapsed: 0.029 s
% 12.62/2.36 % (1741635)Peak memory usage: 11 MB
% 12.62/2.36 % (1741635)Instructions burned: 34 (million)
% 12.62/2.36 % (1741638)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=2512525290:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2985 on theBenchmark for (2985ds/66Mi)
% 12.62/2.36 % (1741641)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1661812862:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2985 on theBenchmark for (2985ds/22Mi)
% 12.62/2.36 % (1741641)Instruction limit reached!
% 12.62/2.36 % (1741641)------------------------------
% 12.62/2.36 % (1741641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.62/2.36 % (1741641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.36 % (1741641)CaDiCaL version: 2.1.3
% 12.62/2.36 % (1741641)Termination reason: Instruction limit
% 12.62/2.36 % (1741641)Termination phase: shuffling
% 12.62/2.36 % (1741641)Time elapsed: 0.012 s
% 12.62/2.36 % (1741641)Peak memory usage: 10 MB
% 12.62/2.36 % (1741641)Instructions burned: 22 (million)
% 12.62/2.36 % (1741636)Instruction limit reached!
% 12.62/2.36 % (1741636)------------------------------
% 12.62/2.36 % (1741636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.62/2.36 % (1741636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.36 % (1741636)CaDiCaL version: 2.1.3
% 12.62/2.36 % (1741636)Termination reason: Instruction limit
% 12.62/2.36 % (1741636)Termination phase: SInE selection
% 12.62/2.36 % (1741636)Time elapsed: 0.043 s
% 12.62/2.36 % (1741636)Peak memory usage: 11 MB
% 12.62/2.36 % (1741636)Instructions burned: 93 (million)
% 12.62/2.36 % (1741619)Instruction limit reached!
% 12.62/2.36 % (1741619)------------------------------
% 12.62/2.36 % (1741619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.62/2.36 % (1741619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.36 % (1741619)CaDiCaL version: 2.1.3
% 12.62/2.36 % (1741619)Termination reason: Instruction limit
% 12.62/2.36 % (1741619)Termination phase: Saturation
% 12.62/2.36 % (1741619)Time elapsed: 0.475 s
% 12.62/2.36 % (1741619)Peak memory usage: 20 MB
% 12.62/2.36 % (1741619)Instructions burned: 571 (million)
% 12.62/2.36 % (1741646)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3795174868:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/28Mi)
% 12.62/2.36 % (1741638)Instruction limit reached!
% 12.62/2.36 % (1741638)------------------------------
% 12.62/2.36 % (1741638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.62/2.36 % (1741638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.62/2.36 % (1741638)CaDiCaL version: 2.1.3
% 12.62/2.36 % (1741638)Termination reason: Instruction limit
% 13.67/2.56 % (1741638)Termination phase: Preprocessing 3
% 13.67/2.56 % (1741638)Time elapsed: 0.054 s
% 13.67/2.56 % (1741638)Peak memory usage: 12 MB
% 13.67/2.56 % (1741638)Instructions burned: 67 (million)
% 13.67/2.56 % (1741645)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=3441166874:i=338:bd=all:ins=4:rtra=on_2985 on theBenchmark for (2985ds/338Mi)
% 13.67/2.56 % (1741646)Instruction limit reached!
% 13.67/2.56 % (1741646)------------------------------
% 13.67/2.56 % (1741646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.56 % (1741646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.56 % (1741646)CaDiCaL version: 2.1.3
% 13.67/2.56 % (1741646)Termination reason: Instruction limit
% 13.67/2.56 % (1741646)Termination phase: shuffling
% 13.67/2.56 % (1741646)Time elapsed: 0.015 s
% 13.67/2.56 % (1741646)Peak memory usage: 11 MB
% 13.67/2.56 % (1741646)Instructions burned: 30 (million)
% 13.67/2.56 % (1741647)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 13.67/2.56 % (1741647)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2389448365:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2984 on theBenchmark for (2984ds/137Mi)
% 13.67/2.56 % (1741650)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=2472392304:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2984 on theBenchmark for (2984ds/340Mi)
% 13.67/2.56 % (1741652)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=3090611377:i=227:sd=1:bd=all:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/227Mi)
% 13.67/2.56 % (1741610)Instruction limit reached!
% 13.67/2.56 % (1741610)------------------------------
% 13.67/2.56 % (1741610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.56 % (1741610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.56 % (1741610)CaDiCaL version: 2.1.3
% 13.67/2.56 % (1741610)Termination reason: Instruction limit
% 13.67/2.56 % (1741610)Termination phase: Saturation
% 13.67/2.56 % (1741610)Time elapsed: 0.736 s
% 13.67/2.56 % (1741610)Peak memory usage: 17 MB
% 13.67/2.56 % (1741610)Instructions burned: 874 (million)
% 13.67/2.56 % (1741657)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 13.67/2.56 % (1741657)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2251524474:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/373Mi)
% 13.67/2.56 % (1741647)Instruction limit reached!
% 13.67/2.56 % (1741647)------------------------------
% 13.67/2.56 % (1741647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.56 % (1741647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.56 % (1741647)CaDiCaL version: 2.1.3
% 13.67/2.56 % (1741647)Termination reason: Instruction limit
% 13.67/2.56 % (1741647)Termination phase: Property scanning
% 13.67/2.56 % (1741647)Time elapsed: 0.109 s
% 13.67/2.56 % (1741647)Peak memory usage: 12 MB
% 13.67/2.56 % (1741647)Instructions burned: 138 (million)
% 13.67/2.56 % (1741631)Instruction limit reached!
% 13.67/2.56 % (1741631)------------------------------
% 13.67/2.56 % (1741631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.56 % (1741631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.56 % (1741631)CaDiCaL version: 2.1.3
% 13.67/2.56 % (1741631)Termination reason: Instruction limit
% 13.67/2.56 % (1741631)Termination phase: Saturation
% 13.67/2.56 % (1741631)Time elapsed: 0.381 s
% 13.67/2.56 % (1741631)Peak memory usage: 18 MB
% 13.67/2.56 % (1741631)Instructions burned: 495 (million)
% 13.67/2.56 % (1741659)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=538590162:i=116:ep=RSTC:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/116Mi)
% 13.67/2.56 % (1741650)Instruction limit reached!
% 13.67/2.56 % (1741650)------------------------------
% 13.67/2.56 % (1741650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.56 % (1741650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.56 % (1741650)CaDiCaL version: 2.1.3
% 15.22/2.94 % (1741650)Termination reason: Instruction limit
% 15.22/2.94 % (1741650)Termination phase: Saturation
% 15.22/2.94 % (1741650)Time elapsed: 0.144 s
% 15.22/2.94 % (1741650)Peak memory usage: 15 MB
% 15.22/2.94 % (1741650)Instructions burned: 340 (million)
% 15.22/2.94 % (1741661)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=878593430:i=575:rtra=on_2983 on theBenchmark for (2983ds/575Mi)
% 15.22/2.94 % (1741662)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1593781207:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2983 on theBenchmark for (2983ds/270Mi)
% 15.22/2.94 % (1741652)Instruction limit reached!
% 15.22/2.94 % (1741652)------------------------------
% 15.22/2.94 % (1741652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.94 % (1741652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.94 % (1741652)CaDiCaL version: 2.1.3
% 15.22/2.94 % (1741652)Termination reason: Instruction limit
% 15.22/2.94 % (1741652)Termination phase: Saturation
% 15.22/2.94 % (1741652)Time elapsed: 0.182 s
% 15.22/2.94 % (1741652)Peak memory usage: 14 MB
% 15.22/2.94 % (1741652)Instructions burned: 228 (million)
% 15.22/2.94 % (1741665)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=3925432213: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_2982 on theBenchmark for (2982ds/9840Mi)
% 15.22/2.94 % (1741659)Instruction limit reached!
% 15.22/2.94 % (1741659)------------------------------
% 15.22/2.94 % (1741659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.94 % (1741659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.94 % (1741659)CaDiCaL version: 2.1.3
% 15.22/2.94 % (1741659)Termination reason: Instruction limit
% 15.22/2.94 % (1741659)Termination phase: Property scanning
% 15.22/2.94 % (1741659)Time elapsed: 0.102 s
% 15.22/2.94 % (1741659)Peak memory usage: 13 MB
% 15.22/2.94 % (1741659)Instructions burned: 117 (million)
% 15.22/2.94 % (1741645)Instruction limit reached!
% 15.22/2.94 % (1741645)------------------------------
% 15.22/2.94 % (1741645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.94 % (1741645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.94 % (1741645)CaDiCaL version: 2.1.3
% 15.22/2.94 % (1741645)Termination reason: Instruction limit
% 15.22/2.94 % (1741645)Termination phase: Saturation
% 15.22/2.94 % (1741645)Time elapsed: 0.268 s
% 15.22/2.94 % (1741645)Peak memory usage: 19 MB
% 15.22/2.94 % (1741645)Instructions burned: 339 (million)
% 15.22/2.94 % (1741667)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2420887930:i=421:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/421Mi)
% 15.22/2.94 % (1741668)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
% 15.22/2.94 % (1741668)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=1297473772:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/270Mi)
% 15.22/2.94 % (1741657)Instruction limit reached!
% 15.22/2.94 % (1741657)------------------------------
% 15.22/2.94 % (1741657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.94 % (1741657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.94 % (1741657)CaDiCaL version: 2.1.3
% 15.22/2.94 % (1741657)Termination reason: Instruction limit
% 15.22/2.94 % (1741657)Termination phase: Saturation
% 15.22/2.94 % (1741657)Time elapsed: 0.299 s
% 15.22/2.94 % (1741657)Peak memory usage: 14 MB
% 15.22/2.94 % (1741657)Instructions burned: 373 (million)
% 15.22/2.94 % (1741662)Instruction limit reached!
% 15.22/2.94 % (1741662)------------------------------
% 15.22/2.94 % (1741662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.22/2.94 % (1741662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/2.94 % (1741662)CaDiCaL version: 2.1.3
% 15.22/2.94 % (1741662)Termination reason: Instruction limit
% 15.22/2.94 % (1741662)Termination phase: Saturation
% 15.22/2.94 % (1741662)Time elapsed: 0.214 s
% 15.22/2.94 % (1741662)Peak memory usage: 14 MB
% 20.18/3.33 % (1741662)Instructions burned: 271 (million)
% 20.18/3.33 % (1741671)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2074127879:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2980 on theBenchmark for (2980ds/31Mi)
% 20.18/3.33 % (1741661)Instruction limit reached!
% 20.18/3.33 % (1741661)------------------------------
% 20.18/3.33 % (1741661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.33 % (1741661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.33 % (1741661)CaDiCaL version: 2.1.3
% 20.18/3.33 % (1741661)Termination reason: Instruction limit
% 20.18/3.33 % (1741661)Termination phase: Saturation
% 20.18/3.33 % (1741661)Time elapsed: 0.244 s
% 20.18/3.33 % (1741661)Peak memory usage: 16 MB
% 20.18/3.33 % (1741661)Instructions burned: 576 (million)
% 20.18/3.33 % (1741672)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 20.18/3.33 % (1741672)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
% 20.18/3.33 % (1741672)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=176062314:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2980 on theBenchmark for (2980ds/1440Mi)
% 20.18/3.33 % (1741671)Instruction limit reached!
% 20.18/3.33 % (1741671)------------------------------
% 20.18/3.33 % (1741671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.33 % (1741671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.33 % (1741671)CaDiCaL version: 2.1.3
% 20.18/3.33 % (1741671)Termination reason: Instruction limit
% 20.18/3.33 % (1741671)Termination phase: shuffling
% 20.18/3.33 % (1741671)Time elapsed: 0.027 s
% 20.18/3.33 % (1741671)Peak memory usage: 10 MB
% 20.18/3.33 % (1741671)Instructions burned: 32 (million)
% 20.18/3.33 % (1741674)dis+10_2_sil=128000:si=on:random_seed=3549031315:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2980 on theBenchmark for (2980ds/339Mi)
% 20.18/3.33 % (1741676)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2593082486:i=111:add=on:fgj=on:rtra=on:fdi=1024_2980 on theBenchmark for (2980ds/111Mi)
% 20.18/3.33 % (1741668)Instruction limit reached!
% 20.18/3.33 % (1741668)------------------------------
% 20.18/3.33 % (1741668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.33 % (1741668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.33 % (1741668)CaDiCaL version: 2.1.3
% 20.18/3.33 % (1741668)Termination reason: Instruction limit
% 20.18/3.33 % (1741668)Termination phase: Saturation
% 20.18/3.33 % (1741668)Time elapsed: 0.216 s
% 20.18/3.33 % (1741668)Peak memory usage: 15 MB
% 20.18/3.33 % (1741668)Instructions burned: 271 (million)
% 20.18/3.33 % (1741679)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=3411573242:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2979 on theBenchmark for (2979ds/122Mi)
% 20.18/3.33 % (1741676)Instruction limit reached!
% 20.18/3.33 % (1741676)------------------------------
% 20.18/3.33 % (1741676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.33 % (1741676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.33 % (1741676)CaDiCaL version: 2.1.3
% 20.18/3.33 % (1741676)Termination reason: Instruction limit
% 20.18/3.33 % (1741676)Termination phase: Property scanning
% 20.18/3.33 % (1741676)Time elapsed: 0.089 s
% 20.18/3.33 % (1741676)Peak memory usage: 12 MB
% 20.18/3.33 % (1741676)Instructions burned: 111 (million)
% 20.18/3.33 % (1741681)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=3396721951:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2979 on theBenchmark for (2979ds/136Mi)
% 20.18/3.33 % (1741679)Instruction limit reached!
% 20.18/3.33 % (1741679)------------------------------
% 20.18/3.33 % (1741679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.18/3.33 % (1741679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.18/3.33 % (1741679)CaDiCaL version: 2.1.3
% 20.18/3.33 % (1741679)Termination reason: Instruction limit
% 20.18/3.33 % (1741679)Termination phase: Property scanning
% 20.65/3.50 % (1741679)Time elapsed: 0.054 s
% 20.65/3.50 % (1741679)Peak memory usage: 12 MB
% 20.65/3.50 % (1741679)Instructions burned: 123 (million)
% 20.65/3.50 % (1741667)Instruction limit reached!
% 20.65/3.50 % (1741667)------------------------------
% 20.65/3.50 % (1741667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.65/3.50 % (1741667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.65/3.50 % (1741667)CaDiCaL version: 2.1.3
% 20.65/3.50 % (1741667)Termination reason: Instruction limit
% 20.65/3.50 % (1741667)Termination phase: Saturation
% 20.65/3.50 % (1741667)Time elapsed: 0.332 s
% 20.65/3.50 % (1741667)Peak memory usage: 16 MB
% 20.65/3.50 % (1741667)Instructions burned: 422 (million)
% 20.65/3.50 % (1741684)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3256332002:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2978 on theBenchmark for (2978ds/232Mi)
% 20.65/3.50 % (1741685)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=931159704:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2978 on theBenchmark for (2978ds/1254Mi)
% 20.65/3.50 % (1741681)Instruction limit reached!
% 20.65/3.50 % (1741681)------------------------------
% 20.65/3.50 % (1741681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.65/3.50 % (1741681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.65/3.50 % (1741681)CaDiCaL version: 2.1.3
% 20.65/3.50 % (1741681)Termination reason: Instruction limit
% 20.65/3.50 % (1741681)Termination phase: Property scanning
% 20.65/3.50 % (1741681)Time elapsed: 0.109 s
% 20.65/3.50 % (1741681)Peak memory usage: 12 MB
% 20.65/3.50 % (1741681)Instructions burned: 137 (million)
% 20.65/3.50 % (1741674)Instruction limit reached!
% 20.65/3.50 % (1741674)------------------------------
% 20.65/3.50 % (1741674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.65/3.50 % (1741674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.65/3.50 % (1741674)CaDiCaL version: 2.1.3
% 20.65/3.50 % (1741674)Termination reason: Instruction limit
% 20.65/3.50 % (1741674)Termination phase: Saturation
% 20.65/3.50 % (1741674)Time elapsed: 0.274 s
% 20.65/3.50 % (1741674)Peak memory usage: 16 MB
% 20.65/3.50 % (1741674)Instructions burned: 339 (million)
% 20.65/3.50 % (1741684)Instruction limit reached!
% 20.65/3.50 % (1741684)------------------------------
% 20.65/3.50 % (1741684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.65/3.50 % (1741684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.65/3.50 % (1741684)CaDiCaL version: 2.1.3
% 20.65/3.50 % (1741684)Termination reason: Instruction limit
% 20.65/3.50 % (1741684)Termination phase: Saturation
% 20.65/3.50 % (1741684)Time elapsed: 0.103 s
% 20.65/3.50 % (1741684)Peak memory usage: 15 MB
% 20.65/3.50 % (1741684)Instructions burned: 232 (million)
% 20.65/3.50 % (1741689)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 20.65/3.50 % (1741689)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=1333147392:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2977 on theBenchmark for (2977ds/281Mi)
% 20.65/3.50 % (1741690)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=753926432:i=619:add=on:rtra=on_2977 on theBenchmark for (2977ds/619Mi)
% 20.65/3.50 % (1741691)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=1673097249:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2977 on theBenchmark for (2977ds/865Mi)
% 20.65/3.50 % (1741689)Instruction limit reached!
% 20.65/3.50 % (1741689)------------------------------
% 20.65/3.50 % (1741689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.65/3.50 % (1741689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.65/3.50 % (1741689)CaDiCaL version: 2.1.3
% 20.65/3.50 % (1741689)Termination reason: Instruction limit
% 20.65/3.50 % (1741689)Termination phase: Saturation
% 20.65/3.50 % (1741689)Time elapsed: 0.219 s
% 20.65/3.50 % (1741689)Peak memory usage: 14 MB
% 20.65/3.50 % (1741689)Instructions burned: 281 (million)
% 20.65/3.50 % (1741695)lrs+10_1_sil=128000:si=on:urr=on:random_seed=351916915:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2975 on theBenchmark for (2975ds/212Mi)
% 21.36/3.51 % (1741690)Instruction limit reached!
% 21.36/3.51 % (1741690)------------------------------
% 21.36/3.51 % (1741690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741690)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741690)Termination reason: Instruction limit
% 21.36/3.51 % (1741690)Termination phase: Saturation
% 21.36/3.51 % (1741690)Time elapsed: 0.267 s
% 21.36/3.51 % (1741690)Peak memory usage: 16 MB
% 21.36/3.51 % (1741690)Instructions burned: 619 (million)
% 21.36/3.51 % (1741697)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=801076266:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2974 on theBenchmark for (2974ds/130Mi)
% 21.36/3.51 % (1741697)Instruction limit reached!
% 21.36/3.51 % (1741697)------------------------------
% 21.36/3.51 % (1741697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741697)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741697)Termination reason: Instruction limit
% 21.36/3.51 % (1741697)Termination phase: Property scanning
% 21.36/3.51 % (1741697)Time elapsed: 0.055 s
% 21.36/3.51 % (1741697)Peak memory usage: 12 MB
% 21.36/3.51 % (1741697)Instructions burned: 132 (million)
% 21.36/3.51 % (1741700)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1162900991:st=1.5:i=346:rtra=on:ss=axioms_2973 on theBenchmark for (2973ds/346Mi)
% 21.36/3.51 % (1741695)Instruction limit reached!
% 21.36/3.51 % (1741695)------------------------------
% 21.36/3.51 % (1741695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741695)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741695)Termination reason: Instruction limit
% 21.36/3.51 % (1741695)Termination phase: Saturation
% 21.36/3.51 % (1741695)Time elapsed: 0.148 s
% 21.36/3.51 % (1741695)Peak memory usage: 14 MB
% 21.36/3.51 % (1741695)Instructions burned: 212 (million)
% 21.36/3.51 % (1741703)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=2883642110:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2973 on theBenchmark for (2973ds/152Mi)
% 21.36/3.51 % (1741703)Instruction limit reached!
% 21.36/3.51 % (1741703)------------------------------
% 21.36/3.51 % (1741703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741703)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741703)Termination reason: Instruction limit
% 21.36/3.51 % (1741703)Termination phase: Property scanning
% 21.36/3.51 % (1741703)Time elapsed: 0.099 s
% 21.36/3.51 % (1741703)Peak memory usage: 13 MB
% 21.36/3.51 % (1741703)Instructions burned: 152 (million)
% 21.36/3.51 % (1741700)Instruction limit reached!
% 21.36/3.51 % (1741700)------------------------------
% 21.36/3.51 % (1741700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741700)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741700)Termination reason: Instruction limit
% 21.36/3.51 % (1741700)Termination phase: Saturation
% 21.36/3.51 % (1741700)Time elapsed: 0.146 s
% 21.36/3.51 % (1741700)Peak memory usage: 16 MB
% 21.36/3.51 % (1741700)Instructions burned: 350 (million)
% 21.36/3.51 % (1741705)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1950013132:i=75:ep=R:rtra=on:ntd=on_2972 on theBenchmark for (2972ds/75Mi)
% 21.36/3.51 % (1741706)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=2611807692:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2972 on theBenchmark for (2972ds/387Mi)
% 21.36/3.51 % (1741705)Instruction limit reached!
% 21.36/3.51 % (1741705)------------------------------
% 21.36/3.51 % (1741705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741705)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741705)Termination reason: Instruction limit
% 21.36/3.51 % (1741705)Termination phase: Property scanning
% 21.36/3.51 % (1741705)Time elapsed: 0.059 s
% 21.36/3.51 % (1741705)Peak memory usage: 11 MB
% 21.36/3.51 % (1741705)Instructions burned: 75 (million)
% 21.36/3.51 % (1741709)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=1751388277:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2971 on theBenchmark for (2971ds/148Mi)
% 21.36/3.51 % (1741691)Instruction limit reached!
% 21.36/3.51 % (1741691)------------------------------
% 21.36/3.51 % (1741691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741691)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741691)Termination reason: Instruction limit
% 21.36/3.51 % (1741691)Termination phase: Saturation
% 21.36/3.51 % (1741691)Time elapsed: 0.655 s
% 21.36/3.51 % (1741691)Peak memory usage: 21 MB
% 21.36/3.51 % (1741691)Instructions burned: 865 (million)
% 21.36/3.51 % (1741672)Instruction limit reached!
% 21.36/3.51 % (1741672)------------------------------
% 21.36/3.51 % (1741672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741672)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741672)Termination reason: Instruction limit
% 21.36/3.51 % (1741672)Termination phase: Saturation
% 21.36/3.51 % (1741672)Time elapsed: 0.993 s
% 21.36/3.51 % (1741672)Peak memory usage: 27 MB
% 21.36/3.51 % (1741672)Instructions burned: 1440 (million)
% 21.36/3.51 % (1741685) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1741486-1741685"...
% 21.36/3.51 % (1741713)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=1177532510:i=161:piset=and:rtra=on:ntd=on_2970 on theBenchmark for (2970ds/161Mi)
% 21.36/3.51 % (1741706)Instruction limit reached!
% 21.36/3.51 % (1741706)------------------------------
% 21.36/3.51 % (1741706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741706)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741706)Termination reason: Instruction limit
% 21.36/3.51 % (1741706)Termination phase: Saturation
% 21.36/3.51 % (1741706)Time elapsed: 0.167 s
% 21.36/3.51 % (1741706)Peak memory usage: 16 MB
% 21.36/3.51 % (1741706)Instructions burned: 388 (million)
% 21.36/3.51 % (1741714)lrs+10_1_sil=128000:si=on:random_seed=3870605008:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2970 on theBenchmark for (2970ds/888Mi)
% 21.36/3.51 % (1741716)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=2842204997:i=136:add=on:ins=4:rtra=on:sup=off_2970 on theBenchmark for (2970ds/136Mi)
% 21.36/3.51 % (1741709)Instruction limit reached!
% 21.36/3.51 % (1741709)------------------------------
% 21.36/3.51 % (1741709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741709)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741709)Termination reason: Instruction limit
% 21.36/3.51 % (1741709)Termination phase: Saturation
% 21.36/3.51 % (1741709)Time elapsed: 0.124 s
% 21.36/3.51 % (1741709)Peak memory usage: 13 MB
% 21.36/3.51 % (1741709)Instructions burned: 148 (million)
% 21.36/3.51 % (1741716)Instruction limit reached!
% 21.36/3.51 % (1741716)------------------------------
% 21.36/3.51 % (1741716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741716)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741716)Termination reason: Instruction limit
% 21.36/3.51 % (1741716)Termination phase: Property scanning
% 21.36/3.51 % (1741716)Time elapsed: 0.058 s
% 21.36/3.51 % (1741716)Peak memory usage: 12 MB
% 21.36/3.51 % (1741716)Instructions burned: 138 (million)
% 21.36/3.51 % (1741719)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=2859818573:i=88:s2at=3:nm=2:rtra=on:rawr=on_2969 on theBenchmark for (2969ds/88Mi)
% 21.36/3.51 % (1741713)Instruction limit reached!
% 21.36/3.51 % (1741713)------------------------------
% 21.36/3.51 % (1741713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.51 % (1741713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.51 % (1741713)CaDiCaL version: 2.1.3
% 21.36/3.51 % (1741721)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2131976686:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2969 on theBenchmark for (2969ds/93Mi)
% 21.36/3.51 % (1741713)Termination reason: Instruction limit
% 21.36/3.51 % (1741713)Termination phase: Saturation
% 21.36/3.51 % (1741713)Time elapsed: 0.103 s
% 21.36/3.51 % (1741713)Peak memory usage: 14 MB
% 21.36/3.51 % (1741713)Instructions burned: 162 (million)
% 21.36/3.51 % (1741685)...printing done.
% 21.36/3.51 % (1741685)Refutation found. Thanks to Tanya!
% 21.36/3.51 % SZS status Theorem for theBenchmark
% 21.36/3.51 % SZS output start Proof for theBenchmark
% 21.36/3.51 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 21.36/3.51 thf(func_def_0, type, in: ($i > $i > $o)).
% 21.36/3.51 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 21.36/3.51 thf(func_def_3, type, setextAx: $o).
% 21.36/3.51 thf(func_def_5, type, emptysetAx: $o).
% 21.36/3.51 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 21.36/3.51 thf(func_def_7, type, setadjoinAx: $o).
% 21.36/3.51 thf(func_def_8, type, powerset: ($i > $i)).
% 21.36/3.51 thf(func_def_9, type, powersetAx: $o).
% 21.36/3.51 thf(func_def_10, type, setunion: ($i > $i)).
% 21.36/3.51 thf(func_def_11, type, setunionAx: $o).
% 21.36/3.51 thf(func_def_13, type, omega0Ax: $o).
% 21.36/3.51 thf(func_def_14, type, omegaSAx: $o).
% 21.36/3.51 thf(func_def_15, type, omegaIndAx: $o).
% 21.36/3.51 thf(func_def_16, type, replAx: $o).
% 21.36/3.51 thf(func_def_17, type, foundationAx: $o).
% 21.36/3.51 thf(func_def_18, type, wellorderingAx: $o).
% 21.36/3.51 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 21.36/3.51 thf(func_def_20, type, descrp: $o).
% 21.36/3.51 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 21.36/3.51 thf(func_def_22, type, dsetconstrI: $o).
% 21.36/3.51 thf(func_def_23, type, dsetconstrEL: $o).
% 21.36/3.51 thf(func_def_24, type, dsetconstrER: $o).
% 21.36/3.51 thf(func_def_25, type, exuE1: $o).
% 21.36/3.51 thf(func_def_26, type, prop2set: ($o > $i)).
% 21.36/3.51 thf(func_def_27, type, prop2setE: $o).
% 21.36/3.51 thf(func_def_28, type, emptysetE: $o).
% 21.36/3.51 thf(func_def_29, type, emptysetimpfalse: $o).
% 21.36/3.51 thf(func_def_30, type, notinemptyset: $o).
% 21.36/3.51 thf(func_def_31, type, exuE3e: $o).
% 21.36/3.51 thf(func_def_32, type, setext: $o).
% 21.36/3.51 thf(func_def_33, type, emptyI: $o).
% 21.36/3.51 thf(func_def_34, type, noeltsimpempty: $o).
% 21.36/3.51 thf(func_def_35, type, setbeta: $o).
% 21.36/3.51 thf(func_def_36, type, nonempty: ($i > $o)).
% 21.36/3.51 thf(func_def_37, type, nonemptyE1: $o).
% 21.36/3.51 thf(func_def_38, type, nonemptyI: $o).
% 21.36/3.51 thf(func_def_39, type, nonemptyI1: $o).
% 21.36/3.51 thf(func_def_40, type, setadjoinIL: $o).
% 21.36/3.51 thf(func_def_41, type, emptyinunitempty: $o).
% 21.36/3.51 thf(func_def_42, type, setadjoinIR: $o).
% 21.36/3.51 thf(func_def_43, type, setadjoinE: $o).
% 21.36/3.51 thf(func_def_44, type, setadjoinOr: $o).
% 21.36/3.51 thf(func_def_45, type, setoftrueEq: $o).
% 21.36/3.51 thf(func_def_46, type, powersetI: $o).
% 21.36/3.51 thf(func_def_47, type, emptyinPowerset: $o).
% 21.36/3.51 thf(func_def_48, type, emptyInPowerset: $o).
% 21.36/3.51 thf(func_def_49, type, powersetE: $o).
% 21.36/3.51 thf(func_def_50, type, setunionI: $o).
% 21.36/3.51 thf(func_def_51, type, setunionE: $o).
% 21.36/3.51 thf(func_def_52, type, subPowSU: $o).
% 21.36/3.51 thf(func_def_53, type, exuE2: $o).
% 21.36/3.51 thf(func_def_54, type, nonemptyImpWitness: $o).
% 21.36/3.51 thf(func_def_55, type, uniqinunit: $o).
% 21.36/3.51 thf(func_def_56, type, notinsingleton: $o).
% 21.36/3.51 thf(func_def_57, type, eqinunit: $o).
% 21.36/3.51 thf(func_def_58, type, singletonsswitch: $o).
% 21.36/3.51 thf(func_def_59, type, upairsetE: $o).
% 21.36/3.51 thf(func_def_60, type, upairsetIL: $o).
% 21.36/3.51 thf(func_def_61, type, upairsetIR: $o).
% 21.36/3.51 thf(func_def_62, type, emptyE1: $o).
% 21.36/3.51 thf(func_def_63, type, vacuousDall: $o).
% 21.36/3.51 thf(func_def_64, type, quantDeMorgan1: $o).
% 21.36/3.51 thf(func_def_65, type, quantDeMorgan2: $o).
% 21.36/3.51 thf(func_def_66, type, quantDeMorgan3: $o).
% 21.36/3.52 thf(func_def_67, type, quantDeMorgan4: $o).
% 21.36/3.52 thf(func_def_68, type, prop2setI: $o).
% 21.36/3.52 thf(func_def_69, type, set2prop: ($i > $o)).
% 21.36/3.52 thf(func_def_70, type, prop2set2propI: $o).
% 21.36/3.52 thf(func_def_71, type, notdexE: $o).
% 21.36/3.52 thf(func_def_72, type, notdallE: $o).
% 21.36/3.52 thf(func_def_73, type, exuI1: $o).
% 21.36/3.52 thf(func_def_74, type, exuI3: $o).
% 21.36/3.52 thf(func_def_75, type, exuI2: $o).
% 21.36/3.52 thf(func_def_76, type, inCongP: $o).
% 21.36/3.52 thf(func_def_77, type, in__Cong: $o).
% 21.36/3.52 thf(func_def_78, type, exuE3u: $o).
% 21.36/3.52 thf(func_def_79, type, exu__Cong: $o).
% 21.36/3.52 thf(func_def_80, type, emptyset__Cong: $o).
% 21.36/3.52 thf(func_def_81, type, setadjoin__Cong: $o).
% 21.36/3.52 thf(func_def_82, type, powerset__Cong: $o).
% 21.36/3.52 thf(func_def_83, type, setunion__Cong: $o).
% 21.36/3.52 thf(func_def_84, type, omega__Cong: $o).
% 21.36/3.52 thf(func_def_85, type, exuEu: $o).
% 21.36/3.52 thf(func_def_86, type, descr__Cong: $o).
% 21.36/3.52 thf(func_def_87, type, dsetconstr__Cong: $o).
% 21.36/3.52 thf(func_def_88, type, subset: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_91, type, subsetI1: $o).
% 21.36/3.52 thf(func_def_92, type, eqimpsubset2: $o).
% 21.36/3.52 thf(func_def_93, type, eqimpsubset1: $o).
% 21.36/3.52 thf(func_def_94, type, subsetI2: $o).
% 21.36/3.52 thf(func_def_95, type, emptysetsubset: $o).
% 21.36/3.52 thf(func_def_96, type, subsetE: $o).
% 21.36/3.52 thf(func_def_97, type, subsetE2: $o).
% 21.36/3.52 thf(func_def_98, type, notsubsetI: $o).
% 21.36/3.52 thf(func_def_99, type, notequalI1: $o).
% 21.36/3.52 thf(func_def_100, type, notequalI2: $o).
% 21.36/3.52 thf(func_def_101, type, subsetRefl: $o).
% 21.36/3.52 thf(func_def_102, type, subsetTrans: $o).
% 21.36/3.52 thf(func_def_103, type, setadjoinSub: $o).
% 21.36/3.52 thf(func_def_104, type, setadjoinSub2: $o).
% 21.36/3.52 thf(func_def_105, type, subset2powerset: $o).
% 21.36/3.52 thf(func_def_106, type, setextsub: $o).
% 21.36/3.52 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 21.36/3.52 thf(func_def_108, type, powersetI1: $o).
% 21.36/3.52 thf(func_def_109, type, powersetE1: $o).
% 21.36/3.52 thf(func_def_110, type, inPowerset: $o).
% 21.36/3.52 thf(func_def_111, type, powersetsubset: $o).
% 21.36/3.52 thf(func_def_112, type, sepInPowerset: $o).
% 21.36/3.52 thf(func_def_113, type, sepSubset: $o).
% 21.36/3.52 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 21.36/3.52 thf(func_def_115, type, binunionIL: $o).
% 21.36/3.52 thf(func_def_116, type, upairset2IR: $o).
% 21.36/3.52 thf(func_def_117, type, binunionIR: $o).
% 21.36/3.52 thf(func_def_118, type, binunionEcases: $o).
% 21.36/3.52 thf(func_def_119, type, binunionE: $o).
% 21.36/3.52 thf(func_def_120, type, binunionLsub: $o).
% 21.36/3.52 thf(func_def_121, type, binunionRsub: $o).
% 21.36/3.52 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 21.36/3.52 thf(func_def_123, type, binintersectI: $o).
% 21.36/3.52 thf(func_def_124, type, binintersectSubset5: $o).
% 21.36/3.52 thf(func_def_125, type, binintersectEL: $o).
% 21.36/3.52 thf(func_def_126, type, binintersectLsub: $o).
% 21.36/3.52 thf(func_def_127, type, binintersectSubset2: $o).
% 21.36/3.52 thf(func_def_128, type, binintersectSubset3: $o).
% 21.36/3.52 thf(func_def_129, type, binintersectER: $o).
% 21.36/3.52 thf(func_def_130, type, disjointsetsI1: $o).
% 21.36/3.52 thf(func_def_131, type, binintersectRsub: $o).
% 21.36/3.52 thf(func_def_132, type, binintersectSubset4: $o).
% 21.36/3.52 thf(func_def_133, type, binintersectSubset1: $o).
% 21.36/3.52 thf(func_def_134, type, bs114d: $o).
% 21.36/3.52 thf(func_def_135, type, regular: ($i > $o)).
% 21.36/3.52 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 21.36/3.52 thf(func_def_137, type, setminusI: $o).
% 21.36/3.52 thf(func_def_138, type, setminusEL: $o).
% 21.36/3.52 thf(func_def_139, type, setminusER: $o).
% 21.36/3.52 thf(func_def_140, type, setminusSubset2: $o).
% 21.36/3.52 thf(func_def_141, type, setminusERneg: $o).
% 21.36/3.52 thf(func_def_142, type, setminusELneg: $o).
% 21.36/3.52 thf(func_def_143, type, setminusILneg: $o).
% 21.36/3.52 thf(func_def_144, type, setminusIRneg: $o).
% 21.36/3.52 thf(func_def_145, type, setminusLsub: $o).
% 21.36/3.52 thf(func_def_146, type, setminusSubset1: $o).
% 21.36/3.52 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 21.36/3.52 thf(func_def_148, type, symdiffE: $o).
% 21.36/3.52 thf(func_def_149, type, symdiffI1: $o).
% 21.36/3.52 thf(func_def_150, type, symdiffI2: $o).
% 21.36/3.52 thf(func_def_151, type, symdiffIneg1: $o).
% 21.36/3.52 thf(func_def_152, type, symdiffIneg2: $o).
% 21.36/3.52 thf(func_def_153, type, iskpair: ($i > $o)).
% 21.36/3.52 thf(func_def_154, type, secondinupair: $o).
% 21.36/3.52 thf(func_def_155, type, setukpairIL: $o).
% 21.36/3.52 thf(func_def_156, type, setukpairIR: $o).
% 21.36/3.52 thf(func_def_157, type, kpairiskpair: $o).
% 21.36/3.52 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 21.36/3.52 thf(func_def_159, type, kpairp: $o).
% 21.36/3.52 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 21.36/3.52 thf(func_def_161, type, singletonsubset: $o).
% 21.36/3.52 thf(func_def_162, type, singletoninpowerset: $o).
% 21.36/3.52 thf(func_def_163, type, singletoninpowunion: $o).
% 21.36/3.52 thf(func_def_164, type, upairset2E: $o).
% 21.36/3.52 thf(func_def_165, type, upairsubunion: $o).
% 21.36/3.52 thf(func_def_166, type, upairinpowunion: $o).
% 21.36/3.52 thf(func_def_167, type, ubforcartprodlem1: $o).
% 21.36/3.52 thf(func_def_168, type, ubforcartprodlem2: $o).
% 21.36/3.52 thf(func_def_169, type, ubforcartprodlem3: $o).
% 21.36/3.52 thf(func_def_170, type, cartprodpairin: $o).
% 21.36/3.52 thf(func_def_171, type, cartprodmempair1: $o).
% 21.36/3.52 thf(func_def_172, type, cartprodmempair: $o).
% 21.36/3.52 thf(func_def_173, type, setunionE2: $o).
% 21.36/3.52 thf(func_def_174, type, setunionsingleton1: $o).
% 21.36/3.52 thf(func_def_175, type, setunionsingleton2: $o).
% 21.36/3.52 thf(func_def_176, type, setunionsingleton: $o).
% 21.36/3.52 thf(func_def_177, type, singleton: ($i > $o)).
% 21.36/3.52 thf(func_def_178, type, singletonprop: $o).
% 21.36/3.52 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 21.36/3.52 thf(func_def_180, type, ex1E1: $o).
% 21.36/3.52 thf(func_def_181, type, ex1I: $o).
% 21.36/3.52 thf(func_def_182, type, ex1I2: $o).
% 21.36/3.52 thf(func_def_183, type, singletonsuniq: $o).
% 21.36/3.52 thf(func_def_184, type, atmost1p: ($i > $o)).
% 21.36/3.52 thf(func_def_185, type, atleast2p: ($i > $o)).
% 21.36/3.52 thf(func_def_186, type, atmost2p: ($i > $o)).
% 21.36/3.52 thf(func_def_187, type, upairsetp: ($i > $o)).
% 21.36/3.52 thf(func_def_188, type, setukpairinjL1: $o).
% 21.36/3.52 thf(func_def_189, type, kfstsingleton: $o).
% 21.36/3.52 thf(func_def_190, type, theprop: $o).
% 21.36/3.52 thf(func_def_191, type, kfst: ($i > $i)).
% 21.36/3.52 thf(func_def_192, type, kfstpairEq: $o).
% 21.36/3.52 thf(func_def_193, type, cartprodfstin: $o).
% 21.36/3.52 thf(func_def_194, type, setukpairinjL2: $o).
% 21.36/3.52 thf(func_def_195, type, setukpairinjL: $o).
% 21.36/3.52 thf(func_def_196, type, setukpairinjR11: $o).
% 21.36/3.52 thf(func_def_197, type, setukpairinjR12: $o).
% 21.36/3.52 thf(func_def_198, type, setukpairinjR1: $o).
% 21.36/3.52 thf(func_def_199, type, upairequniteq: $o).
% 21.36/3.52 thf(func_def_200, type, setukpairinjR2: $o).
% 21.36/3.52 thf(func_def_201, type, setukpairinjR: $o).
% 21.36/3.52 thf(func_def_202, type, ksndsingleton: $o).
% 21.36/3.52 thf(func_def_203, type, ksnd: ($i > $i)).
% 21.36/3.52 thf(func_def_204, type, ksndpairEq: $o).
% 21.36/3.52 thf(func_def_205, type, kpairsurjEq: $o).
% 21.36/3.52 thf(func_def_206, type, cartprodsndin: $o).
% 21.36/3.52 thf(func_def_207, type, cartprodpairmemEL: $o).
% 21.36/3.52 thf(func_def_208, type, cartprodpairmemER: $o).
% 21.36/3.52 thf(func_def_209, type, cartprodmempaircEq: $o).
% 21.36/3.52 thf(func_def_210, type, cartprodfstpairEq: $o).
% 21.36/3.52 thf(func_def_211, type, cartprodsndpairEq: $o).
% 21.36/3.52 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 21.36/3.52 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 21.36/3.52 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 21.36/3.52 thf(func_def_215, type, dpsetconstrI: $o).
% 21.36/3.52 thf(func_def_216, type, dpsetconstrSub: $o).
% 21.36/3.52 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 21.36/3.52 thf(func_def_218, type, dpsetconstrERa: $o).
% 21.36/3.52 thf(func_def_219, type, dpsetconstrEL1: $o).
% 21.36/3.52 thf(func_def_220, type, dpsetconstrEL2: $o).
% 21.36/3.52 thf(func_def_221, type, dpsetconstrER: $o).
% 21.36/3.52 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 21.36/3.52 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 21.36/3.52 thf(func_def_224, type, funcImageSingleton: $o).
% 21.36/3.52 thf(func_def_225, type, apProp: $o).
% 21.36/3.52 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 21.36/3.52 thf(func_def_227, type, app: $o).
% 21.36/3.52 thf(func_def_228, type, infuncsetfunc: $o).
% 21.36/3.52 thf(func_def_229, type, ap2p: $o).
% 21.36/3.52 thf(func_def_230, type, funcinfuncset: $o).
% 21.36/3.52 thf(func_def_231, type, lamProp: $o).
% 21.36/3.52 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 21.36/3.52 thf(func_def_233, type, lamp: $o).
% 21.36/3.52 thf(func_def_234, type, lam2p: $o).
% 21.36/3.52 thf(func_def_235, type, brelnall1: $o).
% 21.36/3.52 thf(func_def_236, type, brelnall2: $o).
% 21.36/3.52 thf(func_def_237, type, ex1E2: $o).
% 21.36/3.52 thf(func_def_238, type, funcGraphProp1: $o).
% 21.36/3.52 thf(func_def_239, type, funcGraphProp3: $o).
% 21.36/3.52 thf(func_def_240, type, funcGraphProp2: $o).
% 21.36/3.52 thf(func_def_241, type, funcextLem: $o).
% 21.36/3.52 thf(func_def_242, type, funcGraphProp4: $o).
% 21.36/3.52 thf(func_def_243, type, subbreln: $o).
% 21.36/3.52 thf(func_def_244, type, eqbreln: $o).
% 21.36/3.52 thf(func_def_245, type, funcext: $o).
% 21.36/3.52 thf(func_def_246, type, funcext2: $o).
% 21.36/3.52 thf(func_def_247, type, ap2apEq1: $o).
% 21.36/3.52 thf(func_def_248, type, ap2apEq2: $o).
% 21.36/3.52 thf(func_def_249, type, beta1: $o).
% 21.36/3.52 thf(func_def_250, type, eta1: $o).
% 21.36/3.52 thf(func_def_251, type, lam2lamEq: $o).
% 21.36/3.52 thf(func_def_252, type, beta2: $o).
% 21.36/3.52 thf(func_def_253, type, eta2: $o).
% 21.36/3.52 thf(func_def_254, type, iffalseProp1: $o).
% 21.36/3.52 thf(func_def_255, type, iffalseProp2: $o).
% 21.36/3.52 thf(func_def_256, type, iftrueProp1: $o).
% 21.36/3.52 thf(func_def_257, type, iftrueProp2: $o).
% 21.36/3.52 thf(func_def_258, type, ifSingleton: $o).
% 21.36/3.52 thf(func_def_259, type, if: ($i > $o > $i > $i > $i)).
% 21.36/3.52 thf(func_def_260, type, ifp: $o).
% 21.36/3.52 thf(func_def_261, type, theeq: $o).
% 21.36/3.52 thf(func_def_262, type, iftrue: $o).
% 21.36/3.52 thf(func_def_263, type, iffalse: $o).
% 21.36/3.52 thf(func_def_264, type, iftrueorfalse: $o).
% 21.36/3.52 thf(func_def_265, type, binintersectT_lem: $o).
% 21.36/3.52 thf(func_def_266, type, binunionT_lem: $o).
% 21.36/3.52 thf(func_def_267, type, powersetT_lem: $o).
% 21.36/3.52 thf(func_def_268, type, setminusT_lem: $o).
% 21.36/3.52 thf(func_def_269, type, complementT_lem: $o).
% 21.36/3.52 thf(func_def_270, type, setextT: $o).
% 21.36/3.52 thf(func_def_271, type, subsetTI: $o).
% 21.36/3.52 thf(func_def_272, type, powersetTI1: $o).
% 21.36/3.52 thf(func_def_273, type, powersetTE1: $o).
% 21.36/3.52 thf(func_def_274, type, complementTI1: $o).
% 21.36/3.52 thf(func_def_275, type, complementTE1: $o).
% 21.36/3.52 thf(func_def_276, type, binintersectTELcontra: $o).
% 21.36/3.52 thf(func_def_277, type, binintersectTERcontra: $o).
% 21.36/3.52 thf(func_def_278, type, contrasubsetT: $o).
% 21.36/3.52 thf(func_def_279, type, contrasubsetT1: $o).
% 21.36/3.52 thf(func_def_280, type, contrasubsetT2: $o).
% 21.36/3.52 thf(func_def_281, type, contrasubsetT3: $o).
% 21.36/3.52 thf(func_def_282, type, doubleComplementI1: $o).
% 21.36/3.52 thf(func_def_283, type, doubleComplementE1: $o).
% 21.36/3.52 thf(func_def_284, type, doubleComplementSub1: $o).
% 21.36/3.52 thf(func_def_285, type, doubleComplementSub2: $o).
% 21.36/3.52 thf(func_def_286, type, doubleComplementEq: $o).
% 21.36/3.52 thf(func_def_287, type, complementTnotintersectT: $o).
% 21.36/3.52 thf(func_def_288, type, complementImpComplementIntersect: $o).
% 21.36/3.52 thf(func_def_289, type, complementSubsetComplementIntersect: $o).
% 21.36/3.52 thf(func_def_290, type, complementInPowersetComplementIntersect: $o).
% 21.36/3.52 thf(func_def_291, type, contraSubsetComplement: $o).
% 21.36/3.52 thf(func_def_292, type, complementTcontraSubset: $o).
% 21.36/3.52 thf(func_def_293, type, binunionTILcontra: $o).
% 21.36/3.52 thf(func_def_294, type, binunionTIRcontra: $o).
% 21.36/3.52 thf(func_def_295, type, inIntersectImpInUnion: $o).
% 21.36/3.52 thf(func_def_296, type, inIntersectImpInUnion2: $o).
% 21.36/3.52 thf(func_def_297, type, inIntersectImpInIntersectUnions: $o).
% 21.36/3.52 thf(func_def_298, type, intersectInPowersetIntersectUnions: $o).
% 21.36/3.52 thf(func_def_299, type, inComplementUnionImpNotIn1: $o).
% 21.36/3.52 thf(func_def_300, type, inComplementUnionImpInComplement1: $o).
% 21.36/3.52 thf(func_def_301, type, binunionTE: $o).
% 21.36/3.52 thf(func_def_302, type, binunionTEcontra: $o).
% 21.36/3.52 thf(func_def_303, type, demorgan2a1: $o).
% 21.36/3.52 thf(func_def_304, type, complementUnionInPowersetComplement: $o).
% 21.36/3.52 thf(func_def_305, type, demorgan2a2: $o).
% 21.36/3.52 thf(func_def_306, type, demorgan1a: $o).
% 21.36/3.52 thf(func_def_307, type, demorgan1b: $o).
% 21.36/3.52 thf(func_def_308, type, demorgan1: $o).
% 21.36/3.52 thf(func_def_309, type, demorgan2a: $o).
% 21.36/3.52 thf(func_def_310, type, demorgan2b2: $o).
% 21.36/3.52 thf(func_def_311, type, demorgan2b: $o).
% 21.36/3.52 thf(func_def_312, type, demorgan2: $o).
% 21.36/3.52 thf(func_def_313, type, woz13rule0: $o).
% 21.36/3.52 thf(func_def_314, type, woz13rule1: $o).
% 21.36/3.52 thf(func_def_315, type, woz13rule2: $o).
% 21.36/3.52 thf(func_def_316, type, woz13rule3: $o).
% 21.36/3.52 thf(func_def_317, type, woz13rule4: $o).
% 21.36/3.52 thf(func_def_318, type, woz1_1: $o).
% 21.36/3.52 thf(func_def_319, type, woz1_2: $o).
% 21.36/3.52 thf(func_def_320, type, woz1_3: $o).
% 21.36/3.52 thf(func_def_321, type, woz1_4: $o).
% 21.36/3.52 thf(func_def_322, type, woz1_5: $o).
% 21.36/3.52 thf(func_def_323, type, breln1: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_324, type, breln1all2: $o).
% 21.36/3.52 thf(func_def_325, type, breln1Set: ($i > $i)).
% 21.36/3.52 thf(func_def_326, type, breln1SetBreln1: $o).
% 21.36/3.52 thf(func_def_327, type, transitive: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_328, type, antisymmetric: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_329, type, reflexive: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_330, type, refltransitive: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_331, type, refllinearorder: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_332, type, reflwellordering: ($i > $i > $o)).
% 21.36/3.52 thf(func_def_333, type, choice2fnsingleton: $o).
% 21.36/3.52 thf(func_def_334, type, setOfPairsIsBReln1: $o).
% 21.36/3.52 thf(func_def_335, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 21.36/3.52 thf(func_def_336, type, vNOT: ($o > $o)).
% 21.36/3.52 thf(func_def_337, type, db0: !>[X0: $tType]:(X0)).
% 21.36/3.52 thf(func_def_338, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 21.36/3.52 thf(func_def_339, type, vIMP: ($o > $o > $o)).
% 21.36/3.52 thf(func_def_340, type, db1: !>[X0: $tType]:(X0)).
% 21.36/3.52 thf(func_def_341, type, db2: !>[X0: $tType]:(X0)).
% 21.36/3.52 thf(func_def_342, type, db3: !>[X0: $tType]:(X0)).
% 21.36/3.52 thf(func_def_343, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 21.36/3.52 thf(func_def_344, type, vAND: ($o > $o > $o)).
% 21.36/3.52 thf(func_def_345, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 21.36/3.52 thf(func_def_346, type, db4: !>[X0: $tType]:(X0)).
% 21.36/3.52 thf(func_def_347, type, db5: !>[X0: $tType]:(X0)).
% 21.36/3.52 thf(func_def_348, type, vOR: ($o > $o > $o)).
% 21.36/3.52 thf(func_def_349, type, vIFF: ($o > $o > $o)).
% 21.36/3.52 thf(func_def_352, type, db6: !>[X0: $tType]:(X0)).
% 21.36/3.52 thf(func_def_353, type, sF0: $o).
% 21.36/3.52 thf(func_def_354, type, sF1: $o).
% 21.36/3.52 thf(func_def_355, type, sF2: $o).
% 21.36/3.52 thf(func_def_356, type, sF3: $o).
% 21.36/3.52 thf(func_def_357, type, sF4: $o).
% 21.36/3.52 thf(func_def_358, type, sF5: $o).
% 21.36/3.52 thf(func_def_359, type, sF6: $o).
% 21.36/3.52 thf(func_def_360, type, sF7: $o).
% 21.36/3.52 thf(func_def_361, type, sF8: $o).
% 21.36/3.52 thf(func_def_362, type, sF9: $o).
% 21.36/3.52 thf(func_def_363, type, sF10: $o).
% 21.36/3.52 thf(func_def_364, type, sF11: $o).
% 21.36/3.52 thf(func_def_365, type, sF12: $o).
% 21.36/3.52 thf(func_def_366, type, sF13: $o).
% 21.36/3.52 thf(func_def_367, type, sF14: $o).
% 21.36/3.52 thf(func_def_368, type, sF15: $o).
% 21.36/3.52 thf(func_def_369, type, sF16: $o).
% 21.36/3.52 thf(func_def_370, type, sF17: $o).
% 21.36/3.52 thf(func_def_371, type, sF18: $o).
% 21.36/3.52 thf(func_def_372, type, sF19: $o).
% 21.36/3.52 thf(func_def_373, type, sF20: $o).
% 21.36/3.52 thf(func_def_374, type, sF21: $o).
% 21.36/3.52 thf(func_def_375, type, sF22: $o).
% 21.36/3.52 thf(func_def_376, type, sF23: $o).
% 21.36/3.52 thf(func_def_377, type, sF24: $o).
% 21.36/3.52 thf(func_def_378, type, sF25: $o).
% 21.36/3.52 thf(func_def_379, type, sF26: $o).
% 21.36/3.52 thf(func_def_380, type, sF27: $o).
% 21.36/3.52 thf(func_def_381, type, sF28: $o).
% 21.36/3.52 thf(func_def_382, type, sF29: $o).
% 21.36/3.52 thf(func_def_383, type, sF30: $o).
% 21.36/3.52 thf(func_def_384, type, sF31: $o).
% 21.36/3.52 thf(func_def_385, type, sF32: $o).
% 21.36/3.52 thf(func_def_386, type, sF33: $o).
% 21.36/3.52 thf(func_def_387, type, sF34: $o).
% 21.36/3.52 thf(func_def_388, type, sF35: $o).
% 21.36/3.52 thf(func_def_389, type, sF36: $o).
% 21.36/3.52 thf(func_def_390, type, sF37: $o).
% 21.36/3.52 thf(func_def_391, type, sF38: $o).
% 21.36/3.52 thf(func_def_392, type, sF39: $o).
% 21.36/3.52 thf(func_def_393, type, sF40: $o).
% 21.36/3.52 thf(func_def_394, type, sF41: $o).
% 21.36/3.52 thf(func_def_395, type, sF42: $o).
% 21.36/3.52 thf(func_def_396, type, sF43: $o).
% 21.36/3.52 thf(func_def_397, type, sF44: $o).
% 21.36/3.52 thf(func_def_398, type, sF45: $o).
% 21.36/3.52 thf(func_def_399, type, sF46: $o).
% 21.36/3.52 thf(func_def_400, type, sF47: $o).
% 21.36/3.52 thf(func_def_401, type, sF48: $o).
% 21.36/3.52 thf(func_def_402, type, sF49: $o).
% 21.36/3.52 thf(func_def_403, type, sF50: $o).
% 21.36/3.52 thf(func_def_404, type, sF51: $o).
% 21.36/3.52 thf(func_def_405, type, sF52: $o).
% 21.36/3.52 thf(func_def_406, type, sF53: $o).
% 21.36/3.52 thf(func_def_407, type, sF54: $o).
% 21.36/3.52 thf(func_def_408, type, sF55: $o).
% 21.36/3.52 thf(func_def_409, type, sF56: $o).
% 21.36/3.52 thf(func_def_410, type, sF57: $o).
% 21.36/3.52 thf(func_def_411, type, sF58: $o).
% 21.36/3.52 thf(func_def_412, type, sF59: $o).
% 21.36/3.52 thf(func_def_413, type, sF60: $o).
% 21.36/3.52 thf(func_def_414, type, sF61: $o).
% 21.36/3.52 thf(func_def_415, type, sF62: $o).
% 21.36/3.52 thf(func_def_416, type, sF63: $o).
% 21.36/3.52 thf(func_def_417, type, sF64: $o).
% 21.36/3.52 thf(func_def_418, type, sF65: $o).
% 21.36/3.52 thf(func_def_419, type, sF66: $o).
% 21.36/3.52 thf(func_def_420, type, sF67: $o).
% 21.36/3.52 thf(func_def_421, type, sF68: $o).
% 21.36/3.52 thf(func_def_422, type, sF69: $o).
% 21.36/3.52 thf(func_def_423, type, sF70: $o).
% 21.36/3.52 thf(func_def_424, type, sF71: $o).
% 21.36/3.52 thf(func_def_425, type, sF72: $o).
% 21.36/3.52 thf(func_def_426, type, sF73: $o).
% 21.36/3.52 thf(func_def_427, type, sF74: $o).
% 21.36/3.52 thf(func_def_428, type, sF75: $o).
% 21.36/3.52 thf(func_def_429, type, sF76: $o).
% 21.36/3.52 thf(func_def_430, type, sF77: $o).
% 21.36/3.52 thf(func_def_431, type, sF78: $o).
% 21.36/3.52 thf(func_def_432, type, sF79: $o).
% 21.36/3.52 thf(func_def_433, type, sF80: $o).
% 21.36/3.52 thf(func_def_434, type, sF81: $o).
% 21.36/3.52 thf(func_def_435, type, sF82: $o).
% 21.36/3.52 thf(func_def_436, type, sF83: $o).
% 21.36/3.52 thf(func_def_437, type, sF84: $o).
% 21.36/3.52 thf(func_def_438, type, sF85: $o).
% 21.36/3.52 thf(func_def_439, type, sF86: $o).
% 21.36/3.52 thf(func_def_440, type, sF87: $o).
% 21.36/3.52 thf(func_def_441, type, sF88: $o).
% 21.36/3.52 thf(func_def_442, type, sF89: $o).
% 21.36/3.52 thf(func_def_443, type, sF90: $o).
% 21.36/3.52 thf(func_def_444, type, sF91: $o).
% 21.36/3.52 thf(func_def_445, type, sF92: $o).
% 21.36/3.52 thf(func_def_446, type, sF93: $o).
% 21.36/3.52 thf(func_def_447, type, sF94: $o).
% 21.36/3.52 thf(func_def_448, type, sF95: $o).
% 21.36/3.52 thf(func_def_449, type, sF96: $o).
% 21.36/3.52 thf(func_def_450, type, sF97: $o).
% 21.36/3.52 thf(func_def_451, type, sF98: $o).
% 21.36/3.52 thf(func_def_452, type, sF99: $o).
% 21.36/3.52 thf(func_def_453, type, sF100: $o).
% 21.36/3.52 thf(func_def_454, type, sF101: $o).
% 21.36/3.52 thf(func_def_455, type, sF102: $o).
% 21.36/3.52 thf(func_def_456, type, sF103: $o).
% 21.36/3.52 thf(func_def_457, type, sF104: $o).
% 21.36/3.52 thf(func_def_458, type, sF105: $o).
% 21.36/3.52 thf(func_def_459, type, sF106: $o).
% 21.36/3.52 thf(func_def_460, type, sF107: $o).
% 21.36/3.52 thf(func_def_461, type, sF108: $o).
% 21.36/3.52 thf(func_def_462, type, sF109: $o).
% 21.36/3.52 thf(func_def_463, type, sF110: $o).
% 21.36/3.52 thf(func_def_464, type, sF111: $o).
% 21.36/3.52 thf(func_def_465, type, sF112: $o).
% 21.36/3.52 thf(func_def_466, type, sF113: $o).
% 21.36/3.52 thf(func_def_467, type, sF114: $o).
% 21.36/3.52 thf(func_def_468, type, sF115: $o).
% 21.36/3.52 thf(func_def_469, type, sF116: $o).
% 21.36/3.52 thf(func_def_470, type, sF117: $o).
% 21.36/3.52 thf(func_def_471, type, sF118: $o).
% 21.36/3.52 thf(func_def_472, type, sF119: $o).
% 21.36/3.52 thf(func_def_473, type, sF120: $o).
% 21.36/3.52 thf(func_def_474, type, sF121: $o).
% 21.36/3.52 thf(func_def_475, type, sF122: $o).
% 21.36/3.52 thf(func_def_476, type, sF123: $o).
% 21.36/3.52 thf(func_def_477, type, sF124: $o).
% 21.36/3.52 thf(func_def_478, type, sF125: $o).
% 21.36/3.52 thf(func_def_479, type, sF126: $o).
% 21.36/3.52 thf(func_def_480, type, sF127: $o).
% 21.36/3.52 thf(func_def_481, type, sF128: $o).
% 21.36/3.52 thf(func_def_482, type, sF129: $o).
% 21.36/3.52 thf(func_def_483, type, sF130: $o).
% 21.36/3.52 thf(func_def_484, type, sF131: $o).
% 21.36/3.52 thf(func_def_485, type, sF132: $o).
% 21.36/3.52 thf(func_def_486, type, sF133: $o).
% 21.36/3.52 thf(func_def_487, type, sF134: $o).
% 21.36/3.52 thf(func_def_488, type, sF135: $o).
% 21.36/3.52 thf(func_def_489, type, sF136: $o).
% 21.36/3.52 thf(func_def_490, type, sF137: $o).
% 21.36/3.52 thf(func_def_491, type, sF138: $o).
% 21.36/3.52 thf(func_def_492, type, sF139: $o).
% 21.36/3.52 thf(func_def_493, type, sF140: $o).
% 21.36/3.52 thf(func_def_494, type, sF141: $o).
% 21.36/3.52 thf(func_def_495, type, sF142: $o).
% 21.36/3.52 thf(func_def_496, type, sF143: $o).
% 21.36/3.52 thf(func_def_497, type, sF144: $o).
% 21.36/3.52 thf(func_def_498, type, sF145: $o).
% 21.36/3.52 thf(func_def_499, type, sF146: $o).
% 21.36/3.52 thf(func_def_500, type, sF147: $o).
% 21.36/3.52 thf(func_def_501, type, sF148: $o).
% 21.36/3.52 thf(func_def_502, type, sF149: $o).
% 21.36/3.52 thf(func_def_503, type, sF150: $o).
% 21.36/3.52 thf(func_def_504, type, sF151: $o).
% 21.36/3.52 thf(func_def_505, type, sF152: $o).
% 21.36/3.52 thf(func_def_506, type, sF153: $o).
% 21.36/3.52 thf(func_def_507, type, sF154: $o).
% 21.36/3.52 thf(func_def_508, type, sF155: $o).
% 21.36/3.52 thf(func_def_509, type, sF156: $o).
% 21.36/3.52 thf(func_def_510, type, sF157: $o).
% 21.36/3.52 thf(func_def_511, type, sF158: $o).
% 21.36/3.52 thf(func_def_512, type, sF159: $o).
% 21.36/3.52 thf(func_def_513, type, sF160: $o).
% 21.36/3.52 thf(func_def_514, type, sF161: $o).
% 21.36/3.52 thf(func_def_515, type, sF162: $o).
% 21.36/3.52 thf(func_def_516, type, sF163: $o).
% 21.36/3.52 thf(func_def_517, type, sF164: $o).
% 21.36/3.52 thf(func_def_518, type, sF165: $o).
% 21.36/3.52 thf(func_def_519, type, sF166: $o).
% 21.36/3.52 thf(func_def_520, type, sF167: $o).
% 21.36/3.52 thf(func_def_521, type, sF168: $o).
% 21.36/3.52 thf(func_def_522, type, sF169: $o).
% 21.36/3.52 thf(func_def_523, type, sF170: $o).
% 21.36/3.52 thf(func_def_524, type, sF171: $o).
% 21.36/3.52 thf(func_def_525, type, sF172: $o).
% 21.36/3.52 thf(func_def_526, type, sF173: $o).
% 21.36/3.52 thf(func_def_527, type, sF174: $o).
% 21.36/3.52 thf(func_def_528, type, sF175: $o).
% 21.36/3.52 thf(func_def_529, type, sF176: $o).
% 21.36/3.52 thf(func_def_530, type, sF177: $o).
% 21.36/3.52 thf(func_def_531, type, sF178: $o).
% 21.36/3.52 thf(func_def_532, type, sF179: $o).
% 21.36/3.52 thf(func_def_533, type, sF180: $o).
% 21.36/3.52 thf(func_def_534, type, sF181: $o).
% 21.36/3.52 thf(func_def_535, type, sF182: $o).
% 21.36/3.52 thf(func_def_536, type, sF183: $o).
% 21.36/3.52 thf(func_def_537, type, sF184: $o).
% 21.36/3.52 thf(func_def_538, type, sF185: $o).
% 21.36/3.52 thf(func_def_539, type, sF186: $o).
% 21.36/3.52 thf(func_def_540, type, sF187: $o).
% 21.36/3.52 thf(func_def_541, type, sF188: $o).
% 21.36/3.52 thf(func_def_542, type, sF189: $o).
% 21.36/3.52 thf(func_def_543, type, sF190: $o).
% 21.36/3.52 thf(func_def_544, type, sF191: $o).
% 21.36/3.52 thf(func_def_545, type, sF192: $o).
% 21.36/3.52 thf(func_def_546, type, sF193: $o).
% 21.36/3.52 thf(func_def_547, type, sF194: $o).
% 21.36/3.52 thf(func_def_548, type, sF195: $o).
% 21.36/3.52 thf(func_def_549, type, sF196: $o).
% 21.36/3.52 thf(func_def_550, type, sF197: $o).
% 21.36/3.52 thf(func_def_551, type, sF198: $o).
% 21.36/3.52 thf(func_def_552, type, sF199: $o).
% 21.36/3.52 thf(func_def_553, type, sF200: $o).
% 21.36/3.52 thf(func_def_554, type, sF201: $o).
% 21.36/3.52 thf(func_def_555, type, sF202: $o).
% 21.36/3.52 thf(func_def_556, type, sF203: $o).
% 21.36/3.52 thf(func_def_557, type, sF204: $o).
% 21.36/3.52 thf(func_def_558, type, sF205: $o).
% 21.36/3.52 thf(func_def_559, type, sF206: $o).
% 21.36/3.52 thf(func_def_560, type, sF207: $o).
% 21.36/3.52 thf(func_def_561, type, sF208: $o).
% 21.36/3.52 thf(func_def_562, type, sF209: $o).
% 21.36/3.52 thf(func_def_563, type, sF210: $o).
% 21.36/3.52 thf(func_def_564, type, sF211: $o).
% 21.36/3.52 thf(func_def_565, type, sF212: $o).
% 21.36/3.52 thf(func_def_566, type, sF213: $o).
% 21.36/3.52 thf(func_def_567, type, sF214: $o).
% 21.36/3.52 thf(func_def_568, type, sF215: $o).
% 21.36/3.52 thf(func_def_569, type, sF216: $o).
% 21.36/3.52 thf(func_def_570, type, sF217: $o).
% 21.36/3.52 thf(func_def_571, type, sF218: $o).
% 21.36/3.52 thf(func_def_572, type, sF219: $o).
% 21.36/3.52 thf(func_def_573, type, sF220: $o).
% 21.36/3.52 thf(func_def_574, type, sF221: $o).
% 21.36/3.52 thf(func_def_575, type, sF222: $o).
% 21.36/3.52 thf(func_def_576, type, sF223: $o).
% 21.36/3.52 thf(func_def_577, type, sF224: $o).
% 21.36/3.52 thf(func_def_578, type, sF225: $o).
% 21.36/3.52 thf(func_def_579, type, sF226: $o).
% 21.36/3.52 thf(func_def_580, type, sF227: $o).
% 21.36/3.52 thf(func_def_581, type, sF228: $o).
% 21.36/3.52 thf(func_def_582, type, sF229: $o).
% 21.36/3.52 thf(func_def_583, type, sF230: $o).
% 21.36/3.52 thf(func_def_584, type, sF231: $o).
% 21.36/3.52 thf(func_def_585, type, sF232: $o).
% 21.36/3.52 thf(func_def_586, type, sF233: $o).
% 21.36/3.52 thf(func_def_587, type, sF234: $o).
% 21.36/3.52 thf(func_def_588, type, sF235: $o).
% 21.36/3.52 thf(func_def_589, type, sF236: $o).
% 21.36/3.52 thf(func_def_590, type, sF237: $o).
% 21.36/3.52 thf(func_def_591, type, sF238: $o).
% 21.36/3.52 thf(func_def_592, type, sF239: $o).
% 21.36/3.52 thf(func_def_593, type, sF240: $o).
% 21.36/3.52 thf(func_def_594, type, sF241: $o).
% 21.36/3.52 thf(func_def_595, type, sF242: $o).
% 21.36/3.52 thf(func_def_596, type, sF243: $o).
% 21.36/3.52 thf(func_def_597, type, sF244: $o).
% 21.36/3.52 thf(func_def_598, type, sF245: $o).
% 21.36/3.52 thf(func_def_599, type, sF246: $o).
% 21.36/3.52 thf(func_def_600, type, sF247: $o).
% 21.36/3.52 thf(func_def_601, type, sF248: $o).
% 21.36/3.52 thf(func_def_602, type, sF249: $o).
% 21.36/3.52 thf(func_def_603, type, sF250: $o).
% 21.36/3.52 thf(func_def_604, type, sF251: $o).
% 21.36/3.52 thf(func_def_605, type, sF252: $o).
% 21.36/3.52 thf(func_def_606, type, sF253: $o).
% 21.36/3.52 thf(func_def_607, type, sF254: $o).
% 21.36/3.52 thf(func_def_608, type, sF255: $o).
% 21.36/3.52 thf(func_def_609, type, sF256: $o).
% 21.36/3.52 thf(func_def_610, type, sF257: $o).
% 21.36/3.52 thf(func_def_611, type, sF258: $o).
% 21.36/3.52 thf(func_def_612, type, sF259: $o).
% 21.36/3.52 thf(func_def_613, type, sF260: $o).
% 21.36/3.52 thf(func_def_614, type, sF261: $o).
% 21.36/3.52 thf(func_def_615, type, sF262: $o).
% 21.36/3.52 thf(func_def_616, type, sF263: $o).
% 21.36/3.52 thf(func_def_617, type, sF264: $o).
% 21.36/3.52 thf(func_def_618, type, sF265: $o).
% 21.36/3.52 thf(func_def_619, type, sF266: $o).
% 21.36/3.52 thf(func_def_620, type, sF267: $o).
% 21.36/3.52 thf(func_def_621, type, sF268: $o).
% 21.36/3.52 thf(func_def_622, type, sF269: $o).
% 21.36/3.52 thf(func_def_623, type, sF270: $o).
% 21.36/3.52 thf(func_def_624, type, sF271: $o).
% 21.36/3.52 thf(func_def_625, type, sF272: $o).
% 21.36/3.52 thf(func_def_626, type, sF273: $o).
% 21.36/3.52 thf(func_def_627, type, sF274: $o).
% 21.36/3.52 thf(func_def_628, type, sF275: $o).
% 21.36/3.52 thf(func_def_629, type, sF276: $o).
% 21.36/3.52 thf(func_def_630, type, sF277: $o).
% 21.36/3.52 thf(func_def_631, type, sF278: $o).
% 21.36/3.52 thf(func_def_632, type, sF279: $o).
% 21.36/3.52 thf(func_def_633, type, sF280: $o).
% 21.36/3.52 thf(func_def_634, type, sF281: $o).
% 21.36/3.52 thf(func_def_635, type, sF282: $o).
% 21.36/3.52 thf(func_def_636, type, sF283: $o).
% 21.36/3.52 thf(func_def_637, type, sF284: $o).
% 21.36/3.52 thf(func_def_638, type, sF285: $o).
% 21.36/3.52 thf(func_def_639, type, sF286: $o).
% 21.36/3.52 thf(func_def_640, type, sF287: $o).
% 21.36/3.52 thf(func_def_641, type, sF288: $o).
% 21.36/3.52 thf(func_def_642, type, sF289: $o).
% 21.36/3.52 thf(f1,axiom,(
% 21.36/3.52 ((^[X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu)).
% 21.36/3.52 thf(f3,axiom,(
% 21.36/3.52 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx)).
% 21.36/3.52 thf(f4,axiom,(
% 21.36/3.52 (! [X1 : $i,X2 : $i,X0 : $i] : (((X2 = X0) | (in @ X2 @ X1)) <=> (in @ X2 @ (setadjoin @ X0 @ X1))) = setadjoinAx)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx)).
% 21.36/3.52 thf(f5,axiom,(
% 21.36/3.52 (powersetAx = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx)).
% 21.36/3.52 thf(f7,axiom,(
% 21.36/3.52 (omega0Ax = ((in @ emptyset @ omega)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax)).
% 21.36/3.52 thf(f8,axiom,(
% 21.36/3.52 (! [X0 : $i] : ((in @ X0 @ omega) => (in @ (setadjoin @ X0 @ X0) @ omega)) = omegaSAx)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx)).
% 21.36/3.52 thf(f9,axiom,(
% 21.36/3.52 (omegaIndAx = ! [X0 : $i] : ((! [X1 : $i] : (((in @ X1 @ omega) & (in @ X1 @ X0)) => (in @ (setadjoin @ X1 @ X1) @ X0)) & (in @ emptyset @ X0)) => ! [X1 : $i] : ((in @ X1 @ omega) => (in @ X1 @ X0))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx)).
% 21.36/3.52 thf(f11,axiom,(
% 21.36/3.52 (foundationAx = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : (~ ? [X1 : $i] : ((in @ X1 @ X0) & (in @ X1 @ X2)) & (in @ X2 @ X0))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx)).
% 21.36/3.52 thf(f13,axiom,(
% 21.36/3.52 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => (X0 @ (descr @ (^[X1 : $i] : ((X0 @ X1)))))) = descrp)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp)).
% 21.36/3.52 thf(f14,axiom,(
% 21.36/3.52 (! [X2 : $i,X1 : ($i > $o),X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))) = dsetconstrI)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI)).
% 21.36/3.52 thf(f15,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL)).
% 21.36/3.52 thf(f16,axiom,(
% 21.36/3.52 (! [X2 : $i,X0 : $i,X1 : ($i > $o)] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (X1 @ X2)) = dsetconstrER)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 21.36/3.52 thf(f17,axiom,(
% 21.36/3.52 (exuE1 = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1)).
% 21.36/3.52 thf(f18,axiom,(
% 21.36/3.52 (prop2setE = ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE)).
% 21.36/3.52 thf(f19,axiom,(
% 21.36/3.52 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 21.36/3.52 thf(f20,axiom,(
% 21.36/3.52 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse)).
% 21.36/3.52 thf(f21,axiom,(
% 21.36/3.52 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset)).
% 21.36/3.52 thf(f22,axiom,(
% 21.36/3.52 (exuE3e = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e)).
% 21.36/3.52 thf(f24,axiom,(
% 21.36/3.52 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = emptyI)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI)).
% 21.36/3.52 thf(f25,axiom,(
% 21.36/3.52 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = noeltsimpempty)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty)).
% 21.36/3.52 thf(f26,axiom,(
% 21.36/3.52 (setbeta = ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : ((in @ X2 @ X0) => ((X1 @ X2) <=> (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta)).
% 21.36/3.52 thf(f27,axiom,(
% 21.36/3.52 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty)).
% 21.36/3.52 thf(f28,axiom,(
% 21.36/3.52 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1)).
% 21.36/3.52 thf(f29,axiom,(
% 21.36/3.52 (nonemptyI = ! [X2 : $i,X1 : ($i > $o),X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI)).
% 21.36/3.52 thf(f30,axiom,(
% 21.36/3.52 (nonemptyI1 = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1)).
% 21.36/3.52 thf(f31,axiom,(
% 21.36/3.52 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL)).
% 21.36/3.52 thf(f32,axiom,(
% 21.36/3.52 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty)).
% 21.36/3.52 thf(f33,axiom,(
% 21.36/3.52 (setadjoinIR = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR)).
% 21.36/3.52 thf(f35,axiom,(
% 21.36/3.52 (setadjoinOr = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ((in @ X2 @ X1) | (X2 = X0))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr)).
% 21.36/3.52 thf(f36,axiom,(
% 21.36/3.52 (! [X0 : $i] : (((dsetconstr @ X0 @ (^[X1 : $i] : ($true)))) = X0) = setoftrueEq)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq)).
% 21.36/3.52 thf(f37,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 21.36/3.52 thf(f38,axiom,(
% 21.36/3.52 (emptyinPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset)).
% 21.36/3.52 thf(f39,axiom,(
% 21.36/3.52 (emptyInPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset)).
% 21.36/3.52 thf(f40,axiom,(
% 21.36/3.52 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 21.36/3.52 thf(f41,axiom,(
% 21.36/3.52 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))) = setunionI)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI)).
% 21.36/3.52 thf(f42,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)) = setunionE)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE)).
% 21.36/3.52 thf(f43,axiom,(
% 21.36/3.52 (subPowSU = ! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU)).
% 21.36/3.52 thf(f45,axiom,(
% 21.36/3.52 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 21.36/3.52 thf(f46,axiom,(
% 21.36/3.52 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 21.36/3.52 thf(f47,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))) = notinsingleton)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton)).
% 21.36/3.52 thf(f48,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))) = eqinunit)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit)).
% 21.36/3.52 thf(f49,axiom,(
% 21.36/3.52 (singletonsswitch = ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch)).
% 21.36/3.52 thf(f51,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = upairsetIL)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL)).
% 21.36/3.52 thf(f52,axiom,(
% 21.36/3.52 (upairsetIR = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR)).
% 21.36/3.52 thf(f53,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((((dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))) = emptyset) => $false)) = emptyE1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1)).
% 21.36/3.52 thf(f54,axiom,(
% 21.36/3.52 (! [X0 : ($i > $o),X1 : $i] : ((in @ X1 @ emptyset) => (X0 @ X1)) = vacuousDall)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall)).
% 21.36/3.52 thf(f55,axiom,(
% 21.36/3.52 (! [X1 : ($i > $o),X0 : $i] : (~ ! [X2 : $i] : ((in @ X2 @ X0) => (X1 @ X2)) => ? [X2 : $i] : ((in @ X2 @ X0) & ~(X1 @ X2))) = quantDeMorgan1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1)).
% 21.36/3.52 thf(f56,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2)) => ~ ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2))) = quantDeMorgan2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2)).
% 21.36/3.52 thf(f57,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : ($i > $o)] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2))) = quantDeMorgan3)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3)).
% 21.36/3.52 thf(f58,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & ~(X1 @ X2)) => ~ ! [X2 : $i] : ((in @ X2 @ X0) => (X1 @ X2))) = quantDeMorgan4)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4)).
% 21.36/3.52 thf(f59,axiom,(
% 21.36/3.52 (! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))) = prop2setI)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI)).
% 21.36/3.52 thf(f61,axiom,(
% 21.36/3.52 (notdexE = ! [X1 : ($i > $o),X0 : $i] : (~ ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE)).
% 21.36/3.52 thf(f63,axiom,(
% 21.36/3.52 (exuI1 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1)).
% 21.36/3.52 thf(f64,axiom,(
% 21.36/3.52 (! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1)))))) = exuI3)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3)).
% 21.36/3.52 thf(f65,axiom,(
% 21.36/3.52 (exuI2 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2)) => (exu @ (^[X1 : $i] : ((X0 @ X1))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2)).
% 21.36/3.52 thf(f66,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1)))) = inCongP)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP)).
% 21.36/3.52 thf(f67,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => ((in @ X3 @ X1) <=> (in @ X2 @ X0)))) = in__Cong)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong)).
% 21.36/3.52 thf(f68,axiom,(
% 21.36/3.52 (exuE3u = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u)).
% 21.36/3.52 thf(f70,axiom,(
% 21.36/3.52 (emptyset__Cong = (emptyset = emptyset))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong)).
% 21.36/3.52 thf(f71,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => (((setadjoin @ X0 @ X2)) = ((setadjoin @ X1 @ X3))))) = setadjoin__Cong)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong)).
% 21.36/3.52 thf(f72,axiom,(
% 21.36/3.52 (powerset__Cong = ! [X1 : $i,X0 : $i] : ((X0 = X1) => (((powerset @ X0)) = ((powerset @ X1)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong)).
% 21.36/3.52 thf(f73,axiom,(
% 21.36/3.52 (setunion__Cong = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setunion @ X0)) = ((setunion @ X1)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong)).
% 21.36/3.52 thf(f74,axiom,(
% 21.36/3.52 (omega__Cong = (omega = omega))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong)).
% 21.36/3.52 thf(f75,axiom,(
% 21.36/3.52 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuEu)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu)).
% 21.36/3.52 thf(f78,axiom,(
% 21.36/3.52 (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 21.36/3.52 thf(f79,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2)).
% 21.36/3.52 thf(f80,axiom,(
% 21.36/3.52 (eqimpsubset1 = ! [X1 : $i,X0 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1)).
% 21.36/3.52 thf(f81,axiom,(
% 21.36/3.52 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 21.36/3.52 thf(f82,axiom,(
% 21.36/3.52 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset)).
% 21.36/3.52 thf(f84,axiom,(
% 21.36/3.52 (subsetE2 = ! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2)).
% 21.36/3.52 thf(f85,axiom,(
% 21.36/3.52 (notsubsetI = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI)).
% 21.36/3.52 thf(f86,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)) = notequalI1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1)).
% 21.36/3.52 thf(f87,axiom,(
% 21.36/3.52 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (X0 != X1))) = notequalI2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2)).
% 21.36/3.52 thf(f88,axiom,(
% 21.36/3.52 (subsetRefl = ! [X0 : $i] : (subset @ X0 @ X0))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl)).
% 21.36/3.52 thf(f89,axiom,(
% 21.36/3.52 (! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))) = subsetTrans)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans)).
% 21.36/3.52 thf(f90,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)) = setadjoinSub)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub)).
% 21.36/3.52 thf(f91,axiom,(
% 21.36/3.52 (setadjoinSub2 = ! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X2) => (subset @ X0 @ (setadjoin @ X1 @ X2))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2)).
% 21.36/3.52 thf(f92,axiom,(
% 21.36/3.52 (subset2powerset = ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset)).
% 21.36/3.52 thf(f94,axiom,(
% 21.36/3.52 (! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)) = subsetemptysetimpeq)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq)).
% 21.36/3.52 thf(f95,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1)).
% 21.36/3.52 thf(f96,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)) = powersetE1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1)).
% 21.36/3.52 thf(f97,axiom,(
% 21.36/3.52 (! [X0 : $i] : (in @ X0 @ (powerset @ X0)) = inPowerset)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset)).
% 21.36/3.52 thf(f98,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))) = powersetsubset)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset)).
% 21.36/3.52 thf(f99,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : ($i > $o)] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ (powerset @ X0)) = sepInPowerset)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset)).
% 21.36/3.52 thf(f100,axiom,(
% 21.36/3.52 (sepSubset = ! [X1 : ($i > $o),X0 : $i] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ X0))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset)).
% 21.36/3.52 thf(f102,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = upairset2IR)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR)).
% 21.36/3.52 thf(f105,axiom,(
% 21.36/3.52 (binunionE = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X0) | (in @ X2 @ X1))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE)).
% 21.36/3.52 thf(f106,axiom,(
% 21.36/3.52 (binunionLsub = ! [X1 : $i,X0 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub)).
% 21.36/3.52 thf(f107,axiom,(
% 21.36/3.52 (binunionRsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub)).
% 21.36/3.52 thf(f110,axiom,(
% 21.36/3.52 (binintersectEL = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL)).
% 21.36/3.52 thf(f111,axiom,(
% 21.36/3.52 (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub)).
% 21.36/3.52 thf(f112,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0)) = binintersectSubset2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2)).
% 21.36/3.52 thf(f113,axiom,(
% 21.36/3.52 (binintersectSubset3 = ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3)).
% 21.36/3.52 thf(f114,axiom,(
% 21.36/3.52 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)).
% 21.36/3.52 thf(f115,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (((binintersect @ X0 @ X1)) = emptyset)) = disjointsetsI1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1)).
% 21.36/3.52 thf(f116,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1) = binintersectRsub)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub)).
% 21.36/3.52 thf(f118,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)) = binintersectSubset1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1)).
% 21.36/3.52 thf(f120,axiom,(
% 21.36/3.52 (setminusI = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI)).
% 21.36/3.52 thf(f123,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (((setminus @ X0 @ X1)) = emptyset)) = setminusSubset2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2)).
% 21.36/3.52 thf(f124,axiom,(
% 21.36/3.52 (! [X1 : $i,X2 : $i,X0 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = setminusERneg)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg)).
% 21.36/3.52 thf(f126,axiom,(
% 21.36/3.52 (setminusILneg = ! [X1 : $i,X0 : $i,X2 : $i] : (~(in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X0 @ X1))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg)).
% 21.36/3.52 thf(f127,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1))) = setminusIRneg)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg)).
% 21.36/3.52 thf(f128,axiom,(
% 21.36/3.52 (setminusLsub = ! [X1 : $i,X0 : $i] : (subset @ (setminus @ X0 @ X1) @ X0))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub)).
% 21.36/3.52 thf(f129,axiom,(
% 21.36/3.52 (setminusSubset1 = ! [X0 : $i,X1 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1)).
% 21.36/3.52 thf(f130,axiom,(
% 21.36/3.52 (symdiffE = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (symdiff @ X0 @ X1)) => ! [X3 : $o] : (((in @ X2 @ X0) => (~(in @ X2 @ X1) => X3)) => ((~(in @ X2 @ X0) => ((in @ X2 @ X1) => X3)) => X3))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE)).
% 21.36/3.52 thf(f131,axiom,(
% 21.36/3.52 (symdiffI1 = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (symdiff @ X0 @ X1)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1)).
% 21.36/3.52 thf(f132,axiom,(
% 21.36/3.52 (! [X1 : $i,X2 : $i,X0 : $i] : (~(in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (symdiff @ X0 @ X1)))) = symdiffI2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2)).
% 21.36/3.52 thf(f133,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => ~(in @ X2 @ (symdiff @ X0 @ X1)))) = symdiffIneg1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1)).
% 21.36/3.52 thf(f135,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair)).
% 21.36/3.52 thf(f136,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = setukpairIL)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL)).
% 21.36/3.52 thf(f137,axiom,(
% 21.36/3.52 (setukpairIR = ! [X1 : $i,X0 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR)).
% 21.36/3.52 thf(f138,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair)).
% 21.36/3.52 thf(f139,axiom,(
% 21.36/3.52 (kpairp = ! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp)).
% 21.36/3.52 thf(f140,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (subset @ (setadjoin @ X1 @ emptyset) @ X0)) = singletonsubset)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset)).
% 21.36/3.52 thf(f141,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0))) = singletoninpowerset)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset)).
% 21.36/3.52 thf(f148,axiom,(
% 21.36/3.52 (ubforcartprodlem3 = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3)).
% 21.36/3.52 thf(f149,axiom,(
% 21.36/3.52 (cartprodpairin = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin)).
% 21.36/3.52 thf(f150,axiom,(
% 21.36/3.52 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)))) = cartprodmempair1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 21.36/3.52 thf(f151,axiom,(
% 21.36/3.52 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (iskpair @ X2)) = cartprodmempair)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair)).
% 21.36/3.52 thf(f152,axiom,(
% 21.36/3.52 (setunionE2 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2)).
% 21.36/3.52 thf(f153,axiom,(
% 21.36/3.52 (! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0) = setunionsingleton1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1)).
% 21.36/3.52 thf(f154,axiom,(
% 21.36/3.52 (setunionsingleton2 = ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2)).
% 21.36/3.52 thf(f155,axiom,(
% 21.36/3.52 (! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset))) = X0) = setunionsingleton)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton)).
% 21.36/3.52 thf(f157,axiom,(
% 21.36/3.52 (! [X1 : ($i > $o),X0 : $i] : ((ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) => ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2))) = ex1E1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1)).
% 21.36/3.52 thf(f159,axiom,(
% 21.36/3.52 (! [X1 : ($i > $o),X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))))) = ex1I2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2)).
% 21.36/3.52 thf(f162,axiom,(
% 21.36/3.52 (kfstsingleton = ! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : ((in @ (setadjoin @ X1 @ emptyset) @ X0)))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton)).
% 21.36/3.52 thf(f163,axiom,(
% 21.36/3.52 (theprop = ! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop)).
% 21.36/3.52 thf(f164,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : (((kfst @ (kpair @ X0 @ X1))) = X0) = kfstpairEq)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq)).
% 21.36/3.52 thf(f165,axiom,(
% 21.36/3.52 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (kfst @ X2) @ X0)) = cartprodfstin)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin)).
% 21.36/3.52 thf(f167,axiom,(
% 21.36/3.52 (setukpairinjL = ! [X3 : $i,X0 : $i,X2 : $i,X1 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X0 = X2)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL)).
% 21.36/3.52 thf(f168,axiom,(
% 21.36/3.52 (setukpairinjR11 = ! [X1 : $i,X0 : $i] : ((X0 = X1) => (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11)).
% 21.36/3.52 thf(f171,axiom,(
% 21.36/3.52 (upairequniteq = ! [X1 : $i,X2 : $i,X0 : $i] : ((((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) => (X0 = X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq)).
% 21.36/3.52 thf(f172,axiom,(
% 21.36/3.52 (! [X3 : $i,X0 : $i,X1 : $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)) = setukpairinjR2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR2)).
% 21.36/3.52 thf(f175,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1) = ksndpairEq)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq)).
% 21.36/3.52 thf(f177,axiom,(
% 21.36/3.52 (cartprodsndin = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (ksnd @ X2) @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin)).
% 21.36/3.52 thf(f179,axiom,(
% 21.36/3.52 (! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) => (in @ X3 @ X1)) = cartprodpairmemER)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER)).
% 21.36/3.52 thf(f180,axiom,(
% 21.36/3.52 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kpair @ X2 @ X3)) = ((kpair @ X2 @ X3))))) = cartprodmempaircEq)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq)).
% 21.36/3.52 thf(f181,axiom,(
% 21.36/3.52 (cartprodfstpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kfst @ (kpair @ X2 @ X3))) = X2))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq)).
% 21.36/3.52 thf(f182,axiom,(
% 21.36/3.52 (cartprodsndpairEq = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((ksnd @ (kpair @ X2 @ X3))) = X3))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq)).
% 21.36/3.52 thf(f183,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (((kpair @ (kfst @ X2) @ (ksnd @ X2))) = X2)) = cartprodpairsurjEq)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq)).
% 21.36/3.52 thf(f184,axiom,(
% 21.36/3.52 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 21.36/3.52 thf(f185,axiom,(
% 21.36/3.52 (dpsetconstrI = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),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)))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)).
% 21.36/3.52 thf(f189,axiom,(
% 21.36/3.52 (dpsetconstrEL1 = ! [X4 : $i,X0 : $i,X3 : $i,X1 : $i,X2 : ($i > $i > $o)] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X3 @ X0)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL1)).
% 21.36/3.52 thf(f190,axiom,(
% 21.36/3.52 (! [X2 : ($i > $i > $o),X1 : $i,X4 : $i,X0 : $i,X3 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X4 @ X1)) = dpsetconstrEL2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL2)).
% 21.36/3.52 thf(f193,axiom,(
% 21.36/3.52 (! [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)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apProp)).
% 21.36/3.52 thf(f194,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))) = app)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app)).
% 21.36/3.52 thf(f196,axiom,(
% 21.36/3.52 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))) = ap2p)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p)).
% 21.36/3.52 thf(f197,axiom,(
% 21.36/3.52 (funcinfuncset = ! [X0 : $i,X2 : $i,X1 : $i] : ((func @ X0 @ X1 @ X2) => (in @ X2 @ (funcSet @ X0 @ X1))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset)).
% 21.36/3.52 thf(f198,axiom,(
% 21.36/3.52 (lamProp = ! [X2 : ($i > $i),X1 : $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)))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamProp)).
% 21.36/3.52 thf(f199,axiom,(
% 21.36/3.52 (lamp = ! [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)))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp)).
% 21.36/3.52 thf(f202,axiom,(
% 21.36/3.52 (! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4)))) = brelnall2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2)).
% 21.36/3.52 thf(f203,axiom,(
% 21.36/3.52 (ex1E2 = ! [X1 : ($i > $o),X0 : $i] : ((ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3)))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2)).
% 21.36/3.52 thf(f204,axiom,(
% 21.36/3.52 (! [X1 : $i,X2 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))) = funcGraphProp1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1)).
% 21.36/3.52 thf(f205,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))) = funcGraphProp3)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp3)).
% 21.36/3.52 thf(f208,axiom,(
% 21.36/3.52 (funcGraphProp4 = ! [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))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp4)).
% 21.36/3.52 thf(f213,axiom,(
% 21.36/3.52 (ap2apEq1 = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ X2 @ X3)) = ((ap @ X0 @ X1 @ X2 @ X3))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq1)).
% 21.36/3.52 thf(f214,axiom,(
% 21.36/3.52 (ap2apEq2 = ! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ X2 @ X3)) = ((ap @ X0 @ X1 @ X2 @ X3))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq2)).
% 21.36/3.52 thf(f215,axiom,(
% 21.36/3.52 (! [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3)) = ((X2 @ X3))))) = beta1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1)).
% 21.36/3.52 thf(f217,axiom,(
% 21.36/3.52 (lam2lamEq = ! [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (((lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3))))) = ((lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2lamEq)).
% 21.36/3.52 thf(f218,axiom,(
% 21.36/3.52 (! [X2 : ($i > $i),X0 : $i,X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((X2 @ X3)) = ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3))))) = beta2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta2)).
% 21.36/3.52 thf(f219,axiom,(
% 21.36/3.52 (eta2 = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (((lam @ X0 @ X1 @ (^[X3 : $i] : ((ap @ X0 @ X1 @ X2 @ X3))))) = X2)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta2)).
% 21.36/3.52 thf(f220,axiom,(
% 21.36/3.52 (iffalseProp1 = ! [X0 : $i,X2 : $i,X1 : $o] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X1 & (X4 = X2)) | ((X4 = X3) & ~X1)))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp1)).
% 21.36/3.52 thf(f224,axiom,(
% 21.36/3.52 (ifSingleton = ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : ((~X1 & (X4 = X3)) | (X1 & (X4 = X2)))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton)).
% 21.36/3.52 thf(f226,axiom,(
% 21.36/3.52 (theeq = ! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq)).
% 21.36/3.52 thf(f227,axiom,(
% 21.36/3.52 (! [X2 : $i,X0 : $i,X1 : $o] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (((if @ X0 @ X1 @ X2 @ X3)) = X2)))) = iftrue)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue)).
% 21.36/3.52 thf(f229,axiom,(
% 21.36/3.52 (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))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse)).
% 21.36/3.52 thf(f230,axiom,(
% 21.36/3.52 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem)).
% 21.36/3.52 thf(f232,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) = powersetT_lem)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem)).
% 21.36/3.52 thf(f233,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X0)))) = setminusT_lem)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem)).
% 21.36/3.52 thf(f234,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 21.36/3.52 thf(f238,axiom,(
% 21.36/3.52 (! [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)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTE1)).
% 21.36/3.52 thf(f239,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1))))) = complementTI1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTI1)).
% 21.36/3.52 thf(f245,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ X2) => (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))) = contrasubsetT2)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT2)).
% 21.36/3.52 thf(f247,axiom,(
% 21.36/3.52 (doubleComplementI1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1)).
% 21.36/3.52 thf(f248,axiom,(
% 21.36/3.52 (doubleComplementE1 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1))) => (in @ X2 @ X1)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1)).
% 21.36/3.52 thf(f250,axiom,(
% 21.36/3.52 (doubleComplementSub2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1)))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub2)).
% 21.36/3.52 thf(f251,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (X1 = ((setminus @ X0 @ (setminus @ X0 @ X1))))) = doubleComplementEq)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq)).
% 21.36/3.52 thf(f252,axiom,(
% 21.36/3.52 (! [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 @ (binintersect @ X1 @ X2)))))) = complementTnotintersectT)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT)).
% 21.36/3.52 thf(f254,axiom,(
% 21.36/3.52 (complementSubsetComplementIntersect = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect)).
% 21.36/3.52 thf(f255,axiom,(
% 21.36/3.52 (! [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)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementInPowersetComplementIntersect)).
% 21.36/3.52 thf(f256,axiom,(
% 21.36/3.52 (contraSubsetComplement = ! [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))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement)).
% 21.36/3.52 thf(f257,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))) = complementTcontraSubset)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTcontraSubset)).
% 21.36/3.52 thf(f258,axiom,(
% 21.36/3.52 (! [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)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra)).
% 21.36/3.52 thf(f263,axiom,(
% 21.36/3.52 (intersectInPowersetIntersectUnions = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions)).
% 21.36/3.52 thf(f264,axiom,(
% 21.36/3.52 (inComplementUnionImpNotIn1 = ! [X0 : $i,X1 : $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 @ X1))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpNotIn1)).
% 21.36/3.52 thf(f265,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $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)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpInComplement1)).
% 21.36/3.52 thf(f268,axiom,(
% 21.36/3.52 (demorgan2a1 = ! [X0 : $i,X1 : $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)))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a1)).
% 21.36/3.52 thf(f269,axiom,(
% 21.36/3.52 (complementUnionInPowersetComplement = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementUnionInPowersetComplement)).
% 21.36/3.52 thf(f272,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = demorgan1b)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1b)).
% 21.36/3.52 thf(f277,axiom,(
% 21.36/3.52 (demorgan2 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (((setminus @ X0 @ (binunion @ X1 @ X2))) = ((binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2)).
% 21.36/3.52 thf(f278,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (binintersect @ X1 @ X2)) => (in @ X3 @ X0)))) = woz13rule0)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule0)).
% 21.36/3.52 thf(f279,axiom,(
% 21.36/3.52 (woz13rule1 = ! [X1 : $i,X0 : $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))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule1)).
% 21.36/3.52 thf(f280,axiom,(
% 21.36/3.52 (woz13rule2 = ! [X1 : $i,X0 : $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))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule2)).
% 21.36/3.52 thf(f281,axiom,(
% 21.36/3.52 (woz13rule3 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule3)).
% 21.36/3.52 thf(f285,axiom,(
% 21.36/3.52 (woz1_3 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_3)).
% 21.36/3.52 thf(f286,axiom,(
% 21.36/3.52 (woz1_4 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_4)).
% 21.36/3.52 thf(f287,axiom,(
% 21.36/3.52 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))) = woz1_5)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_5)).
% 21.36/3.52 thf(f288,axiom,(
% 21.36/3.52 ((^[X0 : $i, X1 : $i] : ((breln @ X0 @ X0 @ X1))) = breln1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1)).
% 21.36/3.52 thf(f289,axiom,(
% 21.36/3.52 (breln1all2 = ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($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)))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all2)).
% 21.36/3.52 thf(f290,axiom,(
% 21.36/3.52 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (breln1Set @ X0)) => (breln1 @ X0 @ X1)) = breln1SetBreln1)),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1SetBreln1)).
% 21.36/3.52 thf(f293,conjecture,(
% 21.36/3.52 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 => ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 21.36/3.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all1)).
% 21.36/3.52 thf(f294,negated_conjecture,(
% 21.36/3.52 ~(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 => ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 21.36/3.52 inference(negated_conjecture,[status(cth)],[f293])).
% 21.36/3.52 thf(f295,plain,(
% 21.36/3.52 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 21.36/3.52 inference(rectify,[],[f3])).
% 21.36/3.52 thf(f296,plain,(
% 21.36/3.52 (emptysetAx = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 21.36/3.52 inference(fool_elimination,[],[f295])).
% 21.36/3.52 thf(f299,plain,(
% 21.36/3.52 (! [X0 : $i,X1 : ($i > $o)] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X0) => ~(X1 @ X3))) = quantDeMorgan3)),
% 21.36/3.52 inference(rectify,[],[f57])).
% 21.36/3.52 thf(f300,plain,(
% 21.36/3.52 (quantDeMorgan3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))))))))))),
% 21.36/3.52 inference(fool_elimination,[],[f299])).
% 21.36/3.52 thf(f301,plain,(
% 21.36/3.52 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X0 @ X2)) => (iskpair @ X1)) = cartprodmempair)),
% 21.36/3.52 inference(rectify,[],[f151])).
% 21.36/3.52 thf(f302,plain,(
% 21.36/3.52 (cartprodmempair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1))))))))))),
% 21.36/3.52 inference(fool_elimination,[],[f301])).
% 21.36/3.52 thf(f303,plain,(
% 21.36/3.52 (binintersectSubset3 = ! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0)))),
% 21.36/3.52 inference(rectify,[],[f113])).
% 21.36/3.53 thf(f304,plain,(
% 21.36/3.53 (binintersectSubset3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f303])).
% 21.36/3.53 thf(f305,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ X2) => (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))) = contrasubsetT2)),
% 21.36/3.53 inference(rectify,[],[f245])).
% 21.36/3.53 thf(f306,plain,(
% 21.36/3.53 (contrasubsetT2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ Y2) => (subset @ (setminus @ Y1 @ Y2) @ (setminus @ Y1 @ Y0)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f305])).
% 21.36/3.53 thf(f311,plain,(
% 21.36/3.53 (setunionsingleton = ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0)))))),
% 21.36/3.53 inference(fool_elimination,[],[f155])).
% 21.36/3.53 thf(f312,plain,(
% 21.36/3.53 (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))))))),
% 21.36/3.53 inference(rectify,[],[f214])).
% 21.36/3.53 thf(f313,plain,(
% 21.36/3.53 (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))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f312])).
% 21.36/3.53 thf(f316,plain,(
% 21.36/3.53 (cartprodpairin = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)))))),
% 21.36/3.53 inference(rectify,[],[f149])).
% 21.36/3.53 thf(f317,plain,(
% 21.36/3.53 (cartprodpairin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f316])).
% 21.36/3.53 thf(f320,plain,(
% 21.36/3.53 (! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => ! [X4 : $i] : ((in @ X4 @ X2) => (((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[X5 : $i] : ((X0 @ X5)))) @ X4)) = ((X0 @ X4))))) = beta1)),
% 21.36/3.53 inference(rectify,[],[f215])).
% 21.36/3.53 thf(f321,plain,(
% 21.36/3.53 (beta1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3) = (Y2 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f320])).
% 21.36/3.53 thf(f322,plain,(
% 21.36/3.53 (kfstsingleton = ! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : ((in @ (setadjoin @ X1 @ emptyset) @ X0)))))))),
% 21.36/3.53 inference(rectify,[],[f162])).
% 21.36/3.53 thf(f323,plain,(
% 21.36/3.53 (kfstsingleton = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f322])).
% 21.36/3.53 thf(f328,plain,(
% 21.36/3.53 (! [X0 : ($i > $o),X1 : $i] : ((in @ X1 @ emptyset) => (X0 @ X1)) = vacuousDall)),
% 21.36/3.53 inference(rectify,[],[f54])).
% 21.36/3.53 thf(f329,plain,(
% 21.36/3.53 (vacuousDall = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f328])).
% 21.36/3.53 thf(f330,plain,(
% 21.36/3.53 (exuI1 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X3 : $i] : ((X0 @ X3))))))),
% 21.36/3.53 inference(rectify,[],[f63])).
% 21.36/3.53 thf(f331,plain,(
% 21.36/3.53 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f330])).
% 21.36/3.53 thf(f332,plain,(
% 21.36/3.53 (doubleComplementE1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))) => (in @ X2 @ X0)))))),
% 21.36/3.53 inference(rectify,[],[f248])).
% 21.36/3.53 thf(f333,plain,(
% 21.36/3.53 (doubleComplementE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (setminus @ Y0 @ (setminus @ Y0 @ Y1))) => (in @ Y2 @ Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f332])).
% 21.36/3.53 thf(f342,plain,(
% 21.36/3.53 (setukpairIR = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 21.36/3.53 inference(rectify,[],[f137])).
% 21.36/3.53 thf(f343,plain,(
% 21.36/3.53 (setukpairIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f342])).
% 21.36/3.53 thf(f344,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (binintersect @ X0 @ X2)) => (in @ X3 @ X1)))) = woz13rule0)),
% 21.36/3.53 inference(rectify,[],[f278])).
% 21.36/3.53 thf(f345,plain,(
% 21.36/3.53 (woz13rule0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y1 @ Y2)) => (in @ Y3 @ Y0))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f344])).
% 21.36/3.53 thf(f348,plain,(
% 21.36/3.53 (subPowSU = ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (powerset @ (setunion @ X1)))))),
% 21.36/3.53 inference(rectify,[],[f43])).
% 21.36/3.53 thf(f349,plain,(
% 21.36/3.53 (subPowSU = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f348])).
% 21.36/3.53 thf(f350,plain,(
% 21.36/3.53 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 21.36/3.53 inference(fool_elimination,[],[f27])).
% 21.36/3.53 thf(f353,plain,(
% 21.36/3.53 (doubleComplementI1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 21.36/3.53 inference(rectify,[],[f247])).
% 21.36/3.53 thf(f354,plain,(
% 21.36/3.53 (doubleComplementI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f353])).
% 21.36/3.53 thf(f359,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)) = setadjoinSub)),
% 21.36/3.53 inference(rectify,[],[f90])).
% 21.36/3.53 thf(f360,plain,(
% 21.36/3.53 (setadjoinSub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f359])).
% 21.36/3.53 thf(f361,plain,(
% 21.36/3.53 (inComplementUnionImpNotIn1 = ! [X0 : $i,X1 : $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 @ X1))))))),
% 21.36/3.53 inference(rectify,[],[f264])).
% 21.36/3.53 thf(f362,plain,(
% 21.36/3.53 (inComplementUnionImpNotIn1 = ((!! @ $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 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f361])).
% 21.36/3.53 thf(f363,plain,(
% 21.36/3.53 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 21.36/3.53 inference(rectify,[],[f28])).
% 21.36/3.53 thf(f364,plain,(
% 21.36/3.53 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f363])).
% 21.36/3.53 thf(f365,plain,(
% 21.36/3.53 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = noeltsimpempty)),
% 21.36/3.53 inference(rectify,[],[f25])).
% 21.36/3.53 thf(f366,plain,(
% 21.36/3.53 (noeltsimpempty = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 21.36/3.53 inference(fool_elimination,[],[f365])).
% 21.36/3.53 thf(f369,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (powerset @ X2)) => ((in @ X1 @ X0) => (in @ X1 @ X2))) = powersetE)),
% 21.36/3.53 inference(rectify,[],[f40])).
% 21.36/3.53 thf(f370,plain,(
% 21.36/3.53 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f369])).
% 21.36/3.53 thf(f373,plain,(
% 21.36/3.53 (powerset__Cong = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((powerset @ X0)) = ((powerset @ X1)))))),
% 21.36/3.53 inference(rectify,[],[f72])).
% 21.36/3.53 thf(f374,plain,(
% 21.36/3.53 (powerset__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f373])).
% 21.36/3.53 thf(f377,plain,(
% 21.36/3.53 (funcGraphProp4 = ! [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))))))),
% 21.36/3.53 inference(rectify,[],[f208])).
% 21.36/3.53 thf(f378,plain,(
% 21.36/3.53 (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)))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f377])).
% 21.36/3.53 thf(f381,plain,(
% 21.36/3.53 (complementSubsetComplementIntersect = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (subset @ (setminus @ X1 @ X0) @ (setminus @ X1 @ (binintersect @ X0 @ X2))))))),
% 21.36/3.53 inference(rectify,[],[f254])).
% 21.36/3.53 thf(f382,plain,(
% 21.36/3.53 (complementSubsetComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f381])).
% 21.36/3.53 thf(f385,plain,(
% 21.36/3.53 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X1 @ X0)))),
% 21.36/3.53 inference(rectify,[],[f106])).
% 21.36/3.53 thf(f386,plain,(
% 21.36/3.53 (binunionLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f385])).
% 21.36/3.53 thf(f387,plain,(
% 21.36/3.53 (! [X0 : $i] : (((dsetconstr @ X0 @ (^[X1 : $i] : ($true)))) = X0) = setoftrueEq)),
% 21.36/3.53 inference(rectify,[],[f36])).
% 21.36/3.53 thf(f388,plain,(
% 21.36/3.53 (setoftrueEq = ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0)))))),
% 21.36/3.53 inference(fool_elimination,[],[f387])).
% 21.36/3.53 thf(f389,plain,(
% 21.36/3.53 (setbeta = ! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((in @ X0 @ X1) => ((X2 @ X0) <=> (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : ((X2 @ X3))))))))),
% 21.36/3.53 inference(rectify,[],[f26])).
% 21.36/3.53 thf(f390,plain,(
% 21.36/3.53 (setbeta = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f389])).
% 21.36/3.53 thf(f391,plain,(
% 21.36/3.53 (setukpairinjR11 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setadjoin @ X1 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))))),
% 21.36/3.53 inference(rectify,[],[f168])).
% 21.36/3.53 thf(f392,plain,(
% 21.36/3.53 (setukpairinjR11 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f391])).
% 21.36/3.53 thf(f395,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : (((X1 = X2) | (in @ X1 @ X0)) <=> (in @ X1 @ (setadjoin @ X2 @ X0))) = setadjoinAx)),
% 21.36/3.53 inference(rectify,[],[f4])).
% 21.36/3.53 thf(f396,plain,(
% 21.36/3.53 (setadjoinAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y2) | (Y1 = Y0)) = (in @ Y1 @ (setadjoin @ Y0 @ Y2)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f395])).
% 21.36/3.53 thf(f397,plain,(
% 21.36/3.53 (! [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 @ (binintersect @ X1 @ X2)))))) = complementTnotintersectT)),
% 21.36/3.53 inference(rectify,[],[f252])).
% 21.36/3.53 thf(f398,plain,(
% 21.36/3.53 (complementTnotintersectT = ((!! @ $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 @ (binintersect @ Y0 @ Y2)))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f397])).
% 21.36/3.53 thf(f401,plain,(
% 21.36/3.53 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 21.36/3.53 inference(rectify,[],[f78])).
% 21.36/3.53 thf(f402,plain,(
% 21.36/3.53 (subsetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f401])).
% 21.36/3.53 thf(f403,plain,(
% 21.36/3.53 (woz13rule2 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))))),
% 21.36/3.53 inference(rectify,[],[f280])).
% 21.36/3.53 thf(f404,plain,(
% 21.36/3.53 (woz13rule2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3)))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f403])).
% 21.36/3.53 thf(f407,plain,(
% 21.36/3.53 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 21.36/3.53 inference(rectify,[],[f20])).
% 21.36/3.53 thf(f408,plain,(
% 21.36/3.53 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false)))))),
% 21.36/3.53 inference(fool_elimination,[],[f407])).
% 21.36/3.53 thf(f409,plain,(
% 21.36/3.53 (! [X0 : $i] : ((in @ X0 @ omega) => (in @ (setadjoin @ X0 @ X0) @ omega)) = omegaSAx)),
% 21.36/3.53 inference(rectify,[],[f8])).
% 21.36/3.53 thf(f410,plain,(
% 21.36/3.53 (omegaSAx = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega))))))),
% 21.36/3.53 inference(fool_elimination,[],[f409])).
% 21.36/3.53 thf(f411,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X3 @ X1) => (in @ X2 @ X0)))) = inCongP)),
% 21.36/3.53 inference(rectify,[],[f66])).
% 21.36/3.53 thf(f412,plain,(
% 21.36/3.53 (inCongP = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) => (in @ Y3 @ Y1))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f411])).
% 21.36/3.53 thf(f413,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))) = singletoninpowerset)),
% 21.36/3.53 inference(rectify,[],[f141])).
% 21.36/3.53 thf(f414,plain,(
% 21.36/3.53 (singletoninpowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f413])).
% 21.36/3.53 thf(f417,plain,(
% 21.36/3.53 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => (in @ X0 @ (setminus @ X2 @ X1)))))),
% 21.36/3.53 inference(rectify,[],[f120])).
% 21.36/3.53 thf(f418,plain,(
% 21.36/3.53 (setminusI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f417])).
% 21.36/3.53 thf(f419,plain,(
% 21.36/3.53 (doubleComplementSub2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1)))),
% 21.36/3.53 inference(rectify,[],[f250])).
% 21.36/3.53 thf(f420,plain,(
% 21.36/3.53 (doubleComplementSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)) @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f419])).
% 21.36/3.53 thf(f425,plain,(
% 21.36/3.53 (demorgan2 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (((setminus @ X1 @ (binunion @ X0 @ X2))) = ((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))))))),
% 21.36/3.53 inference(rectify,[],[f277])).
% 21.36/3.53 thf(f426,plain,(
% 21.36/3.53 (demorgan2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((setminus @ Y0 @ (binunion @ Y1 @ Y2)) = (binintersect @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f425])).
% 21.36/3.53 thf(f427,plain,(
% 21.36/3.53 (woz1_3 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3))))))))),
% 21.36/3.53 inference(rectify,[],[f285])).
% 21.36/3.53 thf(f428,plain,(
% 21.36/3.53 (woz1_3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3)))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f427])).
% 21.36/3.53 thf(f433,plain,(
% 21.36/3.53 (! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X3 : $i] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))) => (exu @ (^[X4 : $i] : ((X0 @ X4)))))) = exuI3)),
% 21.36/3.53 inference(rectify,[],[f64])).
% 21.36/3.53 thf(f434,plain,(
% 21.36/3.53 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f433])).
% 21.36/3.53 thf(f435,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (in @ (kfst @ X1) @ X2)) = cartprodfstin)),
% 21.36/3.53 inference(rectify,[],[f165])).
% 21.36/3.53 thf(f436,plain,(
% 21.36/3.53 (cartprodfstin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f435])).
% 21.36/3.53 thf(f437,plain,(
% 21.36/3.53 (subsetRefl = ! [X0 : $i] : (subset @ X0 @ X0))),
% 21.36/3.53 inference(rectify,[],[f88])).
% 21.36/3.53 thf(f438,plain,(
% 21.36/3.53 (subsetRefl = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))))),
% 21.36/3.53 inference(fool_elimination,[],[f437])).
% 21.36/3.53 thf(f439,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = eqinunit)),
% 21.36/3.53 inference(rectify,[],[f48])).
% 21.36/3.53 thf(f440,plain,(
% 21.36/3.53 (eqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f439])).
% 21.36/3.53 thf(f441,plain,(
% 21.36/3.53 (! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))) = prop2setI)),
% 21.36/3.53 inference(rectify,[],[f59])).
% 21.36/3.53 thf(f442,plain,(
% 21.36/3.53 (prop2setI = ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f441])).
% 21.36/3.53 thf(f443,plain,(
% 21.36/3.53 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 21.36/3.53 inference(rectify,[],[f230])).
% 21.36/3.53 thf(f444,plain,(
% 21.36/3.53 (binintersectT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f443])).
% 21.36/3.53 thf(f447,plain,(
% 21.36/3.53 (notdexE = ! [X0 : ($i > $o),X1 : $i] : (~ ? [X2 : $i] : ((X0 @ X2) & (in @ X2 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ~(X0 @ X3))))),
% 21.36/3.53 inference(rectify,[],[f61])).
% 21.36/3.53 thf(f448,plain,(
% 21.36/3.53 (notdexE = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f447])).
% 21.36/3.53 thf(f449,plain,(
% 21.36/3.53 (dpsetconstrEL1 = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : ($i > $i > $o)] : ((in @ (kpair @ X2 @ X0) @ (dpsetconstr @ X1 @ X3 @ (^[X5 : $i, X6 : $i] : ((X4 @ X5 @ X6))))) => (in @ X2 @ X1)))),
% 21.36/3.53 inference(rectify,[],[f189])).
% 21.36/3.53 thf(f450,plain,(
% 21.36/3.53 (dpsetconstrEL1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (in @ Y2 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f449])).
% 21.36/3.53 thf(f451,plain,(
% 21.36/3.53 (sepSubset = ! [X0 : ($i > $o),X1 : $i] : (subset @ (dsetconstr @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) @ X1))),
% 21.36/3.53 inference(rectify,[],[f100])).
% 21.36/3.53 thf(f452,plain,(
% 21.36/3.53 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ Y0)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f451])).
% 21.36/3.53 thf(f453,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (ap @ X2 @ X0 @ X1 @ X3) @ X0))) = ap2p)),
% 21.36/3.53 inference(rectify,[],[f196])).
% 21.36/3.53 thf(f454,plain,(
% 21.36/3.53 (ap2p = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f453])).
% 21.36/3.53 thf(f457,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1)) = singletonsubset)),
% 21.36/3.53 inference(rectify,[],[f140])).
% 21.36/3.53 thf(f458,plain,(
% 21.36/3.53 (singletonsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f457])).
% 21.36/3.53 thf(f459,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X0) = binintersectRsub)),
% 21.36/3.53 inference(rectify,[],[f116])).
% 21.36/3.53 thf(f460,plain,(
% 21.36/3.53 (binintersectRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f459])).
% 21.36/3.53 thf(f463,plain,(
% 21.36/3.53 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 21.36/3.53 inference(rectify,[],[f31])).
% 21.36/3.53 thf(f464,plain,(
% 21.36/3.53 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f463])).
% 21.36/3.53 thf(f465,plain,(
% 21.36/3.53 (ap2apEq1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (funcSet @ X1 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X1) => (((ap @ X1 @ X2 @ X0 @ X3)) = ((ap @ X1 @ X2 @ X0 @ X3))))))),
% 21.36/3.53 inference(rectify,[],[f213])).
% 21.36/3.53 thf(f466,plain,(
% 21.36/3.53 (ap2apEq1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ Y1 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = (ap @ Y1 @ Y0 @ Y2 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f465])).
% 21.36/3.53 thf(f467,plain,(
% 21.36/3.53 (nonemptyI1 = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))),
% 21.36/3.53 inference(rectify,[],[f30])).
% 21.36/3.53 thf(f468,plain,(
% 21.36/3.53 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0))))))),
% 21.36/3.53 inference(fool_elimination,[],[f467])).
% 21.36/3.53 thf(f471,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (emptyset = ((binintersect @ X1 @ X0)))) = disjointsetsI1)),
% 21.36/3.53 inference(rectify,[],[f115])).
% 21.36/3.53 thf(f472,plain,(
% 21.36/3.53 (disjointsetsI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f471])).
% 21.36/3.53 thf(f473,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))) = notinsingleton)),
% 21.36/3.53 inference(rectify,[],[f47])).
% 21.36/3.53 thf(f474,plain,(
% 21.36/3.53 (notinsingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f473])).
% 21.36/3.53 thf(f475,plain,(
% 21.36/3.53 (cartprodfstpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kfst @ (kpair @ X2 @ X3))) = X2))))),
% 21.36/3.53 inference(rectify,[],[f181])).
% 21.36/3.53 thf(f476,plain,(
% 21.36/3.53 (cartprodfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f475])).
% 21.36/3.53 thf(f477,plain,(
% 21.36/3.53 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 21.36/3.53 inference(fool_elimination,[],[f288])).
% 21.36/3.53 thf(f478,plain,(
% 21.36/3.53 (setunionE2 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X0 @ X2))))),
% 21.36/3.53 inference(rectify,[],[f152])).
% 21.36/3.53 thf(f479,plain,(
% 21.36/3.53 (setunionE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f478])).
% 21.36/3.53 thf(f480,plain,(
% 21.36/3.53 (cartprodsndpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (((ksnd @ (kpair @ X0 @ X3))) = X3))))),
% 21.36/3.53 inference(rectify,[],[f182])).
% 21.36/3.53 thf(f481,plain,(
% 21.36/3.53 (cartprodsndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f480])).
% 21.36/3.53 thf(f482,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))) = app)),
% 21.36/3.53 inference(rectify,[],[f194])).
% 21.36/3.53 thf(f483,plain,(
% 21.36/3.53 (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)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f482])).
% 21.36/3.53 thf(f484,plain,(
% 21.36/3.53 (binunionRsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 21.36/3.53 inference(rectify,[],[f107])).
% 21.36/3.53 thf(f485,plain,(
% 21.36/3.53 (binunionRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f484])).
% 21.36/3.53 thf(f488,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ (binunion @ X0 @ X2)) @ (powerset @ (setminus @ X1 @ X0))))) = woz1_5)),
% 21.36/3.53 inference(rectify,[],[f287])).
% 21.36/3.53 thf(f489,plain,(
% 21.36/3.53 (woz1_5 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ (binunion @ Y1 @ Y2)) @ (powerset @ (setminus @ Y0 @ Y1)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f488])).
% 21.36/3.53 thf(f490,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))) = complementT_lem)),
% 21.36/3.53 inference(rectify,[],[f234])).
% 21.36/3.53 thf(f491,plain,(
% 21.36/3.53 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f490])).
% 21.36/3.53 thf(f494,plain,(
% 21.36/3.53 (symdiffI1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (~(in @ X2 @ X0) => (in @ X2 @ (symdiff @ X1 @ X0)))))),
% 21.36/3.53 inference(rectify,[],[f131])).
% 21.36/3.53 thf(f495,plain,(
% 21.36/3.53 (symdiffI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f494])).
% 21.36/3.53 thf(f496,plain,(
% 21.36/3.53 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f184])).
% 21.36/3.53 thf(f497,plain,(
% 21.36/3.53 (! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X0 @ X3) @ X2)) => ! [X4 : $i] : ((in @ X4 @ X1) => (((X0 @ X4)) = ((ap @ X1 @ X2 @ (lam @ X1 @ X2 @ (^[X5 : $i] : ((X0 @ X5)))) @ X4))))) = beta2)),
% 21.36/3.53 inference(rectify,[],[f218])).
% 21.36/3.53 thf(f498,plain,(
% 21.36/3.53 (beta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) = (ap @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f497])).
% 21.36/3.53 thf(f499,plain,(
% 21.36/3.53 (! [X0 : ($i > $o),X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X0 @ X4) & (in @ X4 @ X1)) => (ex1 @ X1 @ (^[X5 : $i] : ((X0 @ X5)))))) = ex1I2)),
% 21.36/3.53 inference(rectify,[],[f159])).
% 21.36/3.53 thf(f500,plain,(
% 21.36/3.53 (ex1I2 = ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f499])).
% 21.36/3.53 thf(f501,plain,(
% 21.36/3.53 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = emptyI)),
% 21.36/3.53 inference(rectify,[],[f24])).
% 21.36/3.53 thf(f502,plain,(
% 21.36/3.53 (emptyI = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 21.36/3.53 inference(fool_elimination,[],[f501])).
% 21.36/3.53 thf(f507,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((subset @ X2 @ X0) => (subset @ X1 @ X0))) = subsetTrans)),
% 21.36/3.53 inference(rectify,[],[f89])).
% 21.36/3.53 thf(f508,plain,(
% 21.36/3.53 (subsetTrans = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y2) => (subset @ Y1 @ Y2)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f507])).
% 21.36/3.53 thf(f509,plain,(
% 21.36/3.53 (! [X0 : ($i > $i > $o),X1 : $i,X2 : $i,X3 : $i,X4 : $i] : ((in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X3 @ X1 @ (^[X5 : $i, X6 : $i] : ((X0 @ X5 @ X6))))) => (in @ X2 @ X1)) = dpsetconstrEL2)),
% 21.36/3.53 inference(rectify,[],[f190])).
% 21.36/3.53 thf(f510,plain,(
% 21.36/3.53 (dpsetconstrEL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ Y1 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (in @ Y2 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f509])).
% 21.36/3.53 thf(f511,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => ? [X3 : $i] : ((in @ X3 @ X2) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X1) & (in @ X4 @ X0)))) = cartprodmempair1)),
% 21.36/3.53 inference(rectify,[],[f150])).
% 21.36/3.53 thf(f512,plain,(
% 21.36/3.53 (cartprodmempair1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & ((kpair @ Y3 @ Y4) = Y1)))) & (in @ Y3 @ Y0)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f511])).
% 21.36/3.53 thf(f517,plain,(
% 21.36/3.53 (emptyset__Cong = ((emptyset = emptyset)))),
% 21.36/3.53 inference(fool_elimination,[],[f70])).
% 21.36/3.53 thf(f518,plain,(
% 21.36/3.53 (notsubsetI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (~(in @ X2 @ X0) => ~(subset @ X1 @ X0))))),
% 21.36/3.53 inference(rectify,[],[f85])).
% 21.36/3.53 thf(f519,plain,(
% 21.36/3.53 (notsubsetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f518])).
% 21.36/3.53 thf(f520,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X0)))) = setminusT_lem)),
% 21.36/3.53 inference(rectify,[],[f233])).
% 21.36/3.53 thf(f521,plain,(
% 21.36/3.53 (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))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f520])).
% 21.36/3.53 thf(f524,plain,(
% 21.36/3.53 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 21.36/3.53 inference(fool_elimination,[],[f32])).
% 21.36/3.53 thf(f525,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1))))) = complementTI1)),
% 21.36/3.53 inference(rectify,[],[f239])).
% 21.36/3.53 thf(f526,plain,(
% 21.36/3.53 (complementTI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f525])).
% 21.36/3.53 thf(f529,plain,(
% 21.36/3.53 (funcinfuncset = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => (in @ X1 @ (funcSet @ X0 @ X2))))),
% 21.36/3.53 inference(rectify,[],[f197])).
% 21.36/3.53 thf(f530,plain,(
% 21.36/3.53 (funcinfuncset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (in @ Y1 @ (funcSet @ Y2 @ Y0)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f529])).
% 21.36/3.53 thf(f531,plain,(
% 21.36/3.53 (complementUnionInPowersetComplement = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ (binunion @ X0 @ X2)) @ (powerset @ (setminus @ X1 @ X0))))))),
% 21.36/3.53 inference(rectify,[],[f269])).
% 21.36/3.53 thf(f532,plain,(
% 21.36/3.53 (complementUnionInPowersetComplement = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ (binunion @ Y1 @ Y2)) @ (powerset @ (setminus @ Y0 @ Y1)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f531])).
% 21.36/3.53 thf(f535,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ X0) => ~(in @ X2 @ (symdiff @ X1 @ X0)))) = symdiffIneg1)),
% 21.36/3.53 inference(rectify,[],[f133])).
% 21.36/3.53 thf(f536,plain,(
% 21.36/3.53 (symdiffIneg1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f535])).
% 21.36/3.53 thf(f537,plain,(
% 21.36/3.53 (omega__Cong = ((omega = omega)))),
% 21.36/3.53 inference(fool_elimination,[],[f74])).
% 21.36/3.53 thf(f538,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X1 @ X0)) = X1)) = binintersectSubset2)),
% 21.36/3.53 inference(rectify,[],[f112])).
% 21.36/3.53 thf(f539,plain,(
% 21.36/3.53 (binintersectSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f538])).
% 21.36/3.53 thf(f540,plain,(
% 21.36/3.53 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 21.36/3.53 inference(rectify,[],[f80])).
% 21.36/3.53 thf(f541,plain,(
% 21.36/3.53 (eqimpsubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f540])).
% 21.36/3.53 thf(f544,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1))) = setminusIRneg)),
% 21.36/3.53 inference(rectify,[],[f127])).
% 21.36/3.53 thf(f545,plain,(
% 21.36/3.53 (setminusIRneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f544])).
% 21.36/3.53 thf(f546,plain,(
% 21.36/3.53 (symdiffE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (symdiff @ X0 @ X2)) => ! [X3 : $o] : (((in @ X1 @ X0) => (~(in @ X1 @ X2) => X3)) => ((~(in @ X1 @ X0) => ((in @ X1 @ X2) => X3)) => X3))))),
% 21.36/3.53 inference(rectify,[],[f130])).
% 21.36/3.53 thf(f547,plain,(
% 21.36/3.53 (symdiffE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f546])).
% 21.36/3.53 thf(f548,plain,(
% 21.36/3.53 (setunionsingleton2 = ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))),
% 21.36/3.53 inference(rectify,[],[f154])).
% 21.36/3.53 thf(f549,plain,(
% 21.36/3.53 (setunionsingleton2 = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f548])).
% 21.36/3.53 thf(f550,plain,(
% 21.36/3.53 (lamProp = ! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => (func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[X4 : $i, X5 : $i] : ((((X0 @ X4)) = X5)))))))),
% 21.36/3.53 inference(rectify,[],[f198])).
% 21.36/3.53 thf(f551,plain,(
% 21.36/3.53 (lamProp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (func @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f550])).
% 21.36/3.53 thf(f554,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2)) => ~ ? [X3 : $i] : ((in @ X3 @ X0) & (X1 @ X3))) = quantDeMorgan2)),
% 21.36/3.53 inference(rectify,[],[f56])).
% 21.36/3.53 thf(f555,plain,(
% 21.36/3.53 (quantDeMorgan2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f554])).
% 21.36/3.53 thf(f558,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))) = complementTcontraSubset)),
% 21.36/3.53 inference(rectify,[],[f257])).
% 21.36/3.53 thf(f559,plain,(
% 21.36/3.53 (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)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f558])).
% 21.36/3.53 thf(f562,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (((kpair @ (kfst @ X2) @ (ksnd @ X2))) = X2)) = cartprodpairsurjEq)),
% 21.36/3.53 inference(rectify,[],[f183])).
% 21.36/3.53 thf(f563,plain,(
% 21.36/3.53 (cartprodpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f562])).
% 21.36/3.53 thf(f564,plain,(
% 21.36/3.53 (upairsetIR = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 21.36/3.53 inference(rectify,[],[f52])).
% 21.36/3.53 thf(f565,plain,(
% 21.36/3.53 (upairsetIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f564])).
% 21.36/3.53 thf(f566,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 21.36/3.53 inference(rectify,[],[f37])).
% 21.36/3.53 thf(f567,plain,(
% 21.36/3.53 (powersetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f566])).
% 21.36/3.53 thf(f568,plain,(
% 21.36/3.53 (upairequniteq = ! [X0 : $i,X1 : $i,X2 : $i] : ((((setadjoin @ X1 @ emptyset)) = ((setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) => (X0 = X2)))),
% 21.36/3.53 inference(rectify,[],[f171])).
% 21.36/3.53 thf(f569,plain,(
% 21.36/3.53 (upairequniteq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => (Y2 = Y0))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f568])).
% 21.36/3.53 thf(f570,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (kpair @ X3 @ (ap @ X2 @ X0 @ X1 @ X3)) @ X1))) = funcGraphProp1)),
% 21.36/3.53 inference(rectify,[],[f204])).
% 21.36/3.53 thf(f571,plain,(
% 21.36/3.53 (funcGraphProp1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y2 @ Y1 @ Y3)) @ Y1)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f570])).
% 21.36/3.53 thf(f572,plain,(
% 21.36/3.53 (setadjoinOr = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X1 @ X2)) => ((in @ X0 @ X2) | (X0 = X1))))),
% 21.36/3.53 inference(rectify,[],[f35])).
% 21.36/3.53 thf(f573,plain,(
% 21.36/3.53 (setadjoinOr = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f572])).
% 21.36/3.53 thf(f576,plain,(
% 21.36/3.53 (singletonsswitch = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 21.36/3.53 inference(rectify,[],[f49])).
% 21.36/3.53 thf(f577,plain,(
% 21.36/3.53 (singletonsswitch = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f576])).
% 21.36/3.53 thf(f580,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 21.36/3.53 inference(rectify,[],[f135])).
% 21.36/3.53 thf(f581,plain,(
% 21.36/3.53 (secondinupair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f580])).
% 21.36/3.53 thf(f582,plain,(
% 21.36/3.53 (nonemptyI = ! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X0 @ X2) => ((X1 @ X0) => (nonempty @ (dsetconstr @ X2 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 21.36/3.53 inference(rectify,[],[f29])).
% 21.36/3.53 thf(f583,plain,(
% 21.36/3.53 (nonemptyI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (nonempty @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f582])).
% 21.36/3.53 thf(f584,plain,(
% 21.36/3.53 (cartprodsndin = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X2 @ X1)) => (in @ (ksnd @ X0) @ X1)))),
% 21.36/3.53 inference(rectify,[],[f177])).
% 21.36/3.53 thf(f585,plain,(
% 21.36/3.53 (cartprodsndin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f584])).
% 21.36/3.53 thf(f586,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset2)),
% 21.36/3.53 inference(rectify,[],[f79])).
% 21.36/3.53 thf(f587,plain,(
% 21.36/3.53 (eqimpsubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f586])).
% 21.36/3.53 thf(f588,plain,(
% 21.36/3.53 (ifSingleton = ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (singleton @ (dsetconstr @ X2 @ (^[X4 : $i] : ((~X0 & (X4 = X3)) | (X0 & (X1 = X4)))))))))),
% 21.36/3.53 inference(rectify,[],[f224])).
% 21.36/3.53 thf(f589,plain,(
% 21.36/3.53 (ifSingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f588])).
% 21.36/3.53 thf(f592,plain,(
% 21.36/3.53 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 21.36/3.53 inference(rectify,[],[f19])).
% 21.36/3.53 thf(f593,plain,(
% 21.36/3.53 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f592])).
% 21.36/3.53 thf(f596,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))) = funcGraphProp3)),
% 21.36/3.53 inference(rectify,[],[f205])).
% 21.36/3.53 thf(f597,plain,(
% 21.36/3.53 (funcGraphProp3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f596])).
% 21.36/3.53 thf(f598,plain,(
% 21.36/3.53 (! [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)),
% 21.36/3.53 inference(rectify,[],[f193])).
% 21.36/3.53 thf(f599,plain,(
% 21.36/3.53 (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)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f598])).
% 21.36/3.53 thf(f600,plain,(
% 21.36/3.53 (woz13rule3 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X0 @ X2) => ((subset @ X0 @ X3) => (subset @ X0 @ (binintersect @ X2 @ X3))))))))),
% 21.36/3.53 inference(rectify,[],[f281])).
% 21.36/3.53 thf(f601,plain,(
% 21.36/3.53 (woz13rule3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => ((subset @ Y1 @ Y3) => (subset @ Y1 @ (binintersect @ Y2 @ Y3)))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f600])).
% 21.36/3.53 thf(f602,plain,(
% 21.36/3.53 (setunion__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f73])).
% 21.36/3.53 thf(f609,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (subset @ (powerset @ X1) @ (powerset @ X0))) = powersetsubset)),
% 21.36/3.53 inference(rectify,[],[f98])).
% 21.36/3.53 thf(f610,plain,(
% 21.36/3.53 (powersetsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f609])).
% 21.36/3.53 thf(f611,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X1 @ (setminus @ X2 @ X0)) => ((in @ X1 @ X2) => (in @ X1 @ X0))) = setminusERneg)),
% 21.36/3.53 inference(rectify,[],[f124])).
% 21.36/3.53 thf(f612,plain,(
% 21.36/3.53 (setminusERneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f611])).
% 21.36/3.53 thf(f617,plain,(
% 21.36/3.53 (exuE1 = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : ((X0 @ X2) & ! [X3 : $i] : ((X0 @ X3) => (X2 = X3)))))),
% 21.36/3.53 inference(rectify,[],[f17])).
% 21.36/3.53 thf(f618,plain,(
% 21.36/3.53 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f617])).
% 21.36/3.53 thf(f623,plain,(
% 21.36/3.53 (lamp = ! [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)))))))),
% 21.36/3.53 inference(rectify,[],[f199])).
% 21.36/3.53 thf(f624,plain,(
% 21.36/3.53 (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)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f623])).
% 21.36/3.53 thf(f625,plain,(
% 21.36/3.53 (eta2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X0 @ X2)) => (((lam @ X0 @ X2 @ (^[X3 : $i] : ((ap @ X0 @ X2 @ X1 @ X3))))) = X1)))),
% 21.36/3.53 inference(rectify,[],[f219])).
% 21.36/3.53 thf(f626,plain,(
% 21.36/3.53 (eta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => ((lam @ Y2 @ Y0 @ (^[Y3 : $i]: (ap @ Y2 @ Y0 @ Y1 @ Y3))) = Y1))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f625])).
% 21.36/3.53 thf(f627,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = setukpairIL)),
% 21.36/3.53 inference(rectify,[],[f136])).
% 21.36/3.53 thf(f628,plain,(
% 21.36/3.53 (setukpairIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f627])).
% 21.36/3.53 thf(f629,plain,(
% 21.36/3.53 (kpairp = ! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)))),
% 21.36/3.53 inference(rectify,[],[f139])).
% 21.36/3.53 thf(f630,plain,(
% 21.36/3.53 (kpairp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f629])).
% 21.36/3.53 thf(f631,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => (X2 => (((if @ X1 @ X2 @ X0 @ X3)) = X0)))) = iftrue)),
% 21.36/3.53 inference(rectify,[],[f227])).
% 21.36/3.53 thf(f632,plain,(
% 21.36/3.53 (iftrue = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y0 => ((if @ Y1 @ Y0 @ Y2 @ Y3) = Y2))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f631])).
% 21.36/3.53 thf(f633,plain,(
% 21.36/3.53 (dpsetconstrI = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),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)))))))))),
% 21.36/3.53 inference(rectify,[],[f185])).
% 21.36/3.53 thf(f634,plain,(
% 21.36/3.53 (dpsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f633])).
% 21.36/3.53 thf(f635,plain,(
% 21.36/3.53 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X2 @ X0)) => (in @ X1 @ X2)))),
% 21.36/3.53 inference(rectify,[],[f110])).
% 21.36/3.53 thf(f636,plain,(
% 21.36/3.53 (binintersectEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f635])).
% 21.36/3.53 thf(f639,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)) = setunionE)),
% 21.36/3.53 inference(rectify,[],[f42])).
% 21.36/3.53 thf(f640,plain,(
% 21.36/3.53 (setunionE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f639])).
% 21.36/3.53 thf(f643,plain,(
% 21.36/3.53 (ex1E2 = ! [X0 : ($i > $o),X1 : $i] : ((ex1 @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X0 @ X3) => ((X0 @ X4) => (X3 = X4)))))))),
% 21.36/3.53 inference(rectify,[],[f203])).
% 21.36/3.53 thf(f644,plain,(
% 21.36/3.53 (ex1E2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f643])).
% 21.36/3.53 thf(f645,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X1 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ (symdiff @ X2 @ X0)))) = symdiffI2)),
% 21.36/3.53 inference(rectify,[],[f132])).
% 21.36/3.53 thf(f646,plain,(
% 21.36/3.53 (symdiffI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f645])).
% 21.36/3.53 thf(f647,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X0 @ X2) => (in @ X1 @ (setunion @ X2)))) = setunionI)),
% 21.36/3.53 inference(rectify,[],[f41])).
% 21.36/3.53 thf(f648,plain,(
% 21.36/3.53 (setunionI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => (in @ Y1 @ (setunion @ Y0))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f647])).
% 21.36/3.53 thf(f649,plain,(
% 21.36/3.53 (demorgan2a1 = ! [X0 : $i,X1 : $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)))))))),
% 21.36/3.53 inference(rectify,[],[f268])).
% 21.36/3.53 thf(f650,plain,(
% 21.36/3.53 (demorgan2a1 = ((!! @ $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 @ (binunion @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f649])).
% 21.36/3.53 thf(f651,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)) = binintersectSubset1)),
% 21.36/3.53 inference(rectify,[],[f118])).
% 21.36/3.53 thf(f652,plain,(
% 21.36/3.53 (binintersectSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f651])).
% 21.36/3.53 thf(f655,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 21.36/3.53 inference(rectify,[],[f15])).
% 21.36/3.53 thf(f656,plain,(
% 21.36/3.53 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f655])).
% 21.36/3.53 thf(f657,plain,(
% 21.36/3.53 (ubforcartprodlem3 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (kpair @ X0 @ X3) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))))))),
% 21.36/3.53 inference(rectify,[],[f148])).
% 21.36/3.53 thf(f658,plain,(
% 21.36/3.53 (ubforcartprodlem3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y0))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f657])).
% 21.36/3.53 thf(f661,plain,(
% 21.36/3.53 (setminusILneg = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X1 @ X0))))),
% 21.36/3.53 inference(rectify,[],[f126])).
% 21.36/3.53 thf(f662,plain,(
% 21.36/3.53 (setminusILneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f661])).
% 21.36/3.53 thf(f665,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3)) => (in @ X1 @ X3)) = cartprodpairmemER)),
% 21.36/3.53 inference(rectify,[],[f179])).
% 21.36/3.53 thf(f666,plain,(
% 21.36/3.53 (cartprodpairmemER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y2) @ (cartprod @ Y3 @ Y0)) => (in @ Y2 @ Y0))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f665])).
% 21.36/3.53 thf(f667,plain,(
% 21.36/3.53 (exuE3e = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : (X0 @ X2)))),
% 21.36/3.53 inference(rectify,[],[f22])).
% 21.36/3.53 thf(f668,plain,(
% 21.36/3.53 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f667])).
% 21.36/3.53 thf(f669,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X1 @ X0))) = X0) = ksndpairEq)),
% 21.36/3.53 inference(rectify,[],[f175])).
% 21.36/3.53 thf(f670,plain,(
% 21.36/3.53 (ksndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f669])).
% 21.36/3.53 thf(f671,plain,(
% 21.36/3.53 (! [X0 : ($i > $o),X1 : $i] : (~ ! [X2 : $i] : ((in @ X2 @ X1) => (X0 @ X2)) => ? [X3 : $i] : ((in @ X3 @ X1) & ~(X0 @ X3))) = quantDeMorgan1)),
% 21.36/3.53 inference(rectify,[],[f55])).
% 21.36/3.53 thf(f672,plain,(
% 21.36/3.53 (quantDeMorgan1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f671])).
% 21.36/3.53 thf(f673,plain,(
% 21.36/3.53 (exuE3u = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3)))))),
% 21.36/3.53 inference(rectify,[],[f68])).
% 21.36/3.53 thf(f674,plain,(
% 21.36/3.53 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f673])).
% 21.36/3.53 thf(f675,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : ($i > $o)] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ (powerset @ X0)) = sepInPowerset)),
% 21.36/3.53 inference(rectify,[],[f99])).
% 21.36/3.53 thf(f676,plain,(
% 21.36/3.53 (sepInPowerset = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ (powerset @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f675])).
% 21.36/3.53 thf(f677,plain,(
% 21.36/3.53 (! [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)),
% 21.36/3.53 inference(rectify,[],[f238])).
% 21.36/3.53 thf(f678,plain,(
% 21.36/3.53 (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))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f677])).
% 21.36/3.53 thf(f679,plain,(
% 21.36/3.53 (! [X0 : $i] : (in @ X0 @ (powerset @ X0)) = inPowerset)),
% 21.36/3.53 inference(rectify,[],[f97])).
% 21.36/3.53 thf(f680,plain,(
% 21.36/3.53 (inPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0))))))),
% 21.36/3.53 inference(fool_elimination,[],[f679])).
% 21.36/3.53 thf(f681,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X0 @ X2) => ((X1 @ X0) => (in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : ((X1 @ X3))))))) = dsetconstrI)),
% 21.36/3.53 inference(rectify,[],[f14])).
% 21.36/3.53 thf(f682,plain,(
% 21.36/3.53 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f681])).
% 21.36/3.53 thf(f683,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & ~(X1 @ X2)) => ~ ! [X3 : $i] : ((in @ X3 @ X0) => (X1 @ X3))) = quantDeMorgan4)),
% 21.36/3.53 inference(rectify,[],[f58])).
% 21.36/3.53 thf(f684,plain,(
% 21.36/3.53 (quantDeMorgan4 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f683])).
% 21.36/3.53 thf(f685,plain,(
% 21.36/3.53 (setadjoinIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (in @ X0 @ (setadjoin @ X1 @ X2))))),
% 21.36/3.53 inference(rectify,[],[f33])).
% 21.36/3.53 thf(f686,plain,(
% 21.36/3.53 (setadjoinIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f685])).
% 21.36/3.53 thf(f687,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) = powersetT_lem)),
% 21.36/3.53 inference(rectify,[],[f232])).
% 21.36/3.53 thf(f688,plain,(
% 21.36/3.53 (powersetT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (powerset @ Y0) @ (powerset @ (powerset @ Y1))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f687])).
% 21.36/3.53 thf(f689,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $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)),
% 21.36/3.53 inference(rectify,[],[f265])).
% 21.36/3.53 thf(f690,plain,(
% 21.36/3.53 (inComplementUnionImpInComplement1 = ((!! @ $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 @ (binunion @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f689])).
% 21.36/3.53 thf(f691,plain,(
% 21.36/3.53 (! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)) = subsetemptysetimpeq)),
% 21.36/3.53 inference(rectify,[],[f94])).
% 21.36/3.53 thf(f692,plain,(
% 21.36/3.53 (subsetemptysetimpeq = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0))))))),
% 21.36/3.53 inference(fool_elimination,[],[f691])).
% 21.36/3.53 thf(f693,plain,(
% 21.36/3.53 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 21.36/3.53 inference(rectify,[],[f81])).
% 21.36/3.53 thf(f694,plain,(
% 21.36/3.53 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f693])).
% 21.36/3.53 thf(f697,plain,(
% 21.36/3.53 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 21.36/3.53 inference(rectify,[],[f21])).
% 21.36/3.53 thf(f698,plain,(
% 21.36/3.53 (notinemptyset = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 21.36/3.53 inference(fool_elimination,[],[f697])).
% 21.36/3.53 thf(f701,plain,(
% 21.36/3.53 (setminusLsub = ! [X0 : $i,X1 : $i] : (subset @ (setminus @ X1 @ X0) @ X1))),
% 21.36/3.53 inference(rectify,[],[f128])).
% 21.36/3.53 thf(f702,plain,(
% 21.36/3.53 (setminusLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f701])).
% 21.36/3.53 thf(f703,plain,(
% 21.36/3.53 (intersectInPowersetIntersectUnions = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3))))))))),
% 21.36/3.53 inference(rectify,[],[f263])).
% 21.36/3.53 thf(f704,plain,(
% 21.36/3.53 (intersectInPowersetIntersectUnions = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3)))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f703])).
% 21.36/3.53 thf(f705,plain,(
% 21.36/3.53 (theeq = ! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))))),
% 21.36/3.53 inference(rectify,[],[f226])).
% 21.36/3.53 thf(f706,plain,(
% 21.36/3.53 (theeq = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f705])).
% 21.36/3.53 thf(f709,plain,(
% 21.36/3.53 (setadjoinSub2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => (subset @ X2 @ (setadjoin @ X1 @ X0))))),
% 21.36/3.53 inference(rectify,[],[f91])).
% 21.36/3.53 thf(f710,plain,(
% 21.36/3.53 (setadjoinSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f709])).
% 21.36/3.53 thf(f715,plain,(
% 21.36/3.53 (! [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)),
% 21.36/3.53 inference(rectify,[],[f258])).
% 21.36/3.53 thf(f716,plain,(
% 21.36/3.53 (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))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f715])).
% 21.36/3.53 thf(f717,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) => (X0 = X2)) = setukpairinjR2)),
% 21.36/3.53 inference(rectify,[],[f172])).
% 21.36/3.53 thf(f718,plain,(
% 21.36/3.53 (setukpairinjR2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y3 = Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f717])).
% 21.36/3.53 thf(f721,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = demorgan1b)),
% 21.36/3.53 inference(rectify,[],[f272])).
% 21.36/3.53 thf(f722,plain,(
% 21.36/3.53 (demorgan1b = ((!! @ $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 @ (binunion @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f721])).
% 21.36/3.53 thf(f725,plain,(
% 21.36/3.53 (foundationAx = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : (~ ? [X3 : $i] : ((in @ X3 @ X0) & (in @ X3 @ X2)) & (in @ X2 @ X0))))),
% 21.36/3.53 inference(rectify,[],[f11])).
% 21.36/3.53 thf(f726,plain,(
% 21.36/3.53 (foundationAx = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f725])).
% 21.36/3.53 thf(f729,plain,(
% 21.36/3.53 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3)))) = exuEu)),
% 21.36/3.53 inference(rectify,[],[f75])).
% 21.36/3.53 thf(f730,plain,(
% 21.36/3.53 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f729])).
% 21.36/3.53 thf(f733,plain,(
% 21.36/3.53 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 21.36/3.53 inference(rectify,[],[f46])).
% 21.36/3.53 thf(f734,plain,(
% 21.36/3.53 (uniqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f733])).
% 21.36/3.53 thf(f735,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)) = powersetE1)),
% 21.36/3.53 inference(rectify,[],[f96])).
% 21.36/3.53 thf(f736,plain,(
% 21.36/3.53 (powersetE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f735])).
% 21.36/3.53 thf(f737,plain,(
% 21.36/3.53 (breln1all2 = ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X0) => (X2 @ X5)))))),
% 21.36/3.53 inference(rectify,[],[f289])).
% 21.36/3.53 thf(f738,plain,(
% 21.36/3.53 (breln1all2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f737])).
% 21.36/3.53 thf(f743,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (((setminus @ X0 @ X1)) = emptyset)) = setminusSubset2)),
% 21.36/3.53 inference(rectify,[],[f123])).
% 21.36/3.53 thf(f744,plain,(
% 21.36/3.53 (setminusSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f743])).
% 21.36/3.53 thf(f745,plain,(
% 21.36/3.53 (! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0) = setunionsingleton1)),
% 21.36/3.53 inference(rectify,[],[f153])).
% 21.36/3.53 thf(f746,plain,(
% 21.36/3.53 (setunionsingleton1 = ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0)))))),
% 21.36/3.53 inference(fool_elimination,[],[f745])).
% 21.36/3.53 thf(f747,plain,(
% 21.36/3.53 (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))))))),
% 21.36/3.53 inference(rectify,[],[f229])).
% 21.36/3.53 thf(f748,plain,(
% 21.36/3.53 (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)))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f747])).
% 21.36/3.53 thf(f751,plain,(
% 21.36/3.53 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 21.36/3.53 inference(rectify,[],[f82])).
% 21.36/3.53 thf(f752,plain,(
% 21.36/3.53 (emptysetsubset = ((!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0)))))),
% 21.36/3.53 inference(fool_elimination,[],[f751])).
% 21.36/3.53 thf(f753,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (X0 != X2))) = notequalI2)),
% 21.36/3.53 inference(rectify,[],[f87])).
% 21.36/3.53 thf(f754,plain,(
% 21.36/3.53 (notequalI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f753])).
% 21.36/3.53 thf(f755,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (X1 = ((setminus @ X0 @ (setminus @ X0 @ X1))))) = doubleComplementEq)),
% 21.36/3.53 inference(rectify,[],[f251])).
% 21.36/3.53 thf(f756,plain,(
% 21.36/3.53 (doubleComplementEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => ((setminus @ Y1 @ (setminus @ Y1 @ Y0)) = Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f755])).
% 21.36/3.53 thf(f759,plain,(
% 21.36/3.53 (iffalseProp1 = ! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X2 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X2 & (X1 = X4)) | ((X4 = X3) & ~X2)))))))))),
% 21.36/3.53 inference(rectify,[],[f220])).
% 21.36/3.53 thf(f760,plain,(
% 21.36/3.53 (iffalseProp1 = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y0) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((~ Y0) & (Y3 = Y4)) | ((Y1 = Y4) & Y0))))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f759])).
% 21.36/3.53 thf(f761,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X2 @ X0) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X0) => (X3 @ X6)))) = brelnall2)),
% 21.36/3.53 inference(rectify,[],[f202])).
% 21.36/3.53 thf(f762,plain,(
% 21.36/3.53 (brelnall2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y0 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f761])).
% 21.36/3.53 thf(f767,plain,(
% 21.36/3.53 ~(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 => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X0) => (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 21.36/3.53 inference(rectify,[],[f294])).
% 21.36/3.53 thf(f768,plain,(
% 21.36/3.53 ($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 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f767])).
% 21.36/3.53 thf(f769,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X2)) = binintersectER)),
% 21.36/3.53 inference(rectify,[],[f114])).
% 21.36/3.53 thf(f770,plain,(
% 21.36/3.53 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f769])).
% 21.36/3.53 thf(f771,plain,(
% 21.36/3.53 (woz1_4 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))))),
% 21.36/3.53 inference(rectify,[],[f286])).
% 21.36/3.53 thf(f772,plain,(
% 21.36/3.53 (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)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f771])).
% 21.36/3.53 thf(f777,plain,(
% 21.36/3.53 (kfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f164])).
% 21.36/3.53 thf(f782,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (breln1Set @ X0)) => (breln1 @ X0 @ X1)) = breln1SetBreln1)),
% 21.36/3.53 inference(rectify,[],[f290])).
% 21.36/3.53 thf(f783,plain,(
% 21.36/3.53 (breln1SetBreln1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (breln1Set @ Y1)) => (breln1 @ Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f782])).
% 21.36/3.53 thf(f784,plain,(
% 21.36/3.53 (! [X0 : ($i > $o),X1 : $i] : ((ex1 @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) => ? [X3 : $i] : ((in @ X3 @ X1) & (X0 @ X3))) = ex1E1)),
% 21.36/3.53 inference(rectify,[],[f157])).
% 21.36/3.53 thf(f785,plain,(
% 21.36/3.53 (ex1E1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f784])).
% 21.36/3.53 thf(f786,plain,(
% 21.36/3.53 (prop2setE = ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 21.36/3.53 inference(rectify,[],[f18])).
% 21.36/3.53 thf(f787,plain,(
% 21.36/3.53 (prop2setE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f786])).
% 21.36/3.53 thf(f788,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = upairsetIL)),
% 21.36/3.53 inference(rectify,[],[f51])).
% 21.36/3.53 thf(f789,plain,(
% 21.36/3.53 (upairsetIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f788])).
% 21.36/3.53 thf(f790,plain,(
% 21.36/3.53 ((^[X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 21.36/3.53 inference(rectify,[],[f1])).
% 21.36/3.53 thf(f791,plain,(
% 21.36/3.53 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 21.36/3.53 inference(fool_elimination,[],[f790])).
% 21.36/3.53 thf(f792,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X2 @ X0) <=> (in @ X3 @ X1)))) = in__Cong)),
% 21.36/3.53 inference(rectify,[],[f67])).
% 21.36/3.53 thf(f793,plain,(
% 21.36/3.53 (in__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f792])).
% 21.36/3.53 thf(f794,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (~(subset @ X1 @ X0) => (X0 != X1)) = notequalI1)),
% 21.36/3.53 inference(rectify,[],[f86])).
% 21.36/3.53 thf(f795,plain,(
% 21.36/3.53 (notequalI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f794])).
% 21.36/3.53 thf(f796,plain,(
% 21.36/3.53 (emptyinPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 21.36/3.53 inference(rectify,[],[f38])).
% 21.36/3.53 thf(f797,plain,(
% 21.36/3.53 (emptyinPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 21.36/3.53 inference(fool_elimination,[],[f796])).
% 21.36/3.53 thf(f800,plain,(
% 21.36/3.53 (emptyInPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 21.36/3.53 inference(rectify,[],[f39])).
% 21.36/3.53 thf(f801,plain,(
% 21.36/3.53 (emptyInPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 21.36/3.53 inference(fool_elimination,[],[f800])).
% 21.36/3.53 thf(f802,plain,(
% 21.36/3.53 (setukpairinjL = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X1 @ X3)) = ((kpair @ X2 @ X0))) => (X1 = X2)))),
% 21.36/3.53 inference(rectify,[],[f167])).
% 21.36/3.53 thf(f803,plain,(
% 21.36/3.53 (setukpairinjL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y0) = (kpair @ Y1 @ Y3)) => (Y2 = Y1))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f802])).
% 21.36/3.53 thf(f804,plain,(
% 21.36/3.53 (lam2lamEq = ! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => (((lam @ X2 @ X1 @ (^[X4 : $i] : ((X0 @ X4))))) = ((lam @ X2 @ X1 @ (^[X5 : $i] : ((X0 @ X5))))))))),
% 21.36/3.53 inference(rectify,[],[f217])).
% 21.36/3.53 thf(f805,plain,(
% 21.36/3.53 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => ((lam @ Y0 @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3))) = (lam @ Y0 @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f804])).
% 21.36/3.53 thf(f806,plain,(
% 21.36/3.53 (setminusSubset1 = ! [X0 : $i,X1 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1)))),
% 21.36/3.53 inference(rectify,[],[f129])).
% 21.36/3.53 thf(f807,plain,(
% 21.36/3.53 (setminusSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f806])).
% 21.36/3.53 thf(f808,plain,(
% 21.36/3.53 (exuI2 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2)) => (exu @ (^[X3 : $i] : ((X0 @ X3))))))),
% 21.36/3.53 inference(rectify,[],[f65])).
% 21.36/3.53 thf(f809,plain,(
% 21.36/3.53 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f808])).
% 21.36/3.53 thf(f818,plain,(
% 21.36/3.53 (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
% 21.36/3.53 inference(rectify,[],[f111])).
% 21.36/3.53 thf(f819,plain,(
% 21.36/3.53 (binintersectLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1)))))))),
% 21.36/3.53 inference(fool_elimination,[],[f818])).
% 21.36/3.53 thf(f820,plain,(
% 21.36/3.53 (powersetAx = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) <=> ! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 21.36/3.53 inference(rectify,[],[f5])).
% 21.36/3.53 thf(f821,plain,(
% 21.36/3.53 (powersetAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f820])).
% 21.36/3.53 thf(f822,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = upairset2IR)),
% 21.36/3.53 inference(rectify,[],[f102])).
% 21.36/3.53 thf(f823,plain,(
% 21.36/3.53 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f822])).
% 21.36/3.53 thf(f824,plain,(
% 21.36/3.53 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))))),
% 21.36/3.53 inference(rectify,[],[f45])).
% 21.36/3.53 thf(f825,plain,(
% 21.36/3.53 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f824])).
% 21.36/3.53 thf(f828,plain,(
% 21.36/3.53 (binunionE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binunion @ X1 @ X2)) => ((in @ X0 @ X1) | (in @ X0 @ X2))))),
% 21.36/3.53 inference(rectify,[],[f105])).
% 21.36/3.53 thf(f829,plain,(
% 21.36/3.53 (binunionE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y0) | (in @ Y2 @ Y1)))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f828])).
% 21.36/3.53 thf(f832,plain,(
% 21.36/3.53 (subset2powerset = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 21.36/3.53 inference(rectify,[],[f92])).
% 21.36/3.53 thf(f833,plain,(
% 21.36/3.53 (subset2powerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f832])).
% 21.36/3.53 thf(f834,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (((kpair @ X0 @ X3)) = ((kpair @ X0 @ X3))))) = cartprodmempaircEq)),
% 21.36/3.53 inference(rectify,[],[f180])).
% 21.36/3.53 thf(f835,plain,(
% 21.36/3.53 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f834])).
% 21.36/3.53 thf(f836,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : ((X2 @ X3))))) => (X2 @ X0)) = dsetconstrER)),
% 21.36/3.53 inference(rectify,[],[f16])).
% 21.36/3.53 thf(f837,plain,(
% 21.36/3.53 (dsetconstrER = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f836])).
% 21.36/3.53 thf(f838,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => (((setadjoin @ X1 @ X2)) = ((setadjoin @ X0 @ X3))))) = setadjoin__Cong)),
% 21.36/3.53 inference(rectify,[],[f71])).
% 21.36/3.53 thf(f839,plain,(
% 21.36/3.53 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f838])).
% 21.36/3.53 thf(f840,plain,(
% 21.36/3.53 (omega0Ax = ((in @ emptyset @ omega)))),
% 21.36/3.53 inference(fool_elimination,[],[f7])).
% 21.36/3.53 thf(f841,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))) = powersetI1)),
% 21.36/3.53 inference(rectify,[],[f95])).
% 21.36/3.53 thf(f842,plain,(
% 21.36/3.53 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f841])).
% 21.36/3.53 thf(f849,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((((dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) = emptyset) => $false)) = emptyE1)),
% 21.36/3.53 inference(rectify,[],[f53])).
% 21.36/3.53 thf(f850,plain,(
% 21.36/3.53 (emptyE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (((dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) = emptyset) => $false))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f849])).
% 21.36/3.53 thf(f851,plain,(
% 21.36/3.53 (theprop = ! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)))),
% 21.36/3.53 inference(rectify,[],[f163])).
% 21.36/3.53 thf(f852,plain,(
% 21.36/3.53 (theprop = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0))))))),
% 21.36/3.53 inference(fool_elimination,[],[f851])).
% 21.36/3.53 thf(f853,plain,(
% 21.36/3.53 (subsetE2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => (~(in @ X0 @ X1) => ~(in @ X0 @ X2))))),
% 21.36/3.53 inference(rectify,[],[f84])).
% 21.36/3.53 thf(f854,plain,(
% 21.36/3.53 (subsetE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f853])).
% 21.36/3.53 thf(f857,plain,(
% 21.36/3.53 (! [X0 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 21.36/3.53 inference(rectify,[],[f138])).
% 21.36/3.53 thf(f858,plain,(
% 21.36/3.53 (kpairiskpair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f857])).
% 21.36/3.53 thf(f859,plain,(
% 21.36/3.53 (! [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)),
% 21.36/3.53 inference(rectify,[],[f255])).
% 21.36/3.53 thf(f860,plain,(
% 21.36/3.53 (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))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f859])).
% 21.36/3.53 thf(f861,plain,(
% 21.36/3.53 (contraSubsetComplement = ! [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))))))))),
% 21.36/3.53 inference(rectify,[],[f256])).
% 21.36/3.53 thf(f862,plain,(
% 21.36/3.53 (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 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y1 @ Y0)))))))))))))))))),
% 21.36/3.53 inference(fool_elimination,[],[f861])).
% 21.36/3.53 thf(f863,plain,(
% 21.36/3.53 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => (X0 @ (descr @ (^[X2 : $i] : ((X0 @ X2)))))) = descrp)),
% 21.36/3.54 inference(rectify,[],[f13])).
% 21.36/3.54 thf(f864,plain,(
% 21.36/3.54 (descrp = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 21.36/3.54 inference(fool_elimination,[],[f863])).
% 21.36/3.54 thf(f865,plain,(
% 21.36/3.54 (omegaIndAx = ! [X0 : $i] : ((! [X1 : $i] : (((in @ X1 @ omega) & (in @ X1 @ X0)) => (in @ (setadjoin @ X1 @ X1) @ X0)) & (in @ emptyset @ X0)) => ! [X2 : $i] : ((in @ X2 @ omega) => (in @ X2 @ X0))))),
% 21.36/3.54 inference(rectify,[],[f9])).
% 21.36/3.54 thf(f866,plain,(
% 21.36/3.54 (omegaIndAx = ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0)))))))))),
% 21.36/3.54 inference(fool_elimination,[],[f865])).
% 21.36/3.54 thf(f869,plain,(
% 21.36/3.54 (woz13rule1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X0 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))))),
% 21.36/3.54 inference(rectify,[],[f279])).
% 21.36/3.54 thf(f870,plain,(
% 21.36/3.54 (woz13rule1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3)))))))))))))))),
% 21.36/3.54 inference(fool_elimination,[],[f869])).
% 21.36/3.54 thf(f871,plain,(
% 21.36/3.54 (emptyinPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f797])).
% 21.36/3.54 thf(f872,plain,(
% 21.36/3.54 (setukpairIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f343])).
% 21.36/3.54 thf(f873,plain,(
% 21.36/3.54 (setadjoinAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y2) | (Y1 = Y0)) = (in @ Y1 @ (setadjoin @ Y0 @ Y2)))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f396])).
% 21.36/3.54 thf(f876,plain,(
% 21.36/3.54 (setminusSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f744])).
% 21.36/3.54 thf(f877,plain,(
% 21.36/3.54 (demorgan2a1 = ((!! @ $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 @ (binunion @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f650])).
% 21.36/3.54 thf(f881,plain,(
% 21.36/3.54 (cartprodmempair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f302])).
% 21.36/3.54 thf(f882,plain,(
% 21.36/3.54 (singletoninpowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f414])).
% 21.36/3.54 thf(f883,plain,(
% 21.36/3.54 (setminusSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f807])).
% 21.36/3.54 thf(f884,plain,(
% 21.36/3.54 (symdiffIneg1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f536])).
% 21.36/3.54 thf(f885,plain,(
% 21.36/3.54 (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)))))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f862])).
% 21.36/3.54 thf(f886,plain,(
% 21.36/3.54 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f370])).
% 21.36/3.54 thf(f887,plain,(
% 21.36/3.54 (setadjoinOr = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0)))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f573])).
% 21.36/3.54 thf(f888,plain,(
% 21.36/3.54 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f331])).
% 21.36/3.54 thf(f890,plain,(
% 21.36/3.54 (vacuousDall = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f329])).
% 21.36/3.54 thf(f891,plain,(
% 21.36/3.54 (sepInPowerset = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ (powerset @ Y1))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f676])).
% 21.36/3.54 thf(f892,plain,(
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% 21.36/3.54 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f618])).
% 21.36/3.54 thf(f1059,plain,(
% 21.36/3.54 (cartprodmempair1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & ((kpair @ Y3 @ Y4) = Y1)))) & (in @ Y3 @ Y0)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f512])).
% 21.36/3.54 thf(f1061,plain,(
% 21.36/3.54 (disjointsetsI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f472])).
% 21.36/3.54 thf(f1062,plain,(
% 21.36/3.54 (woz1_3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3)))))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f428])).
% 21.36/3.54 thf(f1063,plain,(
% 21.36/3.54 (notinemptyset = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f698])).
% 21.36/3.54 thf(f1064,plain,(
% 21.36/3.54 (ifSingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2))))))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f589])).
% 21.36/3.54 thf(f1065,plain,(
% 21.36/3.54 (setminusILneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f662])).
% 21.36/3.54 thf(f1066,plain,(
% 21.36/3.54 (setunion__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f602])).
% 21.36/3.54 thf(f1068,plain,(
% 21.36/3.54 (quantDeMorgan3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f300])).
% 21.36/3.54 thf(f1071,plain,(
% 21.36/3.54 (beta1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3) = (Y2 @ Y3))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f321])).
% 21.36/3.54 thf(f1072,plain,(
% 21.36/3.54 (notdexE = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f448])).
% 21.36/3.54 thf(f1073,plain,(
% 21.36/3.54 (powersetT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (powerset @ Y0) @ (powerset @ (powerset @ Y1))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f688])).
% 21.36/3.54 thf(f1074,plain,(
% 21.36/3.54 (singletonsswitch = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f577])).
% 21.36/3.54 thf(f1075,plain,(
% 21.36/3.54 (ex1E1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f785])).
% 21.36/3.54 thf(f1076,plain,(
% 21.36/3.54 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => ((lam @ Y0 @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3))) = (lam @ Y0 @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f805])).
% 21.36/3.54 thf(f1077,plain,(
% 21.36/3.54 (omegaIndAx = ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f866])).
% 21.36/3.54 thf(f1079,plain,(
% 21.36/3.54 (iftrue = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y0 => ((if @ Y1 @ Y0 @ Y2 @ Y3) = Y2))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f632])).
% 21.36/3.54 thf(f1080,plain,(
% 21.36/3.54 (eqimpsubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f587])).
% 21.36/3.54 thf(f1082,plain,(
% 21.36/3.54 (notinsingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f474])).
% 21.36/3.54 thf(f1083,plain,(
% 21.36/3.54 (descrp = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f864])).
% 21.36/3.54 thf(f1085,plain,(
% 21.36/3.54 (powersetAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f821])).
% 21.36/3.54 thf(f1087,plain,(
% 21.36/3.54 (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))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f640])).
% 21.36/3.54 thf(f1089,plain,(
% 21.36/3.54 (kfstsingleton = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f323])).
% 21.36/3.54 thf(f1091,plain,(
% 21.36/3.54 (powerset__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f374])).
% 21.36/3.54 thf(f1093,plain,(
% 21.36/3.54 (ksndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1)))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f670])).
% 21.36/3.54 thf(f1097,plain,(
% 21.36/3.54 (prop2setE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1)))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f787])).
% 21.36/3.54 thf(f1098,plain,(
% 21.36/3.54 (powersetE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f736])).
% 21.36/3.54 thf(f1100,plain,(
% 21.36/3.54 (cartprodpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f563])).
% 21.36/3.54 thf(f1101,plain,(
% 21.36/3.54 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f825])).
% 21.36/3.54 thf(f1105,plain,(
% 21.36/3.54 (woz13rule1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3)))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f870])).
% 21.36/3.54 thf(f1106,plain,(
% 21.36/3.54 (setunionE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0)))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f479])).
% 21.36/3.54 thf(f1107,plain,(
% 21.36/3.54 (binunionRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f485])).
% 21.36/3.54 thf(f1108,plain,(
% 21.36/3.54 (binunionE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y0) | (in @ Y2 @ Y1)))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f829])).
% 21.36/3.54 thf(f1109,plain,(
% 21.36/3.54 (theeq = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f706])).
% 21.36/3.54 thf(f1110,plain,(
% 21.36/3.54 (cartprodpairmemER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y2) @ (cartprod @ Y3 @ Y0)) => (in @ Y2 @ Y0))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f666])).
% 21.36/3.54 thf(f1112,plain,(
% 21.36/3.54 (ex1I2 = ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f500])).
% 21.36/3.54 thf(f1113,plain,(
% 21.36/3.54 (dpsetconstrEL1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (in @ Y2 @ Y3))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f450])).
% 21.36/3.54 thf(f1115,plain,(
% 21.36/3.54 (emptyset__Cong = ((emptyset = emptyset)))),
% 21.36/3.54 inference(cnf_transformation,[],[f517])).
% 21.36/3.54 thf(f1116,plain,(
% 21.36/3.54 (upairsetIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f789])).
% 21.36/3.54 thf(f1117,plain,(
% 21.36/3.54 (breln1SetBreln1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (breln1Set @ Y1)) => (breln1 @ Y1 @ Y0))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f783])).
% 21.36/3.54 thf(f1120,plain,(
% 21.36/3.54 (subPowSU = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f349])).
% 21.36/3.54 thf(f1121,plain,(
% 21.36/3.54 ($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 => 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% 21.36/3.54 inference(cnf_transformation,[],[f768])).
% 21.36/3.54 thf(f1122,plain,(
% 21.36/3.54 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f842])).
% 21.36/3.54 thf(f1123,plain,(
% 21.36/3.54 (setukpairinjL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y0) = (kpair @ Y1 @ Y3)) => (Y2 = Y1))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f803])).
% 21.36/3.54 thf(f1124,plain,(
% 21.36/3.54 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f809])).
% 21.36/3.54 thf(f1125,plain,(
% 21.36/3.54 (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)))))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f378])).
% 21.36/3.54 thf(f1127,plain,(
% 21.36/3.54 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f464])).
% 21.36/3.54 thf(f1128,plain,(
% 21.36/3.54 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f791])).
% 21.36/3.54 thf(f1132,plain,(
% 21.36/3.54 (emptysetAx = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f296])).
% 21.36/3.54 thf(f1133,plain,(
% 21.36/3.54 (iffalseProp1 = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y0) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((~ Y0) & (Y3 = Y4)) | ((Y1 = Y4) & Y0))))))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f760])).
% 21.36/3.54 thf(f1134,plain,(
% 21.36/3.54 (beta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) = (ap @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f498])).
% 21.36/3.54 thf(f1138,plain,(
% 21.36/3.54 (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)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f483])).
% 21.36/3.54 thf(f1139,plain,(
% 21.36/3.54 (binintersectSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f539])).
% 21.36/3.54 thf(f1142,plain,(
% 21.36/3.54 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f491])).
% 21.36/3.54 thf(f1144,plain,(
% 21.36/3.54 (setminusI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f418])).
% 21.36/3.54 thf(f1145,plain,(
% 21.36/3.54 (symdiffE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f547])).
% 21.36/3.54 thf(f1146,plain,(
% 21.36/3.54 (complementUnionInPowersetComplement = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ (binunion @ Y1 @ Y2)) @ (powerset @ (setminus @ Y0 @ Y1)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f532])).
% 21.36/3.54 thf(f1147,plain,(
% 21.36/3.54 (setminusIRneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f545])).
% 21.36/3.54 thf(f1149,plain,(
% 21.36/3.54 (cartprodfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f476])).
% 21.36/3.54 thf(f1150,plain,(
% 21.36/3.54 (kpairiskpair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f858])).
% 21.36/3.54 thf(f1152,plain,(
% 21.36/3.54 (dsetconstrER = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f837])).
% 21.36/3.54 thf(f1153,plain,(
% 21.36/3.54 (intersectInPowersetIntersectUnions = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3)))))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f704])).
% 21.36/3.54 thf(f1154,plain,(
% 21.36/3.54 (eta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => ((lam @ Y2 @ Y0 @ (^[Y3 : $i]: (ap @ Y2 @ Y0 @ Y1 @ Y3))) = Y1))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f626])).
% 21.36/3.54 thf(f1155,plain,(
% 21.36/3.54 (setunionsingleton1 = ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0)))))),
% 21.36/3.54 inference(cnf_transformation,[],[f746])).
% 21.36/3.54 thf(f1156,plain,(
% 21.36/3.54 (demorgan2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((setminus @ Y0 @ (binunion @ Y1 @ Y2)) = (binintersect @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f426])).
% 21.36/3.54 thf(f1157,plain,(
% 21.36/3.54 (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)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f599])).
% 21.36/3.54 thf(f1159,plain,(
% 21.36/3.54 (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)))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f559])).
% 21.36/3.54 thf(f1160,plain,(
% 21.36/3.54 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2))))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f839])).
% 21.36/3.54 thf(f1162,plain,(
% 21.36/3.54 (binintersectT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f444])).
% 21.36/3.54 thf(f1163,plain,(
% 21.36/3.54 (inPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0))))))),
% 21.36/3.54 inference(cnf_transformation,[],[f680])).
% 21.36/3.54 thf(f1165,definition,(
% 21.36/3.54 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 21.36/3.54 introduced(theory,[fool_exhaustiveness_axiom])).
% 21.36/3.54 thf(f1166,plain,(
% 21.36/3.54 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 21.36/3.54 inference(definition_unfolding,[],[f904,f1027])).
% 21.36/3.54 thf(f1167,plain,(
% 21.36/3.54 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f888,f1128])).
% 21.36/3.54 thf(f1168,plain,(
% 21.36/3.54 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f892,f1128])).
% 21.36/3.54 thf(f1169,plain,(
% 21.36/3.54 (brelnall2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y1 @ Y0 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4))))))))))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f895,f1027])).
% 21.36/3.54 thf(f1170,plain,(
% 21.36/3.54 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => ((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f900,f1055])).
% 21.36/3.54 thf(f1171,plain,(
% 21.36/3.54 (breln1all2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f906,f1166])).
% 21.36/3.54 thf(f1172,plain,(
% 21.36/3.54 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f961,f1128])).
% 21.36/3.54 thf(f1175,plain,(
% 21.36/3.54 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f980,f1128])).
% 21.36/3.54 thf(f1178,plain,(
% 21.36/3.54 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f990,f1128])).
% 21.36/3.54 thf(f1180,plain,(
% 21.36/3.54 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f1021,f1055])).
% 21.36/3.54 thf(f1181,plain,(
% 21.36/3.54 (nonemptyI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((^[Y3 : $i]: (~ (emptyset = Y3))) @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f1053,f1055])).
% 21.36/3.54 thf(f1182,plain,(
% 21.36/3.54 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f1058,f1128])).
% 21.36/3.54 thf(f1183,plain,(
% 21.36/3.54 (descrp = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f1083,f1128])).
% 21.36/3.54 thf(f1187,plain,(
% 21.36/3.54 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f1101,f1055])).
% 21.36/3.54 thf(f1188,plain,(
% 21.36/3.54 (breln1SetBreln1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (breln1Set @ Y1)) => ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y1 @ Y0))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f1117,f1166])).
% 21.36/3.54 thf(f1190,plain,(
% 21.36/3.54 (((~ (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 => (!! @ $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 > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 21.36/3.54 inference(definition_unfolding,[],[f1121,f1166])).
% 21.36/3.54 thf(f1191,plain,(
% 21.36/3.54 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 21.36/3.54 inference(definition_unfolding,[],[f1124,f1128])).
% 21.36/3.54 thf(f1192,definition,(
% 21.36/3.54 (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 > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))))))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 21.36/3.54 thf(f1193,definition,(
% 21.36/3.54 (sF1 = ((setOfPairsIsBReln1 => sF0)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 21.36/3.54 thf(f1194,plain,(
% 21.36/3.54 (((setOfPairsIsBReln1 => sF0)) = sF1)),
% 21.36/3.54 inference(reorient_equations,[],[f1193])).
% 21.36/3.54 thf(f1195,definition,(
% 21.36/3.54 (sF2 = ((choice2fnsingleton => sF1)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 21.36/3.54 thf(f1196,plain,(
% 21.36/3.54 (((choice2fnsingleton => sF1)) = sF2)),
% 21.36/3.54 inference(reorient_equations,[],[f1195])).
% 21.36/3.54 thf(f1197,definition,(
% 21.36/3.54 (sF3 = ((breln1SetBreln1 => sF2)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 21.36/3.54 thf(f1198,definition,(
% 21.36/3.54 (sF4 = ((breln1all2 => sF3)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 21.36/3.54 thf(f1199,definition,(
% 21.36/3.54 (sF5 = ((woz1_5 => sF4)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 21.36/3.54 thf(f1200,definition,(
% 21.36/3.54 (sF6 = ((woz1_4 => sF5)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 21.36/3.54 thf(f1201,plain,(
% 21.36/3.54 (((woz1_4 => sF5)) = sF6)),
% 21.36/3.54 inference(reorient_equations,[],[f1200])).
% 21.36/3.54 thf(f1202,definition,(
% 21.36/3.54 (sF7 = ((woz1_3 => sF6)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 21.36/3.54 thf(f1203,definition,(
% 21.36/3.54 (sF8 = ((woz1_2 => sF7)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
% 21.36/3.54 thf(f1204,definition,(
% 21.36/3.54 (sF9 = ((woz1_1 => sF8)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
% 21.36/3.54 thf(f1205,plain,(
% 21.36/3.54 (((woz1_1 => sF8)) = sF9)),
% 21.36/3.54 inference(reorient_equations,[],[f1204])).
% 21.36/3.54 thf(f1206,definition,(
% 21.36/3.54 (sF10 = ((woz13rule4 => sF9)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
% 21.36/3.54 thf(f1207,definition,(
% 21.36/3.54 (sF11 = ((woz13rule3 => sF10)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
% 21.36/3.54 thf(f1208,definition,(
% 21.36/3.54 (sF12 = ((woz13rule2 => sF11)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 21.36/3.54 thf(f1209,definition,(
% 21.36/3.54 (sF13 = ((woz13rule1 => sF12)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
% 21.36/3.54 thf(f1210,plain,(
% 21.36/3.54 (((woz13rule1 => sF12)) = sF13)),
% 21.36/3.54 inference(reorient_equations,[],[f1209])).
% 21.36/3.54 thf(f1211,definition,(
% 21.36/3.54 (sF14 = ((woz13rule0 => sF13)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
% 21.36/3.54 thf(f1212,plain,(
% 21.36/3.54 (((woz13rule0 => sF13)) = sF14)),
% 21.36/3.54 inference(reorient_equations,[],[f1211])).
% 21.36/3.54 thf(f1213,definition,(
% 21.36/3.54 (sF15 = ((demorgan2 => sF14)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
% 21.36/3.54 thf(f1214,plain,(
% 21.36/3.54 (((demorgan2 => sF14)) = sF15)),
% 21.36/3.54 inference(reorient_equations,[],[f1213])).
% 21.36/3.54 thf(f1215,definition,(
% 21.36/3.54 (sF16 = ((demorgan2b => sF15)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF16])],[function_definition])).
% 21.36/3.54 thf(f1216,plain,(
% 21.36/3.54 (((demorgan2b => sF15)) = sF16)),
% 21.36/3.54 inference(reorient_equations,[],[f1215])).
% 21.36/3.54 thf(f1217,definition,(
% 21.36/3.54 (sF17 = ((demorgan2b2 => sF16)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF17])],[function_definition])).
% 21.36/3.54 thf(f1218,plain,(
% 21.36/3.54 (((demorgan2b2 => sF16)) = sF17)),
% 21.36/3.54 inference(reorient_equations,[],[f1217])).
% 21.36/3.54 thf(f1219,definition,(
% 21.36/3.54 (sF18 = ((demorgan2a => sF17)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF18])],[function_definition])).
% 21.36/3.54 thf(f1220,plain,(
% 21.36/3.54 (((demorgan2a => sF17)) = sF18)),
% 21.36/3.54 inference(reorient_equations,[],[f1219])).
% 21.36/3.54 thf(f1221,definition,(
% 21.36/3.54 (sF19 = ((demorgan1 => sF18)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF19])],[function_definition])).
% 21.36/3.54 thf(f1222,definition,(
% 21.36/3.54 (sF20 = ((demorgan1b => sF19)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF20])],[function_definition])).
% 21.36/3.54 thf(f1223,definition,(
% 21.36/3.54 (sF21 = ((demorgan1a => sF20)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF21])],[function_definition])).
% 21.36/3.54 thf(f1224,plain,(
% 21.36/3.54 (((demorgan1a => sF20)) = sF21)),
% 21.36/3.54 inference(reorient_equations,[],[f1223])).
% 21.36/3.54 thf(f1225,definition,(
% 21.36/3.54 (sF22 = ((demorgan2a2 => sF21)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF22])],[function_definition])).
% 21.36/3.54 thf(f1226,plain,(
% 21.36/3.54 (((demorgan2a2 => sF21)) = sF22)),
% 21.36/3.54 inference(reorient_equations,[],[f1225])).
% 21.36/3.54 thf(f1227,definition,(
% 21.36/3.54 (sF23 = ((complementUnionInPowersetComplement => sF22)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF23])],[function_definition])).
% 21.36/3.54 thf(f1228,plain,(
% 21.36/3.54 (((complementUnionInPowersetComplement => sF22)) = sF23)),
% 21.36/3.54 inference(reorient_equations,[],[f1227])).
% 21.36/3.54 thf(f1229,definition,(
% 21.36/3.54 (sF24 = ((demorgan2a1 => sF23)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF24])],[function_definition])).
% 21.36/3.54 thf(f1230,plain,(
% 21.36/3.54 (((demorgan2a1 => sF23)) = sF24)),
% 21.36/3.54 inference(reorient_equations,[],[f1229])).
% 21.36/3.54 thf(f1231,definition,(
% 21.36/3.54 (sF25 = ((binunionTEcontra => sF24)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF25])],[function_definition])).
% 21.36/3.54 thf(f1232,plain,(
% 21.36/3.54 (((binunionTEcontra => sF24)) = sF25)),
% 21.36/3.54 inference(reorient_equations,[],[f1231])).
% 21.36/3.54 thf(f1233,definition,(
% 21.36/3.54 (sF26 = ((binunionTE => sF25)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF26])],[function_definition])).
% 21.36/3.54 thf(f1234,plain,(
% 21.36/3.54 (((binunionTE => sF25)) = sF26)),
% 21.36/3.54 inference(reorient_equations,[],[f1233])).
% 21.36/3.54 thf(f1235,definition,(
% 21.36/3.54 (sF27 = ((inComplementUnionImpInComplement1 => sF26)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF27])],[function_definition])).
% 21.36/3.54 thf(f1236,definition,(
% 21.36/3.54 (sF28 = ((inComplementUnionImpNotIn1 => sF27)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF28])],[function_definition])).
% 21.36/3.54 thf(f1237,definition,(
% 21.36/3.54 (sF29 = ((intersectInPowersetIntersectUnions => sF28)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF29])],[function_definition])).
% 21.36/3.54 thf(f1238,plain,(
% 21.36/3.54 (((intersectInPowersetIntersectUnions => sF28)) = sF29)),
% 21.36/3.54 inference(reorient_equations,[],[f1237])).
% 21.36/3.54 thf(f1239,definition,(
% 21.36/3.54 (sF30 = ((inIntersectImpInIntersectUnions => sF29)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF30])],[function_definition])).
% 21.36/3.54 thf(f1240,plain,(
% 21.36/3.54 (((inIntersectImpInIntersectUnions => sF29)) = sF30)),
% 21.36/3.54 inference(reorient_equations,[],[f1239])).
% 21.36/3.54 thf(f1241,definition,(
% 21.36/3.54 (sF31 = ((inIntersectImpInUnion2 => sF30)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF31])],[function_definition])).
% 21.36/3.54 thf(f1242,plain,(
% 21.36/3.54 (((inIntersectImpInUnion2 => sF30)) = sF31)),
% 21.36/3.54 inference(reorient_equations,[],[f1241])).
% 21.36/3.54 thf(f1243,definition,(
% 21.36/3.54 (sF32 = ((inIntersectImpInUnion => sF31)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF32])],[function_definition])).
% 21.36/3.54 thf(f1244,plain,(
% 21.36/3.54 (((inIntersectImpInUnion => sF31)) = sF32)),
% 21.36/3.54 inference(reorient_equations,[],[f1243])).
% 21.36/3.54 thf(f1245,definition,(
% 21.36/3.54 (sF33 = ((binunionTIRcontra => sF32)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF33])],[function_definition])).
% 21.36/3.54 thf(f1246,plain,(
% 21.36/3.54 (((binunionTIRcontra => sF32)) = sF33)),
% 21.36/3.54 inference(reorient_equations,[],[f1245])).
% 21.36/3.54 thf(f1247,definition,(
% 21.36/3.54 (sF34 = ((binunionTILcontra => sF33)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF34])],[function_definition])).
% 21.36/3.54 thf(f1248,plain,(
% 21.36/3.54 (((binunionTILcontra => sF33)) = sF34)),
% 21.36/3.54 inference(reorient_equations,[],[f1247])).
% 21.36/3.54 thf(f1249,definition,(
% 21.36/3.54 (sF35 = ((complementTcontraSubset => sF34)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF35])],[function_definition])).
% 21.36/3.54 thf(f1250,definition,(
% 21.36/3.54 (sF36 = ((contraSubsetComplement => sF35)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF36])],[function_definition])).
% 21.36/3.54 thf(f1251,definition,(
% 21.36/3.54 (sF37 = ((complementInPowersetComplementIntersect => sF36)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF37])],[function_definition])).
% 21.36/3.54 thf(f1252,definition,(
% 21.36/3.54 (sF38 = ((complementSubsetComplementIntersect => sF37)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF38])],[function_definition])).
% 21.36/3.54 thf(f1253,definition,(
% 21.36/3.54 (sF39 = ((complementImpComplementIntersect => sF38)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF39])],[function_definition])).
% 21.36/3.54 thf(f1254,definition,(
% 21.36/3.54 (sF40 = ((complementTnotintersectT => sF39)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF40])],[function_definition])).
% 21.36/3.54 thf(f1255,definition,(
% 21.36/3.54 (sF41 = ((doubleComplementEq => sF40)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF41])],[function_definition])).
% 21.36/3.54 thf(f1256,definition,(
% 21.36/3.54 (sF42 = ((doubleComplementSub2 => sF41)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF42])],[function_definition])).
% 21.36/3.54 thf(f1257,plain,(
% 21.36/3.54 (((doubleComplementSub2 => sF41)) = sF42)),
% 21.36/3.54 inference(reorient_equations,[],[f1256])).
% 21.36/3.54 thf(f1258,definition,(
% 21.36/3.54 (sF43 = ((doubleComplementSub1 => sF42)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF43])],[function_definition])).
% 21.36/3.54 thf(f1259,plain,(
% 21.36/3.54 (((doubleComplementSub1 => sF42)) = sF43)),
% 21.36/3.54 inference(reorient_equations,[],[f1258])).
% 21.36/3.54 thf(f1260,definition,(
% 21.36/3.54 (sF44 = ((doubleComplementE1 => sF43)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF44])],[function_definition])).
% 21.36/3.54 thf(f1261,definition,(
% 21.36/3.54 (sF45 = ((doubleComplementI1 => sF44)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF45])],[function_definition])).
% 21.36/3.54 thf(f1262,definition,(
% 21.36/3.54 (sF46 = ((contrasubsetT3 => sF45)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF46])],[function_definition])).
% 21.36/3.54 thf(f1263,plain,(
% 21.36/3.54 (((contrasubsetT3 => sF45)) = sF46)),
% 21.36/3.54 inference(reorient_equations,[],[f1262])).
% 21.36/3.54 thf(f1264,definition,(
% 21.36/3.54 (sF47 = ((contrasubsetT2 => sF46)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF47])],[function_definition])).
% 21.36/3.54 thf(f1265,plain,(
% 21.36/3.54 (((contrasubsetT2 => sF46)) = sF47)),
% 21.36/3.54 inference(reorient_equations,[],[f1264])).
% 21.36/3.54 thf(f1266,definition,(
% 21.36/3.54 (sF48 = ((contrasubsetT1 => sF47)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF48])],[function_definition])).
% 21.36/3.54 thf(f1267,definition,(
% 21.36/3.54 (sF49 = ((contrasubsetT => sF48)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF49])],[function_definition])).
% 21.36/3.54 thf(f1268,plain,(
% 21.36/3.54 (((contrasubsetT => sF48)) = sF49)),
% 21.36/3.54 inference(reorient_equations,[],[f1267])).
% 21.36/3.54 thf(f1269,definition,(
% 21.36/3.54 (sF50 = ((binintersectTERcontra => sF49)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF50])],[function_definition])).
% 21.36/3.54 thf(f1270,definition,(
% 21.36/3.54 (sF51 = ((binintersectTELcontra => sF50)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF51])],[function_definition])).
% 21.36/3.54 thf(f1271,definition,(
% 21.36/3.54 (sF52 = ((complementTE1 => sF51)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF52])],[function_definition])).
% 21.36/3.54 thf(f1272,plain,(
% 21.36/3.54 (((complementTE1 => sF51)) = sF52)),
% 21.36/3.54 inference(reorient_equations,[],[f1271])).
% 21.36/3.54 thf(f1273,definition,(
% 21.36/3.54 (sF53 = ((complementTI1 => sF52)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF53])],[function_definition])).
% 21.36/3.54 thf(f1274,definition,(
% 21.36/3.54 (sF54 = ((powersetTE1 => sF53)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF54])],[function_definition])).
% 21.36/3.54 thf(f1275,plain,(
% 21.36/3.54 (((powersetTE1 => sF53)) = sF54)),
% 21.36/3.54 inference(reorient_equations,[],[f1274])).
% 21.36/3.54 thf(f1276,definition,(
% 21.36/3.54 (sF55 = ((powersetTI1 => sF54)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF55])],[function_definition])).
% 21.36/3.54 thf(f1277,definition,(
% 21.36/3.54 (sF56 = ((subsetTI => sF55)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF56])],[function_definition])).
% 21.36/3.54 thf(f1278,plain,(
% 21.36/3.54 (((subsetTI => sF55)) = sF56)),
% 21.36/3.54 inference(reorient_equations,[],[f1277])).
% 21.36/3.54 thf(f1279,definition,(
% 21.36/3.54 (sF57 = ((setextT => sF56)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF57])],[function_definition])).
% 21.36/3.54 thf(f1280,plain,(
% 21.36/3.54 (((setextT => sF56)) = sF57)),
% 21.36/3.54 inference(reorient_equations,[],[f1279])).
% 21.36/3.54 thf(f1281,definition,(
% 21.36/3.54 (sF58 = ((complementT_lem => sF57)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF58])],[function_definition])).
% 21.36/3.54 thf(f1282,definition,(
% 21.36/3.54 (sF59 = ((setminusT_lem => sF58)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF59])],[function_definition])).
% 21.36/3.54 thf(f1283,plain,(
% 21.36/3.54 (((setminusT_lem => sF58)) = sF59)),
% 21.36/3.54 inference(reorient_equations,[],[f1282])).
% 21.36/3.54 thf(f1284,definition,(
% 21.36/3.54 (sF60 = ((powersetT_lem => sF59)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF60])],[function_definition])).
% 21.36/3.54 thf(f1285,definition,(
% 21.36/3.54 (sF61 = ((binunionT_lem => sF60)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF61])],[function_definition])).
% 21.36/3.54 thf(f1286,plain,(
% 21.36/3.54 (((binunionT_lem => sF60)) = sF61)),
% 21.36/3.54 inference(reorient_equations,[],[f1285])).
% 21.36/3.54 thf(f1287,definition,(
% 21.36/3.54 (sF62 = ((binintersectT_lem => sF61)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF62])],[function_definition])).
% 21.36/3.54 thf(f1288,plain,(
% 21.36/3.54 (((binintersectT_lem => sF61)) = sF62)),
% 21.36/3.54 inference(reorient_equations,[],[f1287])).
% 21.36/3.54 thf(f1289,definition,(
% 21.36/3.54 (sF63 = ((iftrueorfalse => sF62)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF63])],[function_definition])).
% 21.36/3.54 thf(f1290,plain,(
% 21.36/3.54 (((iftrueorfalse => sF62)) = sF63)),
% 21.36/3.54 inference(reorient_equations,[],[f1289])).
% 21.36/3.54 thf(f1291,definition,(
% 21.36/3.54 (sF64 = ((iffalse => sF63)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF64])],[function_definition])).
% 21.36/3.54 thf(f1292,definition,(
% 21.36/3.54 (sF65 = ((iftrue => sF64)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF65])],[function_definition])).
% 21.36/3.54 thf(f1293,definition,(
% 21.36/3.54 (sF66 = ((theeq => sF65)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF66])],[function_definition])).
% 21.36/3.54 thf(f1294,definition,(
% 21.36/3.54 (sF67 = ((ifp => sF66)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF67])],[function_definition])).
% 21.36/3.54 thf(f1295,plain,(
% 21.36/3.54 (((ifp => sF66)) = sF67)),
% 21.36/3.54 inference(reorient_equations,[],[f1294])).
% 21.36/3.54 thf(f1296,definition,(
% 21.36/3.54 (sF68 = ((ifSingleton => sF67)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF68])],[function_definition])).
% 21.36/3.54 thf(f1297,plain,(
% 21.36/3.54 (((ifSingleton => sF67)) = sF68)),
% 21.36/3.54 inference(reorient_equations,[],[f1296])).
% 21.36/3.54 thf(f1298,definition,(
% 21.36/3.54 (sF69 = ((iftrueProp2 => sF68)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF69])],[function_definition])).
% 21.36/3.54 thf(f1299,definition,(
% 21.36/3.54 (sF70 = ((iftrueProp1 => sF69)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF70])],[function_definition])).
% 21.36/3.54 thf(f1300,plain,(
% 21.36/3.54 (((iftrueProp1 => sF69)) = sF70)),
% 21.36/3.54 inference(reorient_equations,[],[f1299])).
% 21.36/3.54 thf(f1301,definition,(
% 21.36/3.54 (sF71 = ((iffalseProp2 => sF70)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF71])],[function_definition])).
% 21.36/3.54 thf(f1302,plain,(
% 21.36/3.54 (((iffalseProp2 => sF70)) = sF71)),
% 21.36/3.54 inference(reorient_equations,[],[f1301])).
% 21.36/3.54 thf(f1303,definition,(
% 21.36/3.54 (sF72 = ((iffalseProp1 => sF71)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF72])],[function_definition])).
% 21.36/3.54 thf(f1304,plain,(
% 21.36/3.54 (((iffalseProp1 => sF71)) = sF72)),
% 21.36/3.54 inference(reorient_equations,[],[f1303])).
% 21.36/3.54 thf(f1305,definition,(
% 21.36/3.54 (sF73 = ((eta2 => sF72)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF73])],[function_definition])).
% 21.36/3.54 thf(f1306,definition,(
% 21.36/3.54 (sF74 = ((beta2 => sF73)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF74])],[function_definition])).
% 21.36/3.54 thf(f1307,definition,(
% 21.36/3.54 (sF75 = ((lam2lamEq => sF74)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF75])],[function_definition])).
% 21.36/3.54 thf(f1308,definition,(
% 21.36/3.54 (sF76 = ((eta1 => sF75)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF76])],[function_definition])).
% 21.36/3.54 thf(f1309,plain,(
% 21.36/3.54 (((eta1 => sF75)) = sF76)),
% 21.36/3.54 inference(reorient_equations,[],[f1308])).
% 21.36/3.54 thf(f1310,definition,(
% 21.36/3.54 (sF77 = ((beta1 => sF76)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF77])],[function_definition])).
% 21.36/3.54 thf(f1311,definition,(
% 21.36/3.54 (sF78 = ((ap2apEq2 => sF77)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF78])],[function_definition])).
% 21.36/3.54 thf(f1312,plain,(
% 21.36/3.54 (((ap2apEq2 => sF77)) = sF78)),
% 21.36/3.54 inference(reorient_equations,[],[f1311])).
% 21.36/3.54 thf(f1313,definition,(
% 21.36/3.54 (sF79 = ((ap2apEq1 => sF78)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF79])],[function_definition])).
% 21.36/3.54 thf(f1314,definition,(
% 21.36/3.54 (sF80 = ((funcext2 => sF79)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF80])],[function_definition])).
% 21.36/3.54 thf(f1315,definition,(
% 21.36/3.54 (sF81 = ((funcext => sF80)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF81])],[function_definition])).
% 21.36/3.54 thf(f1316,plain,(
% 21.36/3.54 (((funcext => sF80)) = sF81)),
% 21.36/3.54 inference(reorient_equations,[],[f1315])).
% 21.36/3.54 thf(f1317,definition,(
% 21.36/3.54 (sF82 = ((eqbreln => sF81)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF82])],[function_definition])).
% 21.36/3.54 thf(f1318,definition,(
% 21.36/3.54 (sF83 = ((subbreln => sF82)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF83])],[function_definition])).
% 21.36/3.54 thf(f1319,plain,(
% 21.36/3.54 (((subbreln => sF82)) = sF83)),
% 21.36/3.54 inference(reorient_equations,[],[f1318])).
% 21.36/3.54 thf(f1320,definition,(
% 21.36/3.54 (sF84 = ((funcGraphProp4 => sF83)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF84])],[function_definition])).
% 21.36/3.54 thf(f1321,plain,(
% 21.36/3.54 (((funcGraphProp4 => sF83)) = sF84)),
% 21.36/3.54 inference(reorient_equations,[],[f1320])).
% 21.36/3.54 thf(f1322,definition,(
% 21.36/3.54 (sF85 = ((funcextLem => sF84)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF85])],[function_definition])).
% 21.36/3.54 thf(f1323,definition,(
% 21.36/3.54 (sF86 = ((funcGraphProp2 => sF85)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF86])],[function_definition])).
% 21.36/3.54 thf(f1324,definition,(
% 21.36/3.54 (sF87 = ((funcGraphProp3 => sF86)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF87])],[function_definition])).
% 21.36/3.54 thf(f1325,definition,(
% 21.36/3.54 (sF88 = ((funcGraphProp1 => sF87)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF88])],[function_definition])).
% 21.36/3.54 thf(f1326,plain,(
% 21.36/3.54 (((funcGraphProp1 => sF87)) = sF88)),
% 21.36/3.54 inference(reorient_equations,[],[f1325])).
% 21.36/3.54 thf(f1327,definition,(
% 21.36/3.54 (sF89 = ((ex1E2 => sF88)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF89])],[function_definition])).
% 21.36/3.54 thf(f1328,definition,(
% 21.36/3.54 (sF90 = ((brelnall2 => sF89)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF90])],[function_definition])).
% 21.36/3.54 thf(f1329,definition,(
% 21.36/3.54 (sF91 = ((brelnall1 => sF90)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF91])],[function_definition])).
% 21.36/3.54 thf(f1330,plain,(
% 21.36/3.54 (((brelnall1 => sF90)) = sF91)),
% 21.36/3.54 inference(reorient_equations,[],[f1329])).
% 21.36/3.54 thf(f1331,definition,(
% 21.36/3.54 (sF92 = ((lam2p => sF91)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF92])],[function_definition])).
% 21.36/3.54 thf(f1332,plain,(
% 21.36/3.54 (((lam2p => sF91)) = sF92)),
% 21.36/3.54 inference(reorient_equations,[],[f1331])).
% 21.36/3.54 thf(f1333,definition,(
% 21.36/3.54 (sF93 = ((lamp => sF92)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF93])],[function_definition])).
% 21.36/3.54 thf(f1334,definition,(
% 21.36/3.54 (sF94 = ((lamProp => sF93)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF94])],[function_definition])).
% 21.36/3.54 thf(f1335,definition,(
% 21.36/3.54 (sF95 = ((funcinfuncset => sF94)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF95])],[function_definition])).
% 21.36/3.54 thf(f1336,definition,(
% 21.36/3.54 (sF96 = ((ap2p => sF95)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF96])],[function_definition])).
% 21.36/3.54 thf(f1337,plain,(
% 21.36/3.54 (((ap2p => sF95)) = sF96)),
% 21.36/3.54 inference(reorient_equations,[],[f1336])).
% 21.36/3.54 thf(f1338,definition,(
% 21.36/3.54 (sF97 = ((infuncsetfunc => sF96)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF97])],[function_definition])).
% 21.36/3.54 thf(f1339,definition,(
% 21.36/3.54 (sF98 = ((app => sF97)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF98])],[function_definition])).
% 21.36/3.54 thf(f1340,plain,(
% 21.36/3.54 (((app => sF97)) = sF98)),
% 21.36/3.54 inference(reorient_equations,[],[f1339])).
% 21.36/3.54 thf(f1341,definition,(
% 21.36/3.54 (sF99 = ((apProp => sF98)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF99])],[function_definition])).
% 21.36/3.54 thf(f1342,definition,(
% 21.36/3.54 (sF100 = ((funcImageSingleton => sF99)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF100])],[function_definition])).
% 21.36/3.54 thf(f1343,plain,(
% 21.36/3.54 (((funcImageSingleton => sF99)) = sF100)),
% 21.36/3.54 inference(reorient_equations,[],[f1342])).
% 21.36/3.54 thf(f1344,definition,(
% 21.36/3.54 (sF101 = ((dpsetconstrER => sF100)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF101])],[function_definition])).
% 21.36/3.54 thf(f1345,plain,(
% 21.36/3.54 (((dpsetconstrER => sF100)) = sF101)),
% 21.36/3.54 inference(reorient_equations,[],[f1344])).
% 21.36/3.54 thf(f1346,definition,(
% 21.36/3.54 (sF102 = ((dpsetconstrEL2 => sF101)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF102])],[function_definition])).
% 21.36/3.54 thf(f1347,definition,(
% 21.36/3.54 (sF103 = ((dpsetconstrEL1 => sF102)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF103])],[function_definition])).
% 21.36/3.54 thf(f1348,definition,(
% 21.36/3.54 (sF104 = ((dpsetconstrERa => sF103)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF104])],[function_definition])).
% 21.36/3.54 thf(f1349,definition,(
% 21.36/3.54 (sF105 = ((setOfPairsIsBReln => sF104)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF105])],[function_definition])).
% 21.36/3.54 thf(f1350,plain,(
% 21.36/3.54 (((setOfPairsIsBReln => sF104)) = sF105)),
% 21.36/3.54 inference(reorient_equations,[],[f1349])).
% 21.36/3.54 thf(f1351,definition,(
% 21.36/3.54 (sF106 = ((dpsetconstrSub => sF105)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF106])],[function_definition])).
% 21.36/3.54 thf(f1352,plain,(
% 21.36/3.54 (((dpsetconstrSub => sF105)) = sF106)),
% 21.36/3.54 inference(reorient_equations,[],[f1351])).
% 21.36/3.54 thf(f1353,definition,(
% 21.36/3.54 (sF107 = ((dpsetconstrI => sF106)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF107])],[function_definition])).
% 21.36/3.54 thf(f1354,plain,(
% 21.36/3.54 (((dpsetconstrI => sF106)) = sF107)),
% 21.36/3.54 inference(reorient_equations,[],[f1353])).
% 21.36/3.54 thf(f1355,definition,(
% 21.36/3.54 (sF108 = ((cartprodpairsurjEq => sF107)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF108])],[function_definition])).
% 21.36/3.54 thf(f1356,definition,(
% 21.36/3.54 (sF109 = ((cartprodsndpairEq => sF108)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF109])],[function_definition])).
% 21.36/3.54 thf(f1357,definition,(
% 21.36/3.54 (sF110 = ((cartprodfstpairEq => sF109)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF110])],[function_definition])).
% 21.36/3.54 thf(f1358,definition,(
% 21.36/3.54 (sF111 = ((cartprodmempaircEq => sF110)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF111])],[function_definition])).
% 21.36/3.54 thf(f1359,definition,(
% 21.36/3.54 (sF112 = ((cartprodpairmemER => sF111)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF112])],[function_definition])).
% 21.36/3.54 thf(f1360,plain,(
% 21.36/3.54 (((cartprodpairmemER => sF111)) = sF112)),
% 21.36/3.54 inference(reorient_equations,[],[f1359])).
% 21.36/3.54 thf(f1361,definition,(
% 21.36/3.54 (sF113 = ((cartprodpairmemEL => sF112)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF113])],[function_definition])).
% 21.36/3.54 thf(f1362,plain,(
% 21.36/3.54 (((cartprodpairmemEL => sF112)) = sF113)),
% 21.36/3.54 inference(reorient_equations,[],[f1361])).
% 21.36/3.54 thf(f1363,definition,(
% 21.36/3.54 (sF114 = ((cartprodsndin => sF113)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF114])],[function_definition])).
% 21.36/3.54 thf(f1364,definition,(
% 21.36/3.54 (sF115 = ((kpairsurjEq => sF114)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF115])],[function_definition])).
% 21.36/3.54 thf(f1365,plain,(
% 21.36/3.54 (((kpairsurjEq => sF114)) = sF115)),
% 21.36/3.54 inference(reorient_equations,[],[f1364])).
% 21.36/3.54 thf(f1366,definition,(
% 21.36/3.54 (sF116 = ((ksndpairEq => sF115)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF116])],[function_definition])).
% 21.36/3.54 thf(f1367,definition,(
% 21.36/3.54 (sF117 = ((ksndsingleton => sF116)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF117])],[function_definition])).
% 21.36/3.54 thf(f1368,definition,(
% 21.36/3.54 (sF118 = ((setukpairinjR => sF117)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF118])],[function_definition])).
% 21.36/3.54 thf(f1369,definition,(
% 21.36/3.54 (sF119 = ((setukpairinjR2 => sF118)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF119])],[function_definition])).
% 21.36/3.54 thf(f1370,plain,(
% 21.36/3.54 (((setukpairinjR2 => sF118)) = sF119)),
% 21.36/3.54 inference(reorient_equations,[],[f1369])).
% 21.36/3.54 thf(f1371,definition,(
% 21.36/3.54 (sF120 = ((upairequniteq => sF119)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF120])],[function_definition])).
% 21.36/3.54 thf(f1372,definition,(
% 21.36/3.54 (sF121 = ((setukpairinjR1 => sF120)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF121])],[function_definition])).
% 21.36/3.54 thf(f1373,definition,(
% 21.36/3.54 (sF122 = ((setukpairinjR12 => sF121)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF122])],[function_definition])).
% 21.36/3.54 thf(f1374,plain,(
% 21.36/3.54 (((setukpairinjR12 => sF121)) = sF122)),
% 21.36/3.54 inference(reorient_equations,[],[f1373])).
% 21.36/3.54 thf(f1375,definition,(
% 21.36/3.54 (sF123 = ((setukpairinjR11 => sF122)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF123])],[function_definition])).
% 21.36/3.54 thf(f1376,plain,(
% 21.36/3.54 (((setukpairinjR11 => sF122)) = sF123)),
% 21.36/3.54 inference(reorient_equations,[],[f1375])).
% 21.36/3.54 thf(f1377,definition,(
% 21.36/3.54 (sF124 = ((setukpairinjL => sF123)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF124])],[function_definition])).
% 21.36/3.54 thf(f1378,definition,(
% 21.36/3.54 (sF125 = ((setukpairinjL2 => sF124)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF125])],[function_definition])).
% 21.36/3.54 thf(f1379,plain,(
% 21.36/3.54 (((setukpairinjL2 => sF124)) = sF125)),
% 21.36/3.54 inference(reorient_equations,[],[f1378])).
% 21.36/3.54 thf(f1380,definition,(
% 21.36/3.54 (sF126 = ((cartprodfstin => sF125)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF126])],[function_definition])).
% 21.36/3.54 thf(f1381,plain,(
% 21.36/3.54 (((cartprodfstin => sF125)) = sF126)),
% 21.36/3.54 inference(reorient_equations,[],[f1380])).
% 21.36/3.54 thf(f1382,definition,(
% 21.36/3.54 (sF127 = ((kfstpairEq => sF126)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF127])],[function_definition])).
% 21.36/3.54 thf(f1383,plain,(
% 21.36/3.54 (((kfstpairEq => sF126)) = sF127)),
% 21.36/3.54 inference(reorient_equations,[],[f1382])).
% 21.36/3.54 thf(f1384,definition,(
% 21.36/3.54 (sF128 = ((theprop => sF127)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF128])],[function_definition])).
% 21.36/3.54 thf(f1385,plain,(
% 21.36/3.54 (((theprop => sF127)) = sF128)),
% 21.36/3.54 inference(reorient_equations,[],[f1384])).
% 21.36/3.54 thf(f1386,definition,(
% 21.36/3.54 (sF129 = ((kfstsingleton => sF128)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF129])],[function_definition])).
% 21.36/3.54 thf(f1387,plain,(
% 21.36/3.54 (((kfstsingleton => sF128)) = sF129)),
% 21.36/3.54 inference(reorient_equations,[],[f1386])).
% 21.36/3.54 thf(f1388,definition,(
% 21.36/3.54 (sF130 = ((setukpairinjL1 => sF129)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF130])],[function_definition])).
% 21.36/3.54 thf(f1389,plain,(
% 21.36/3.54 (((setukpairinjL1 => sF129)) = sF130)),
% 21.36/3.54 inference(reorient_equations,[],[f1388])).
% 21.36/3.54 thf(f1390,definition,(
% 21.36/3.54 (sF131 = ((singletonsuniq => sF130)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF131])],[function_definition])).
% 21.36/3.54 thf(f1391,plain,(
% 21.36/3.54 (((singletonsuniq => sF130)) = sF131)),
% 21.36/3.54 inference(reorient_equations,[],[f1390])).
% 21.36/3.54 thf(f1392,definition,(
% 21.36/3.54 (sF132 = ((ex1I2 => sF131)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF132])],[function_definition])).
% 21.36/3.54 thf(f1393,definition,(
% 21.36/3.54 (sF133 = ((ex1I => sF132)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF133])],[function_definition])).
% 21.36/3.54 thf(f1394,definition,(
% 21.36/3.54 (sF134 = ((ex1E1 => sF133)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF134])],[function_definition])).
% 21.36/3.54 thf(f1395,definition,(
% 21.36/3.54 (sF135 = ((singletonprop => sF134)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF135])],[function_definition])).
% 21.36/3.54 thf(f1396,definition,(
% 21.36/3.54 (sF136 = ((setunionsingleton => sF135)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF136])],[function_definition])).
% 21.36/3.54 thf(f1397,plain,(
% 21.36/3.54 (((setunionsingleton => sF135)) = sF136)),
% 21.36/3.54 inference(reorient_equations,[],[f1396])).
% 21.36/3.54 thf(f1398,definition,(
% 21.36/3.54 (sF137 = ((setunionsingleton2 => sF136)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF137])],[function_definition])).
% 21.36/3.54 thf(f1399,plain,(
% 21.36/3.54 (((setunionsingleton2 => sF136)) = sF137)),
% 21.36/3.54 inference(reorient_equations,[],[f1398])).
% 21.36/3.54 thf(f1400,definition,(
% 21.36/3.54 (sF138 = ((setunionsingleton1 => sF137)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF138])],[function_definition])).
% 21.36/3.54 thf(f1401,definition,(
% 21.36/3.54 (sF139 = ((setunionE2 => sF138)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF139])],[function_definition])).
% 21.36/3.54 thf(f1402,definition,(
% 21.36/3.54 (sF140 = ((cartprodmempair => sF139)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF140])],[function_definition])).
% 21.36/3.54 thf(f1403,definition,(
% 21.36/3.54 (sF141 = ((cartprodmempair1 => sF140)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF141])],[function_definition])).
% 21.36/3.54 thf(f1404,definition,(
% 21.36/3.54 (sF142 = ((cartprodpairin => sF141)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF142])],[function_definition])).
% 21.36/3.54 thf(f1405,definition,(
% 21.36/3.54 (sF143 = ((ubforcartprodlem3 => sF142)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF143])],[function_definition])).
% 21.36/3.54 thf(f1406,definition,(
% 21.36/3.54 (sF144 = ((ubforcartprodlem2 => sF143)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF144])],[function_definition])).
% 21.36/3.54 thf(f1407,definition,(
% 21.36/3.54 (sF145 = ((ubforcartprodlem1 => sF144)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF145])],[function_definition])).
% 21.36/3.54 thf(f1408,definition,(
% 21.36/3.54 (sF146 = ((upairinpowunion => sF145)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF146])],[function_definition])).
% 21.36/3.54 thf(f1409,definition,(
% 21.36/3.54 (sF147 = ((upairsubunion => sF146)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF147])],[function_definition])).
% 21.36/3.54 thf(f1410,plain,(
% 21.36/3.54 (((upairsubunion => sF146)) = sF147)),
% 21.36/3.54 inference(reorient_equations,[],[f1409])).
% 21.36/3.54 thf(f1411,definition,(
% 21.36/3.54 (sF148 = ((upairset2E => sF147)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF148])],[function_definition])).
% 21.36/3.54 thf(f1412,definition,(
% 21.36/3.54 (sF149 = ((singletoninpowunion => sF148)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF149])],[function_definition])).
% 21.36/3.54 thf(f1413,plain,(
% 21.36/3.54 (((singletoninpowunion => sF148)) = sF149)),
% 21.36/3.54 inference(reorient_equations,[],[f1412])).
% 21.36/3.54 thf(f1414,definition,(
% 21.36/3.54 (sF150 = ((singletoninpowerset => sF149)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF150])],[function_definition])).
% 21.36/3.54 thf(f1415,definition,(
% 21.36/3.54 (sF151 = ((singletonsubset => sF150)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF151])],[function_definition])).
% 21.36/3.54 thf(f1416,definition,(
% 21.36/3.54 (sF152 = ((kpairp => sF151)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF152])],[function_definition])).
% 21.36/3.54 thf(f1417,plain,(
% 21.36/3.54 (((kpairp => sF151)) = sF152)),
% 21.36/3.54 inference(reorient_equations,[],[f1416])).
% 21.36/3.54 thf(f1418,definition,(
% 21.36/3.54 (sF153 = ((kpairiskpair => sF152)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF153])],[function_definition])).
% 21.36/3.54 thf(f1419,plain,(
% 21.36/3.54 (((kpairiskpair => sF152)) = sF153)),
% 21.36/3.54 inference(reorient_equations,[],[f1418])).
% 21.36/3.54 thf(f1420,definition,(
% 21.36/3.54 (sF154 = ((setukpairIR => sF153)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF154])],[function_definition])).
% 21.36/3.54 thf(f1421,definition,(
% 21.36/3.54 (sF155 = ((setukpairIL => sF154)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF155])],[function_definition])).
% 21.36/3.54 thf(f1422,definition,(
% 21.36/3.54 (sF156 = ((secondinupair => sF155)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF156])],[function_definition])).
% 21.36/3.54 thf(f1423,definition,(
% 21.36/3.54 (sF157 = ((symdiffIneg2 => sF156)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF157])],[function_definition])).
% 21.36/3.54 thf(f1424,definition,(
% 21.36/3.54 (sF158 = ((symdiffIneg1 => sF157)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF158])],[function_definition])).
% 21.36/3.54 thf(f1425,definition,(
% 21.36/3.54 (sF159 = ((symdiffI2 => sF158)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF159])],[function_definition])).
% 21.36/3.54 thf(f1426,plain,(
% 21.36/3.54 (((symdiffI2 => sF158)) = sF159)),
% 21.36/3.54 inference(reorient_equations,[],[f1425])).
% 21.36/3.54 thf(f1427,definition,(
% 21.36/3.54 (sF160 = ((symdiffI1 => sF159)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF160])],[function_definition])).
% 21.36/3.54 thf(f1428,plain,(
% 21.36/3.54 (((symdiffI1 => sF159)) = sF160)),
% 21.36/3.54 inference(reorient_equations,[],[f1427])).
% 21.36/3.54 thf(f1429,definition,(
% 21.36/3.54 (sF161 = ((symdiffE => sF160)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF161])],[function_definition])).
% 21.36/3.54 thf(f1430,definition,(
% 21.36/3.54 (sF162 = ((setminusSubset1 => sF161)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF162])],[function_definition])).
% 21.36/3.54 thf(f1431,definition,(
% 21.36/3.54 (sF163 = ((setminusLsub => sF162)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF163])],[function_definition])).
% 21.36/3.54 thf(f1432,definition,(
% 21.36/3.54 (sF164 = ((setminusIRneg => sF163)))),
% 21.36/3.54 introduced(definition,[new_symbols(definition,[sF164])],[function_definition])).
% 21.36/3.55 thf(f1433,definition,(
% 21.36/3.55 (sF165 = ((setminusILneg => sF164)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF165])],[function_definition])).
% 21.36/3.55 thf(f1434,definition,(
% 21.36/3.55 (sF166 = ((setminusELneg => sF165)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF166])],[function_definition])).
% 21.36/3.55 thf(f1435,plain,(
% 21.36/3.55 (((setminusELneg => sF165)) = sF166)),
% 21.36/3.55 inference(reorient_equations,[],[f1434])).
% 21.36/3.55 thf(f1436,definition,(
% 21.36/3.55 (sF167 = ((setminusERneg => sF166)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF167])],[function_definition])).
% 21.36/3.55 thf(f1437,plain,(
% 21.36/3.55 (((setminusERneg => sF166)) = sF167)),
% 21.36/3.55 inference(reorient_equations,[],[f1436])).
% 21.36/3.55 thf(f1438,definition,(
% 21.36/3.55 (sF168 = ((setminusSubset2 => sF167)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF168])],[function_definition])).
% 21.36/3.55 thf(f1439,definition,(
% 21.36/3.55 (sF169 = ((setminusER => sF168)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF169])],[function_definition])).
% 21.36/3.55 thf(f1440,plain,(
% 21.36/3.55 (((setminusER => sF168)) = sF169)),
% 21.36/3.55 inference(reorient_equations,[],[f1439])).
% 21.36/3.55 thf(f1441,definition,(
% 21.36/3.55 (sF170 = ((setminusEL => sF169)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF170])],[function_definition])).
% 21.36/3.55 thf(f1442,plain,(
% 21.36/3.55 (((setminusEL => sF169)) = sF170)),
% 21.36/3.55 inference(reorient_equations,[],[f1441])).
% 21.36/3.55 thf(f1443,definition,(
% 21.36/3.55 (sF171 = ((setminusI => sF170)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF171])],[function_definition])).
% 21.36/3.55 thf(f1444,plain,(
% 21.36/3.55 (((setminusI => sF170)) = sF171)),
% 21.36/3.55 inference(reorient_equations,[],[f1443])).
% 21.36/3.55 thf(f1445,definition,(
% 21.36/3.55 (sF172 = ((bs114d => sF171)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF172])],[function_definition])).
% 21.36/3.55 thf(f1446,plain,(
% 21.36/3.55 (((bs114d => sF171)) = sF172)),
% 21.36/3.55 inference(reorient_equations,[],[f1445])).
% 21.36/3.55 thf(f1447,definition,(
% 21.36/3.55 (sF173 = ((binintersectSubset1 => sF172)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF173])],[function_definition])).
% 21.36/3.55 thf(f1448,plain,(
% 21.36/3.55 (((binintersectSubset1 => sF172)) = sF173)),
% 21.36/3.55 inference(reorient_equations,[],[f1447])).
% 21.36/3.55 thf(f1449,definition,(
% 21.36/3.55 (sF174 = ((binintersectSubset4 => sF173)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF174])],[function_definition])).
% 21.36/3.55 thf(f1450,plain,(
% 21.36/3.55 (((binintersectSubset4 => sF173)) = sF174)),
% 21.36/3.55 inference(reorient_equations,[],[f1449])).
% 21.36/3.55 thf(f1451,definition,(
% 21.36/3.55 (sF175 = ((binintersectRsub => sF174)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF175])],[function_definition])).
% 21.36/3.55 thf(f1452,plain,(
% 21.36/3.55 (((binintersectRsub => sF174)) = sF175)),
% 21.36/3.55 inference(reorient_equations,[],[f1451])).
% 21.36/3.55 thf(f1453,definition,(
% 21.36/3.55 (sF176 = ((disjointsetsI1 => sF175)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF176])],[function_definition])).
% 21.36/3.55 thf(f1454,definition,(
% 21.36/3.55 (sF177 = ((binintersectER => sF176)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF177])],[function_definition])).
% 21.36/3.55 thf(f1455,definition,(
% 21.36/3.55 (sF178 = ((binintersectSubset3 => sF177)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF178])],[function_definition])).
% 21.36/3.55 thf(f1456,definition,(
% 21.36/3.55 (sF179 = ((binintersectSubset2 => sF178)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF179])],[function_definition])).
% 21.36/3.55 thf(f1457,definition,(
% 21.36/3.55 (sF180 = ((binintersectLsub => sF179)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF180])],[function_definition])).
% 21.36/3.55 thf(f1458,definition,(
% 21.36/3.55 (sF181 = ((binintersectEL => sF180)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF181])],[function_definition])).
% 21.36/3.55 thf(f1459,definition,(
% 21.36/3.55 (sF182 = ((binintersectSubset5 => sF181)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF182])],[function_definition])).
% 21.36/3.55 thf(f1460,plain,(
% 21.36/3.55 (((binintersectSubset5 => sF181)) = sF182)),
% 21.36/3.55 inference(reorient_equations,[],[f1459])).
% 21.36/3.55 thf(f1461,definition,(
% 21.36/3.55 (sF183 = ((binintersectI => sF182)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF183])],[function_definition])).
% 21.36/3.55 thf(f1462,definition,(
% 21.36/3.55 (sF184 = ((binunionRsub => sF183)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF184])],[function_definition])).
% 21.36/3.55 thf(f1463,definition,(
% 21.36/3.55 (sF185 = ((binunionLsub => sF184)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF185])],[function_definition])).
% 21.36/3.55 thf(f1464,plain,(
% 21.36/3.55 (((binunionLsub => sF184)) = sF185)),
% 21.36/3.55 inference(reorient_equations,[],[f1463])).
% 21.36/3.55 thf(f1465,definition,(
% 21.36/3.55 (sF186 = ((binunionE => sF185)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF186])],[function_definition])).
% 21.36/3.55 thf(f1466,plain,(
% 21.36/3.55 (((binunionE => sF185)) = sF186)),
% 21.36/3.55 inference(reorient_equations,[],[f1465])).
% 21.36/3.55 thf(f1467,definition,(
% 21.36/3.55 (sF187 = ((binunionEcases => sF186)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF187])],[function_definition])).
% 21.36/3.55 thf(f1468,plain,(
% 21.36/3.55 (((binunionEcases => sF186)) = sF187)),
% 21.36/3.55 inference(reorient_equations,[],[f1467])).
% 21.36/3.55 thf(f1469,definition,(
% 21.36/3.55 (sF188 = ((binunionIR => sF187)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF188])],[function_definition])).
% 21.36/3.55 thf(f1470,plain,(
% 21.36/3.55 (((binunionIR => sF187)) = sF188)),
% 21.36/3.55 inference(reorient_equations,[],[f1469])).
% 21.36/3.55 thf(f1471,definition,(
% 21.36/3.55 (sF189 = ((upairset2IR => sF188)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF189])],[function_definition])).
% 21.36/3.55 thf(f1472,definition,(
% 21.36/3.55 (sF190 = ((binunionIL => sF189)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF190])],[function_definition])).
% 21.36/3.55 thf(f1473,definition,(
% 21.36/3.55 (sF191 = ((sepSubset => sF190)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF191])],[function_definition])).
% 21.36/3.55 thf(f1474,plain,(
% 21.36/3.55 (((sepSubset => sF190)) = sF191)),
% 21.36/3.55 inference(reorient_equations,[],[f1473])).
% 21.36/3.55 thf(f1475,definition,(
% 21.36/3.55 (sF192 = ((sepInPowerset => sF191)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF192])],[function_definition])).
% 21.36/3.55 thf(f1476,definition,(
% 21.36/3.55 (sF193 = ((powersetsubset => sF192)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF193])],[function_definition])).
% 21.36/3.55 thf(f1477,plain,(
% 21.36/3.55 (((powersetsubset => sF192)) = sF193)),
% 21.36/3.55 inference(reorient_equations,[],[f1476])).
% 21.36/3.55 thf(f1478,definition,(
% 21.36/3.55 (sF194 = ((inPowerset => sF193)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF194])],[function_definition])).
% 21.36/3.55 thf(f1479,plain,(
% 21.36/3.55 (((inPowerset => sF193)) = sF194)),
% 21.36/3.55 inference(reorient_equations,[],[f1478])).
% 21.36/3.55 thf(f1480,definition,(
% 21.36/3.55 (sF195 = ((powersetE1 => sF194)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF195])],[function_definition])).
% 21.36/3.55 thf(f1481,definition,(
% 21.36/3.55 (sF196 = ((powersetI1 => sF195)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF196])],[function_definition])).
% 21.36/3.55 thf(f1482,plain,(
% 21.36/3.55 (((powersetI1 => sF195)) = sF196)),
% 21.36/3.55 inference(reorient_equations,[],[f1481])).
% 21.36/3.55 thf(f1483,definition,(
% 21.36/3.55 (sF197 = ((subsetemptysetimpeq => sF196)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF197])],[function_definition])).
% 21.36/3.55 thf(f1484,plain,(
% 21.36/3.55 (((subsetemptysetimpeq => sF196)) = sF197)),
% 21.36/3.55 inference(reorient_equations,[],[f1483])).
% 21.36/3.55 thf(f1485,definition,(
% 21.36/3.55 (sF198 = ((setextsub => sF197)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF198])],[function_definition])).
% 21.36/3.55 thf(f1486,plain,(
% 21.36/3.55 (((setextsub => sF197)) = sF198)),
% 21.36/3.55 inference(reorient_equations,[],[f1485])).
% 21.36/3.55 thf(f1487,definition,(
% 21.36/3.55 (sF199 = ((subset2powerset => sF198)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF199])],[function_definition])).
% 21.36/3.55 thf(f1488,plain,(
% 21.36/3.55 (((subset2powerset => sF198)) = sF199)),
% 21.36/3.55 inference(reorient_equations,[],[f1487])).
% 21.36/3.55 thf(f1489,definition,(
% 21.36/3.55 (sF200 = ((setadjoinSub2 => sF199)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF200])],[function_definition])).
% 21.36/3.55 thf(f1490,plain,(
% 21.36/3.55 (((setadjoinSub2 => sF199)) = sF200)),
% 21.36/3.55 inference(reorient_equations,[],[f1489])).
% 21.36/3.55 thf(f1491,definition,(
% 21.36/3.55 (sF201 = ((setadjoinSub => sF200)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF201])],[function_definition])).
% 21.36/3.55 thf(f1492,definition,(
% 21.36/3.55 (sF202 = ((subsetTrans => sF201)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF202])],[function_definition])).
% 21.36/3.55 thf(f1493,plain,(
% 21.36/3.55 (((subsetTrans => sF201)) = sF202)),
% 21.36/3.55 inference(reorient_equations,[],[f1492])).
% 21.36/3.55 thf(f1494,definition,(
% 21.36/3.55 (sF203 = ((subsetRefl => sF202)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF203])],[function_definition])).
% 21.36/3.55 thf(f1495,plain,(
% 21.36/3.55 (((subsetRefl => sF202)) = sF203)),
% 21.36/3.55 inference(reorient_equations,[],[f1494])).
% 21.36/3.55 thf(f1496,definition,(
% 21.36/3.55 (sF204 = ((notequalI2 => sF203)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF204])],[function_definition])).
% 21.36/3.55 thf(f1497,definition,(
% 21.36/3.55 (sF205 = ((notequalI1 => sF204)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF205])],[function_definition])).
% 21.36/3.55 thf(f1498,plain,(
% 21.36/3.55 (((notequalI1 => sF204)) = sF205)),
% 21.36/3.55 inference(reorient_equations,[],[f1497])).
% 21.36/3.55 thf(f1499,definition,(
% 21.36/3.55 (sF206 = ((notsubsetI => sF205)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF206])],[function_definition])).
% 21.36/3.55 thf(f1500,plain,(
% 21.36/3.55 (((notsubsetI => sF205)) = sF206)),
% 21.36/3.55 inference(reorient_equations,[],[f1499])).
% 21.36/3.55 thf(f1501,definition,(
% 21.36/3.55 (sF207 = ((subsetE2 => sF206)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF207])],[function_definition])).
% 21.36/3.55 thf(f1502,definition,(
% 21.36/3.55 (sF208 = ((subsetE => sF207)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF208])],[function_definition])).
% 21.36/3.55 thf(f1503,plain,(
% 21.36/3.55 (((subsetE => sF207)) = sF208)),
% 21.36/3.55 inference(reorient_equations,[],[f1502])).
% 21.36/3.55 thf(f1504,definition,(
% 21.36/3.55 (sF209 = ((emptysetsubset => sF208)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF209])],[function_definition])).
% 21.36/3.55 thf(f1505,plain,(
% 21.36/3.55 (((emptysetsubset => sF208)) = sF209)),
% 21.36/3.55 inference(reorient_equations,[],[f1504])).
% 21.36/3.55 thf(f1506,definition,(
% 21.36/3.55 (sF210 = ((subsetI2 => sF209)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF210])],[function_definition])).
% 21.36/3.55 thf(f1507,plain,(
% 21.36/3.55 (((subsetI2 => sF209)) = sF210)),
% 21.36/3.55 inference(reorient_equations,[],[f1506])).
% 21.36/3.55 thf(f1508,definition,(
% 21.36/3.55 (sF211 = ((eqimpsubset1 => sF210)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF211])],[function_definition])).
% 21.36/3.55 thf(f1509,definition,(
% 21.36/3.55 (sF212 = ((eqimpsubset2 => sF211)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF212])],[function_definition])).
% 21.36/3.55 thf(f1510,plain,(
% 21.36/3.55 (((eqimpsubset2 => sF211)) = sF212)),
% 21.36/3.55 inference(reorient_equations,[],[f1509])).
% 21.36/3.55 thf(f1511,definition,(
% 21.36/3.55 (sF213 = ((subsetI1 => sF212)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF213])],[function_definition])).
% 21.36/3.55 thf(f1512,definition,(
% 21.36/3.55 (sF214 = ((dsetconstr__Cong => sF213)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF214])],[function_definition])).
% 21.36/3.55 thf(f1513,plain,(
% 21.36/3.55 (((dsetconstr__Cong => sF213)) = sF214)),
% 21.36/3.55 inference(reorient_equations,[],[f1512])).
% 21.36/3.55 thf(f1514,definition,(
% 21.36/3.55 (sF215 = ((descr__Cong => sF214)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF215])],[function_definition])).
% 21.36/3.55 thf(f1515,definition,(
% 21.36/3.55 (sF216 = ((exuEu => sF215)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF216])],[function_definition])).
% 21.36/3.55 thf(f1516,plain,(
% 21.36/3.55 (((exuEu => sF215)) = sF216)),
% 21.36/3.55 inference(reorient_equations,[],[f1515])).
% 21.36/3.55 thf(f1517,definition,(
% 21.36/3.55 (sF217 = ((omega__Cong => sF216)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF217])],[function_definition])).
% 21.36/3.55 thf(f1518,plain,(
% 21.36/3.55 (((omega__Cong => sF216)) = sF217)),
% 21.36/3.55 inference(reorient_equations,[],[f1517])).
% 21.36/3.55 thf(f1519,definition,(
% 21.36/3.55 (sF218 = ((setunion__Cong => sF217)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF218])],[function_definition])).
% 21.36/3.55 thf(f1520,definition,(
% 21.36/3.55 (sF219 = ((powerset__Cong => sF218)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF219])],[function_definition])).
% 21.36/3.55 thf(f1521,plain,(
% 21.36/3.55 (((powerset__Cong => sF218)) = sF219)),
% 21.36/3.55 inference(reorient_equations,[],[f1520])).
% 21.36/3.55 thf(f1522,definition,(
% 21.36/3.55 (sF220 = ((setadjoin__Cong => sF219)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF220])],[function_definition])).
% 21.36/3.55 thf(f1523,plain,(
% 21.36/3.55 (((setadjoin__Cong => sF219)) = sF220)),
% 21.36/3.55 inference(reorient_equations,[],[f1522])).
% 21.36/3.55 thf(f1524,definition,(
% 21.36/3.55 (sF221 = ((emptyset__Cong => sF220)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF221])],[function_definition])).
% 21.36/3.55 thf(f1525,plain,(
% 21.36/3.55 (((emptyset__Cong => sF220)) = sF221)),
% 21.36/3.55 inference(reorient_equations,[],[f1524])).
% 21.36/3.55 thf(f1526,definition,(
% 21.36/3.55 (sF222 = ((exu__Cong => sF221)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF222])],[function_definition])).
% 21.36/3.55 thf(f1527,definition,(
% 21.36/3.55 (sF223 = ((exuE3u => sF222)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF223])],[function_definition])).
% 21.36/3.55 thf(f1528,plain,(
% 21.36/3.55 (((exuE3u => sF222)) = sF223)),
% 21.36/3.55 inference(reorient_equations,[],[f1527])).
% 21.36/3.55 thf(f1529,definition,(
% 21.36/3.55 (sF224 = ((in__Cong => sF223)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF224])],[function_definition])).
% 21.36/3.55 thf(f1530,plain,(
% 21.36/3.55 (((in__Cong => sF223)) = sF224)),
% 21.36/3.55 inference(reorient_equations,[],[f1529])).
% 21.36/3.55 thf(f1531,definition,(
% 21.36/3.55 (sF225 = ((inCongP => sF224)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF225])],[function_definition])).
% 21.36/3.55 thf(f1532,plain,(
% 21.36/3.55 (((inCongP => sF224)) = sF225)),
% 21.36/3.55 inference(reorient_equations,[],[f1531])).
% 21.36/3.55 thf(f1533,definition,(
% 21.36/3.55 (sF226 = ((exuI2 => sF225)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF226])],[function_definition])).
% 21.36/3.55 thf(f1534,definition,(
% 21.36/3.55 (sF227 = ((exuI3 => sF226)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF227])],[function_definition])).
% 21.36/3.55 thf(f1535,definition,(
% 21.36/3.55 (sF228 = ((exuI1 => sF227)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF228])],[function_definition])).
% 21.36/3.55 thf(f1536,definition,(
% 21.36/3.55 (sF229 = ((notdallE => sF228)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF229])],[function_definition])).
% 21.36/3.55 thf(f1537,plain,(
% 21.36/3.55 (((notdallE => sF228)) = sF229)),
% 21.36/3.55 inference(reorient_equations,[],[f1536])).
% 21.36/3.55 thf(f1538,definition,(
% 21.36/3.55 (sF230 = ((notdexE => sF229)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF230])],[function_definition])).
% 21.36/3.55 thf(f1539,definition,(
% 21.36/3.55 (sF231 = ((prop2set2propI => sF230)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF231])],[function_definition])).
% 21.36/3.55 thf(f1540,definition,(
% 21.36/3.55 (sF232 = ((prop2setI => sF231)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF232])],[function_definition])).
% 21.36/3.55 thf(f1541,definition,(
% 21.36/3.55 (sF233 = ((quantDeMorgan4 => sF232)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF233])],[function_definition])).
% 21.36/3.55 thf(f1542,definition,(
% 21.36/3.55 (sF234 = ((quantDeMorgan3 => sF233)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF234])],[function_definition])).
% 21.36/3.55 thf(f1543,definition,(
% 21.36/3.55 (sF235 = ((quantDeMorgan2 => sF234)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF235])],[function_definition])).
% 21.36/3.55 thf(f1544,plain,(
% 21.36/3.55 (((quantDeMorgan2 => sF234)) = sF235)),
% 21.36/3.55 inference(reorient_equations,[],[f1543])).
% 21.36/3.55 thf(f1545,definition,(
% 21.36/3.55 (sF236 = ((quantDeMorgan1 => sF235)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF236])],[function_definition])).
% 21.36/3.55 thf(f1546,plain,(
% 21.36/3.55 (((quantDeMorgan1 => sF235)) = sF236)),
% 21.36/3.55 inference(reorient_equations,[],[f1545])).
% 21.36/3.55 thf(f1547,definition,(
% 21.36/3.55 (sF237 = ((vacuousDall => sF236)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF237])],[function_definition])).
% 21.36/3.55 thf(f1548,plain,(
% 21.36/3.55 (((vacuousDall => sF236)) = sF237)),
% 21.36/3.55 inference(reorient_equations,[],[f1547])).
% 21.36/3.55 thf(f1549,definition,(
% 21.36/3.55 (sF238 = ((emptyE1 => sF237)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF238])],[function_definition])).
% 21.36/3.55 thf(f1550,plain,(
% 21.36/3.55 (((emptyE1 => sF237)) = sF238)),
% 21.36/3.55 inference(reorient_equations,[],[f1549])).
% 21.36/3.55 thf(f1551,definition,(
% 21.36/3.55 (sF239 = ((upairsetIR => sF238)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF239])],[function_definition])).
% 21.36/3.55 thf(f1552,definition,(
% 21.36/3.55 (sF240 = ((upairsetIL => sF239)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF240])],[function_definition])).
% 21.36/3.55 thf(f1553,plain,(
% 21.36/3.55 (((upairsetIL => sF239)) = sF240)),
% 21.36/3.55 inference(reorient_equations,[],[f1552])).
% 21.36/3.55 thf(f1554,definition,(
% 21.36/3.55 (sF241 = ((upairsetE => sF240)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF241])],[function_definition])).
% 21.36/3.55 thf(f1555,plain,(
% 21.36/3.55 (((upairsetE => sF240)) = sF241)),
% 21.36/3.55 inference(reorient_equations,[],[f1554])).
% 21.36/3.55 thf(f1556,definition,(
% 21.36/3.55 (sF242 = ((singletonsswitch => sF241)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF242])],[function_definition])).
% 21.36/3.55 thf(f1557,plain,(
% 21.36/3.55 (((singletonsswitch => sF241)) = sF242)),
% 21.36/3.55 inference(reorient_equations,[],[f1556])).
% 21.36/3.55 thf(f1558,definition,(
% 21.36/3.55 (sF243 = ((eqinunit => sF242)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF243])],[function_definition])).
% 21.36/3.55 thf(f1559,plain,(
% 21.36/3.55 (((eqinunit => sF242)) = sF243)),
% 21.36/3.55 inference(reorient_equations,[],[f1558])).
% 21.36/3.55 thf(f1560,definition,(
% 21.36/3.55 (sF244 = ((notinsingleton => sF243)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF244])],[function_definition])).
% 21.36/3.55 thf(f1561,definition,(
% 21.36/3.55 (sF245 = ((uniqinunit => sF244)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF245])],[function_definition])).
% 21.36/3.55 thf(f1562,definition,(
% 21.36/3.55 (sF246 = ((nonemptyImpWitness => sF245)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF246])],[function_definition])).
% 21.36/3.55 thf(f1563,plain,(
% 21.36/3.55 (((nonemptyImpWitness => sF245)) = sF246)),
% 21.36/3.55 inference(reorient_equations,[],[f1562])).
% 21.36/3.55 thf(f1564,definition,(
% 21.36/3.55 (sF247 = ((exuE2 => sF246)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF247])],[function_definition])).
% 21.36/3.55 thf(f1565,definition,(
% 21.36/3.55 (sF248 = ((subPowSU => sF247)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF248])],[function_definition])).
% 21.36/3.55 thf(f1566,plain,(
% 21.36/3.55 (((subPowSU => sF247)) = sF248)),
% 21.36/3.55 inference(reorient_equations,[],[f1565])).
% 21.36/3.55 thf(f1567,definition,(
% 21.36/3.55 (sF249 = ((setunionE => sF248)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF249])],[function_definition])).
% 21.36/3.55 thf(f1568,definition,(
% 21.36/3.55 (sF250 = ((setunionI => sF249)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF250])],[function_definition])).
% 21.36/3.55 thf(f1569,plain,(
% 21.36/3.55 (((setunionI => sF249)) = sF250)),
% 21.36/3.55 inference(reorient_equations,[],[f1568])).
% 21.36/3.55 thf(f1570,definition,(
% 21.36/3.55 (sF251 = ((powersetE => sF250)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF251])],[function_definition])).
% 21.36/3.55 thf(f1571,definition,(
% 21.36/3.55 (sF252 = ((emptyInPowerset => sF251)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF252])],[function_definition])).
% 21.36/3.55 thf(f1572,definition,(
% 21.36/3.55 (sF253 = ((emptyinPowerset => sF252)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF253])],[function_definition])).
% 21.36/3.55 thf(f1573,plain,(
% 21.36/3.55 (((emptyinPowerset => sF252)) = sF253)),
% 21.36/3.55 inference(reorient_equations,[],[f1572])).
% 21.36/3.55 thf(f1574,definition,(
% 21.36/3.55 (sF254 = ((powersetI => sF253)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF254])],[function_definition])).
% 21.36/3.55 thf(f1575,definition,(
% 21.36/3.55 (sF255 = ((setoftrueEq => sF254)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF255])],[function_definition])).
% 21.36/3.55 thf(f1576,definition,(
% 21.36/3.55 (sF256 = ((setadjoinOr => sF255)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF256])],[function_definition])).
% 21.36/3.55 thf(f1577,definition,(
% 21.36/3.55 (sF257 = ((setadjoinE => sF256)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF257])],[function_definition])).
% 21.36/3.55 thf(f1578,definition,(
% 21.36/3.55 (sF258 = ((setadjoinIR => sF257)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF258])],[function_definition])).
% 21.36/3.55 thf(f1579,definition,(
% 21.36/3.55 (sF259 = ((emptyinunitempty => sF258)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF259])],[function_definition])).
% 21.36/3.55 thf(f1580,definition,(
% 21.36/3.55 (sF260 = ((setadjoinIL => sF259)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF260])],[function_definition])).
% 21.36/3.55 thf(f1581,definition,(
% 21.36/3.55 (sF261 = ((nonemptyI1 => sF260)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF261])],[function_definition])).
% 21.36/3.55 thf(f1582,plain,(
% 21.36/3.55 (((nonemptyI1 => sF260)) = sF261)),
% 21.36/3.55 inference(reorient_equations,[],[f1581])).
% 21.36/3.55 thf(f1583,definition,(
% 21.36/3.55 (sF262 = ((nonemptyI => sF261)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF262])],[function_definition])).
% 21.36/3.55 thf(f1584,plain,(
% 21.36/3.55 (((nonemptyI => sF261)) = sF262)),
% 21.36/3.55 inference(reorient_equations,[],[f1583])).
% 21.36/3.55 thf(f1585,definition,(
% 21.36/3.55 (sF263 = ((nonemptyE1 => sF262)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF263])],[function_definition])).
% 21.36/3.55 thf(f1586,plain,(
% 21.36/3.55 (((nonemptyE1 => sF262)) = sF263)),
% 21.36/3.55 inference(reorient_equations,[],[f1585])).
% 21.36/3.55 thf(f1587,definition,(
% 21.36/3.55 (sF264 = ((setbeta => sF263)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF264])],[function_definition])).
% 21.36/3.55 thf(f1588,definition,(
% 21.36/3.55 (sF265 = ((noeltsimpempty => sF264)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF265])],[function_definition])).
% 21.36/3.55 thf(f1589,plain,(
% 21.36/3.55 (((noeltsimpempty => sF264)) = sF265)),
% 21.36/3.55 inference(reorient_equations,[],[f1588])).
% 21.36/3.55 thf(f1590,definition,(
% 21.36/3.55 (sF266 = ((emptyI => sF265)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF266])],[function_definition])).
% 21.36/3.55 thf(f1591,plain,(
% 21.36/3.55 (((emptyI => sF265)) = sF266)),
% 21.36/3.55 inference(reorient_equations,[],[f1590])).
% 21.36/3.55 thf(f1592,definition,(
% 21.36/3.55 (sF267 = ((setext => sF266)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF267])],[function_definition])).
% 21.36/3.55 thf(f1593,definition,(
% 21.36/3.55 (sF268 = ((exuE3e => sF267)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF268])],[function_definition])).
% 21.36/3.55 thf(f1594,definition,(
% 21.36/3.55 (sF269 = ((notinemptyset => sF268)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF269])],[function_definition])).
% 21.36/3.55 thf(f1595,plain,(
% 21.36/3.55 (((notinemptyset => sF268)) = sF269)),
% 21.36/3.55 inference(reorient_equations,[],[f1594])).
% 21.36/3.55 thf(f1596,definition,(
% 21.36/3.55 (sF270 = ((emptysetimpfalse => sF269)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF270])],[function_definition])).
% 21.36/3.55 thf(f1597,plain,(
% 21.36/3.55 (((emptysetimpfalse => sF269)) = sF270)),
% 21.36/3.55 inference(reorient_equations,[],[f1596])).
% 21.36/3.55 thf(f1598,definition,(
% 21.36/3.55 (sF271 = ((emptysetE => sF270)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF271])],[function_definition])).
% 21.36/3.55 thf(f1599,definition,(
% 21.36/3.55 (sF272 = ((prop2setE => sF271)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF272])],[function_definition])).
% 21.36/3.55 thf(f1600,definition,(
% 21.36/3.55 (sF273 = ((exuE1 => sF272)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF273])],[function_definition])).
% 21.36/3.55 thf(f1601,plain,(
% 21.36/3.55 (((exuE1 => sF272)) = sF273)),
% 21.36/3.55 inference(reorient_equations,[],[f1600])).
% 21.36/3.55 thf(f1602,definition,(
% 21.36/3.55 (sF274 = ((dsetconstrER => sF273)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF274])],[function_definition])).
% 21.36/3.55 thf(f1603,plain,(
% 21.36/3.55 (((dsetconstrER => sF273)) = sF274)),
% 21.36/3.55 inference(reorient_equations,[],[f1602])).
% 21.36/3.55 thf(f1604,definition,(
% 21.36/3.55 (sF275 = ((dsetconstrEL => sF274)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF275])],[function_definition])).
% 21.36/3.55 thf(f1605,definition,(
% 21.36/3.55 (sF276 = ((dsetconstrI => sF275)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF276])],[function_definition])).
% 21.36/3.55 thf(f1606,plain,(
% 21.36/3.55 (((dsetconstrI => sF275)) = sF276)),
% 21.36/3.55 inference(reorient_equations,[],[f1605])).
% 21.36/3.55 thf(f1607,definition,(
% 21.36/3.55 (sF277 = ((descrp => sF276)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF277])],[function_definition])).
% 21.36/3.55 thf(f1608,definition,(
% 21.36/3.55 (sF278 = ((wellorderingAx => sF277)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF278])],[function_definition])).
% 21.36/3.55 thf(f1609,plain,(
% 21.36/3.55 (((wellorderingAx => sF277)) = sF278)),
% 21.36/3.55 inference(reorient_equations,[],[f1608])).
% 21.36/3.55 thf(f1610,definition,(
% 21.36/3.55 (sF279 = ((foundationAx => sF278)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF279])],[function_definition])).
% 21.36/3.55 thf(f1611,definition,(
% 21.36/3.55 (sF280 = ((replAx => sF279)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF280])],[function_definition])).
% 21.36/3.55 thf(f1612,definition,(
% 21.36/3.55 (sF281 = ((omegaIndAx => sF280)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF281])],[function_definition])).
% 21.36/3.55 thf(f1613,plain,(
% 21.36/3.55 (((omegaIndAx => sF280)) = sF281)),
% 21.36/3.55 inference(reorient_equations,[],[f1612])).
% 21.36/3.55 thf(f1614,definition,(
% 21.36/3.55 (sF282 = ((omegaSAx => sF281)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF282])],[function_definition])).
% 21.36/3.55 thf(f1615,definition,(
% 21.36/3.55 (sF283 = ((omega0Ax => sF282)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF283])],[function_definition])).
% 21.36/3.55 thf(f1616,plain,(
% 21.36/3.55 (((omega0Ax => sF282)) = sF283)),
% 21.36/3.55 inference(reorient_equations,[],[f1615])).
% 21.36/3.55 thf(f1617,definition,(
% 21.36/3.55 (sF284 = ((setunionAx => sF283)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF284])],[function_definition])).
% 21.36/3.55 thf(f1618,definition,(
% 21.36/3.55 (sF285 = ((powersetAx => sF284)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF285])],[function_definition])).
% 21.36/3.55 thf(f1619,definition,(
% 21.36/3.55 (sF286 = ((setadjoinAx => sF285)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF286])],[function_definition])).
% 21.36/3.55 thf(f1620,definition,(
% 21.36/3.55 (sF287 = ((emptysetAx => sF286)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF287])],[function_definition])).
% 21.36/3.55 thf(f1621,plain,(
% 21.36/3.55 (((emptysetAx => sF286)) = sF287)),
% 21.36/3.55 inference(reorient_equations,[],[f1620])).
% 21.36/3.55 thf(f1622,definition,(
% 21.36/3.55 (sF288 = ((setextAx => sF287)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF288])],[function_definition])).
% 21.36/3.55 thf(f1623,definition,(
% 21.36/3.55 (sF289 = ((~ sF288)))),
% 21.36/3.55 introduced(definition,[new_symbols(definition,[sF289])],[function_definition])).
% 21.36/3.55 thf(f1624,plain,(
% 21.36/3.55 (((~ sF288)) = sF289)),
% 21.36/3.55 inference(reorient_equations,[],[f1623])).
% 21.36/3.55 thf(f1625,plain,(
% 21.36/3.55 ($true = sF289)),
% 21.36/3.55 inference(definition_folding,[],[f1190,f1624,f1622,f1621,f1619,f1618,f1617,f1616,f1614,f1613,f1611,f1610,f1609,f1607,f1606,f1604,f1603,f1601,f1599,f1598,f1597,f1595,f1593,f1592,f1591,f1589,f1587,f1586,f1584,f1582,f1580,f1579,f1578,f1577,f1576,f1575,f1574,f1573,f1571,f1570,f1569,f1567,f1566,f1564,f1563,f1561,f1560,f1559,f1557,f1555,f1553,f1551,f1550,f1548,f1546,f1544,f1542,f1541,f1540,f1539,f1538,f1537,f1535,f1534,f1533,f1532,f1530,f1528,f1526,f1525,f1523,f1521,f1519,f1518,f1516,f1514,f1513,f1511,f1510,f1508,f1507,f1505,f1503,f1501,f1500,f1498,f1496,f1495,f1493,f1491,f1490,f1488,f1486,f1484,f1482,f1480,f1479,f1477,f1475,f1474,f1472,f1471,f1470,f1468,f1466,f1464,f1462,f1461,f1460,f1458,f1457,f1456,f1455,f1454,f1453,f1452,f1450,f1448,f1446,f1444,f1442,f1440,f1438,f1437,f1435,f1433,f1432,f1431,f1430,f1429,f1428,f1426,f1424,f1423,f1422,f1421,f1420,f1419,f1417,f1415,f1414,f1413,f1411,f1410,f1408,f1407,f1406,f1405,f1404,f1403,f1402,f1401,f1400,f1399,f1397,f1395,f1394,f1393,f1392,f1391,f1389,f1387,f1385,f1383,f1381,f1379,f1377,f1376,f1374,f1372,f1371,f1370,f1368,f1367,f1366,f1365,f1363,f1362,f1360,f1358,f1357,f1356,f1355,f1354,f1352,f1350,f1348,f1347,f1346,f1345,f1343,f1341,f1340,f1338,f1337,f1335,f1334,f1333,f1332,f1330,f1328,f1327,f1326,f1324,f1323,f1322,f1321,f1319,f1317,f1316,f1314,f1313,f1312,f1310,f1309,f1307,f1306,f1305,f1304,f1302,f1300,f1298,f1297,f1295,f1293,f1292,f1291,f1290,f1288,f1286,f1284,f1283,f1281,f1280,f1278,f1276,f1275,f1273,f1272,f1270,f1269,f1268,f1266,f1265,f1263,f1261,f1260,f1259,f1257,f1255,f1254,f1253,f1252,f1251,f1250,f1249,f1248,f1246,f1244,f1242,f1240,f1238,f1236,f1235,f1234,f1232,f1230,f1228,f1226,f1224,f1222,f1221,f1220,f1218,f1216,f1214,f1212,f1210,f1208,f1207,f1206,f1205,f1203,f1202,f1201,f1199,f1198,f1197,f1196,f1194,f1192])).
% 21.36/3.55 thf(f1626,plain,(
% 21.36/3.55 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1167])).
% 21.36/3.55 thf(f1627,plain,(
% 21.36/3.55 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1626])).
% 21.36/3.55 thf(f1628,plain,(
% 21.36/3.55 (emptyset__Cong = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f1115])).
% 21.36/3.55 thf(f1629,plain,(
% 21.36/3.55 (dpsetconstrEL1 = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y3))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1113])).
% 21.36/3.55 thf(f1631,plain,(
% 21.36/3.55 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1191])).
% 21.36/3.55 thf(f1633,plain,(
% 21.36/3.55 (dsetconstrER = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1152])).
% 21.36/3.55 thf(f1634,plain,(
% 21.36/3.55 (eta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => ((lam @ Y2 @ Y0 @ (ap @ Y2 @ Y0 @ Y1)) = Y1))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1154])).
% 21.36/3.55 thf(f1635,plain,(
% 21.36/3.55 (omega__Cong = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f956])).
% 21.36/3.55 thf(f1637,plain,(
% 21.36/3.55 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1178])).
% 21.36/3.55 thf(f1638,plain,(
% 21.36/3.55 (ex1E2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f907])).
% 21.36/3.55 thf(f1639,plain,(
% 21.36/3.55 (breln1SetBreln1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (breln1Set @ Y1)) => (subset @ Y0 @ (cartprod @ Y1 @ Y1)))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1188])).
% 21.36/3.55 thf(f1640,plain,(
% 21.36/3.55 (beta2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) = (ap @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ Y2) @ Y3))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1134])).
% 21.36/3.55 thf(f1641,plain,(
% 21.36/3.55 (beta1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3) = (Y2 @ Y3))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1071])).
% 21.36/3.55 thf(f1642,plain,(
% 21.36/3.55 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f905])).
% 21.36/3.55 thf(f1647,plain,(
% 21.36/3.55 (descrp = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0)))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1183])).
% 21.36/3.55 thf(f1648,plain,(
% 21.36/3.55 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1180])).
% 21.36/3.55 thf(f1651,plain,(
% 21.36/3.55 (lamp = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (func @ Y2 @ Y0 @ (lam @ Y2 @ Y0 @ Y1)))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1012])).
% 21.36/3.55 thf(f1652,plain,(
% 21.36/3.55 (emptyE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f947])).
% 21.36/3.55 thf(f1653,plain,(
% 21.36/3.55 (emptyE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset)))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1652])).
% 21.36/3.55 thf(f1654,plain,(
% 21.36/3.55 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1175])).
% 21.36/3.55 thf(f1656,plain,(
% 21.36/3.55 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => ((lam @ Y0 @ Y1 @ Y2) = (lam @ Y0 @ Y1 @ Y2)))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1076])).
% 21.36/3.55 thf(f1657,plain,(
% 21.36/3.55 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => $true)))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1656])).
% 21.36/3.55 thf(f1658,plain,(
% 21.36/3.55 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ($true)))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1657])).
% 21.36/3.55 thf(f1659,plain,(
% 21.36/3.55 (brelnall2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y1 @ Y0)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4))))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1169])).
% 21.36/3.55 thf(f1660,plain,(
% 21.36/3.55 (breln1all2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1171])).
% 21.36/3.55 thf(f1661,plain,(
% 21.36/3.55 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1187])).
% 21.36/3.55 thf(f1662,plain,(
% 21.36/3.55 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1661])).
% 21.36/3.55 thf(f1663,plain,(
% 21.36/3.55 (nonemptyI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1)))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1181])).
% 21.36/3.55 thf(f1665,plain,(
% 21.36/3.55 (dpsetconstrEL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ Y1 @ Y3 @ Y4)) => (in @ Y2 @ Y3))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1007])).
% 21.36/3.55 thf(f1667,plain,(
% 21.36/3.55 (sepInPowerset = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f891])).
% 21.36/3.55 thf(f1669,plain,(
% 21.36/3.55 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => $true))))))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1030])).
% 21.36/3.55 thf(f1670,plain,(
% 21.36/3.55 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1669])).
% 21.36/3.55 thf(f1673,plain,(
% 21.36/3.55 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1182])).
% 21.36/3.55 thf(f1674,plain,(
% 21.36/3.55 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1673])).
% 21.36/3.55 thf(f1675,plain,(
% 21.36/3.55 (lamProp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (func @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (Y2 @ Y3))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f909])).
% 21.36/3.55 thf(f1676,plain,(
% 21.36/3.55 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0)))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1170])).
% 21.36/3.55 thf(f1677,plain,(
% 21.36/3.55 (sF0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1192])).
% 21.36/3.55 thf(f1678,plain,(
% 21.36/3.55 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1168])).
% 21.36/3.55 thf(f1679,plain,(
% 21.36/3.55 (ex1E1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1075])).
% 21.36/3.55 thf(f1680,plain,(
% 21.36/3.55 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0)))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f983])).
% 21.36/3.55 thf(f1681,plain,(
% 21.36/3.55 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => $true))))))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f940])).
% 21.36/3.55 thf(f1682,plain,(
% 21.36/3.55 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1681])).
% 21.36/3.55 thf(f1683,plain,(
% 21.36/3.55 (emptysetsubset = ((!! @ $i @ (subset @ emptyset))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f999])).
% 21.36/3.55 thf(f1684,plain,(
% 21.36/3.55 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f992])).
% 21.36/3.55 thf(f1685,plain,(
% 21.36/3.55 (dpsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ Y1)))))))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f925])).
% 21.36/3.55 thf(f1686,plain,(
% 21.36/3.55 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1172])).
% 21.36/3.55 thf(f1689,plain,(
% 21.36/3.55 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1026])).
% 21.36/3.55 thf(f1690,plain,(
% 21.36/3.55 (setbeta = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1051])).
% 21.36/3.55 thf(f1691,plain,(
% 21.36/3.55 (ex1I2 = ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ Y1)))))))))),
% 21.36/3.55 inference(beta-eta_normalization,[],[f1112])).
% 21.36/3.55 thf(f1692,plain,(
% 21.36/3.55 (ap2apEq1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ Y1 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => $true))))))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f896])).
% 21.36/3.55 thf(f1693,plain,(
% 21.36/3.55 (ap2apEq1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ Y1 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 21.36/3.55 inference(boolean_simplification,[],[f1692])).
% 21.36/3.55 thf(f1694,plain,(
% 21.36/3.55 ($true = ((~ sF288)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1624,f1625])).
% 21.36/3.55 thf(f1695,plain,(
% 21.36/3.55 ($false = sF288)),
% 21.36/3.55 inference(not_proxy_clausification,[],[f1694])).
% 21.36/3.55 thf(f1700,plain,(
% 21.36/3.55 ($false = ((setextAx => sF287)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1622,f1695])).
% 21.36/3.55 thf(f1704,plain,(
% 21.36/3.55 ($false = sF287)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f1700])).
% 21.36/3.55 thf(f1714,plain,(
% 21.36/3.55 ($false = ((emptysetAx => sF286)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1621,f1704])).
% 21.36/3.55 thf(f1721,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => sF286)))),
% 21.36/3.55 inference(forward_demodulation,[],[f1714,f1132])).
% 21.36/3.55 thf(f1722,plain,(
% 21.36/3.55 ($false = sF286)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f1721])).
% 21.36/3.55 thf(f1723,plain,(
% 21.36/3.55 ($true = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f1721])).
% 21.36/3.55 thf(f1732,plain,(
% 21.36/3.55 (notinemptyset = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f1063,f1723])).
% 21.36/3.55 thf(f1733,plain,(
% 21.36/3.55 (emptysetimpfalse = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f1642,f1723])).
% 21.36/3.55 thf(f1736,plain,(
% 21.36/3.55 ($false = ((setadjoinAx => sF285)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1619,f1722])).
% 21.36/3.55 thf(f1739,plain,(
% 21.36/3.55 ((($true => sF268)) = sF269)),
% 21.36/3.55 inference(backward_demodulation,[],[f1595,f1732])).
% 21.36/3.55 thf(f1740,plain,(
% 21.36/3.55 (sF268 = sF269)),
% 21.36/3.55 inference(boolean_simplification,[],[f1739])).
% 21.36/3.55 thf(f1741,plain,(
% 21.36/3.55 (sF270 = (($true => sF269)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1597,f1733])).
% 21.36/3.55 thf(f1742,plain,(
% 21.36/3.55 (sF270 = sF269)),
% 21.36/3.55 inference(boolean_simplification,[],[f1741])).
% 21.36/3.55 thf(f1743,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y2) | (Y1 = Y0)) = (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => sF285)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f1736,f873])).
% 21.36/3.55 thf(f1744,plain,(
% 21.36/3.55 (sF270 = sF268)),
% 21.36/3.55 inference(backward_demodulation,[],[f1740,f1742])).
% 21.36/3.55 thf(f1745,plain,(
% 21.36/3.55 (sF270 = ((exuE3e => sF267)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1593,f1744])).
% 21.36/3.55 thf(f1746,plain,(
% 21.36/3.55 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => sF267)) = sF270)),
% 21.36/3.55 inference(forward_demodulation,[],[f1745,f1637])).
% 21.36/3.55 thf(f1747,plain,(
% 21.36/3.55 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => (setext => sF266))) = sF270)),
% 21.36/3.55 inference(forward_demodulation,[],[f1746,f1592])).
% 21.36/3.55 thf(f1773,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y2) | (Y1 = Y0)) = (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => $true))) | ($false = sF285)),
% 21.36/3.55 inference(superposition,[],[f1743,f1165])).
% 21.36/3.55 thf(f1776,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF285)),
% 21.36/3.55 inference(boolean_simplification,[],[f1773])).
% 21.36/3.55 thf(f1777,plain,(
% 21.36/3.55 ($false = sF285)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f1776])).
% 21.36/3.55 thf(f1781,plain,(
% 21.36/3.55 ($false = ((powersetAx => sF284)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1618,f1777])).
% 21.36/3.55 thf(f1786,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => sF284)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f1781,f1085])).
% 21.36/3.55 thf(f1791,plain,(
% 21.36/3.55 (sF284 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f1786,f1165])).
% 21.36/3.55 thf(f1794,plain,(
% 21.36/3.55 (sF284 = $false) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f1791])).
% 21.36/3.55 thf(f1795,plain,(
% 21.36/3.55 (sF284 = $false)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f1794])).
% 21.36/3.55 thf(f1799,plain,(
% 21.36/3.55 ($false = ((setunionAx => sF283)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1617,f1795])).
% 21.36/3.55 thf(f1808,plain,(
% 21.36/3.55 ($false = sF283)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f1799])).
% 21.36/3.55 thf(f1818,plain,(
% 21.36/3.55 ($false = ((omega0Ax => sF282)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1616,f1808])).
% 21.36/3.55 thf(f1825,plain,(
% 21.36/3.55 ($false = (((in @ emptyset @ omega) => sF282)))),
% 21.36/3.55 inference(forward_demodulation,[],[f1818,f915])).
% 21.36/3.55 thf(f1828,plain,(
% 21.36/3.55 ($false = sF282)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f1825])).
% 21.36/3.55 thf(f1838,plain,(
% 21.36/3.55 ($false = ((omegaSAx => sF281)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1614,f1828])).
% 21.36/3.55 thf(f1843,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => sF281)))),
% 21.36/3.55 inference(forward_demodulation,[],[f1838,f939])).
% 21.36/3.55 thf(f1848,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => $true))) | ($false = sF281)),
% 21.36/3.55 inference(superposition,[],[f1843,f1165])).
% 21.36/3.55 thf(f1851,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF281)),
% 21.36/3.55 inference(boolean_simplification,[],[f1848])).
% 21.36/3.55 thf(f1852,plain,(
% 21.36/3.55 ($false = sF281)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f1851])).
% 21.36/3.55 thf(f1856,plain,(
% 21.36/3.55 ($false = ((omegaIndAx => sF280)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1613,f1852])).
% 21.36/3.55 thf(f1861,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => sF280)))),
% 21.36/3.55 inference(forward_demodulation,[],[f1856,f1077])).
% 21.36/3.55 thf(f1879,plain,(
% 21.36/3.55 ($false = sF266) | (sF270 = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => (setext => $true))))),
% 21.36/3.55 inference(superposition,[],[f1747,f1165])).
% 21.36/3.55 thf(f1887,plain,(
% 21.36/3.55 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => $true)) = sF270) | ($false = sF266)),
% 21.36/3.55 inference(boolean_simplification,[],[f1879])).
% 21.36/3.55 thf(f1888,plain,(
% 21.36/3.55 ($false = sF266) | ($true = sF270)),
% 21.36/3.55 inference(boolean_simplification,[],[f1887])).
% 21.36/3.55 thf(f1896,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => $true))) | ($false = sF280)),
% 21.36/3.55 inference(superposition,[],[f1861,f1165])).
% 21.36/3.55 thf(f1900,plain,(
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% 21.36/3.55 inference(boolean_simplification,[],[f1896])).
% 21.36/3.55 thf(f1901,plain,(
% 21.36/3.55 ($false = sF280)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f1900])).
% 21.36/3.55 thf(f1904,plain,(
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% 21.36/3.55 inference(backward_demodulation,[],[f1611,f1901])).
% 21.36/3.55 thf(f1913,plain,(
% 21.36/3.55 (sF279 = $false) | ($false = ((replAx => $true)))),
% 21.36/3.55 inference(superposition,[],[f1904,f1165])).
% 21.36/3.55 thf(f1917,plain,(
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% 21.36/3.55 inference(boolean_simplification,[],[f1913])).
% 21.36/3.55 thf(f1918,plain,(
% 21.36/3.55 (sF279 = $false)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f1917])).
% 21.36/3.55 thf(f1921,plain,(
% 21.36/3.55 ($false = ((foundationAx => sF278)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1610,f1918])).
% 21.36/3.55 thf(f1928,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => sF278)))),
% 21.36/3.55 inference(forward_demodulation,[],[f1921,f899])).
% 21.36/3.55 thf(f1931,plain,(
% 21.36/3.55 (sF278 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f1928,f1165])).
% 21.36/3.55 thf(f1936,plain,(
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% 21.36/3.55 inference(boolean_simplification,[],[f1931])).
% 21.36/3.55 thf(f1937,plain,(
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% 21.36/3.55 inference(trivial_inequality_removal,[],[f1936])).
% 21.36/3.55 thf(f1945,plain,(
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% 21.36/3.55 inference(backward_demodulation,[],[f1609,f1937])).
% 21.36/3.55 thf(f1948,plain,(
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% 21.36/3.55 inference(superposition,[],[f1945,f1165])).
% 21.36/3.55 thf(f1953,plain,(
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% 21.36/3.55 inference(boolean_simplification,[],[f1948])).
% 21.36/3.55 thf(f1954,plain,(
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% 21.36/3.55 inference(trivial_inequality_removal,[],[f1953])).
% 21.36/3.55 thf(f1962,plain,(
% 21.36/3.55 ($false = ((descrp => sF276)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1607,f1954])).
% 21.36/3.55 thf(f1963,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => sF276)))),
% 21.36/3.55 inference(forward_demodulation,[],[f1962,f1647])).
% 21.36/3.55 thf(f1964,plain,(
% 21.36/3.55 ($false = sF276)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f1963])).
% 21.36/3.55 thf(f1974,plain,(
% 21.36/3.55 ($false = ((dsetconstrI => sF275)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1606,f1964])).
% 21.36/3.55 thf(f1979,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ Y1)))))))))) => sF275)))),
% 21.36/3.55 inference(forward_demodulation,[],[f1974,f1684])).
% 21.36/3.55 thf(f1984,plain,(
% 21.36/3.55 ($false = sF275) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ Y1)))))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f1979,f1165])).
% 21.36/3.55 thf(f1988,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF275)),
% 21.36/3.55 inference(boolean_simplification,[],[f1984])).
% 21.36/3.55 thf(f1989,plain,(
% 21.36/3.55 ($false = sF275)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f1988])).
% 21.36/3.55 thf(f1992,plain,(
% 21.36/3.55 ($false = ((dsetconstrEL => sF274)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1604,f1989])).
% 21.36/3.55 thf(f1997,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => sF274)))),
% 21.36/3.55 inference(forward_demodulation,[],[f1992,f1689])).
% 21.36/3.55 thf(f2000,plain,(
% 21.36/3.55 ($false = sF274) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f1997,f1165])).
% 21.36/3.55 thf(f2003,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF274)),
% 21.36/3.55 inference(boolean_simplification,[],[f2000])).
% 21.36/3.55 thf(f2004,plain,(
% 21.36/3.55 ($false = sF274)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2003])).
% 21.36/3.55 thf(f2008,plain,(
% 21.36/3.55 ($false = ((dsetconstrER => sF273)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1603,f2004])).
% 21.36/3.55 thf(f2015,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => sF273)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2008,f1633])).
% 21.36/3.55 thf(f2018,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => $true))) | ($false = sF273)),
% 21.36/3.55 inference(superposition,[],[f2015,f1165])).
% 21.36/3.55 thf(f2021,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF273)),
% 21.36/3.55 inference(boolean_simplification,[],[f2018])).
% 21.36/3.55 thf(f2022,plain,(
% 21.36/3.55 ($false = sF273)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2021])).
% 21.36/3.55 thf(f2026,plain,(
% 21.36/3.55 (((exuE1 => sF272)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1601,f2022])).
% 21.36/3.55 thf(f2033,plain,(
% 21.36/3.55 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))) => sF272)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f2026,f1674])).
% 21.36/3.55 thf(f2034,plain,(
% 21.36/3.55 ($false = sF272)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2033])).
% 21.36/3.55 thf(f2035,plain,(
% 21.36/3.55 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))))),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2033])).
% 21.36/3.55 thf(f2046,plain,(
% 21.36/3.55 (exuI1 = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f1627,f2035])).
% 21.36/3.55 thf(f2049,plain,(
% 21.36/3.55 ($false = ((prop2setE => sF271)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1599,f2034])).
% 21.36/3.55 thf(f2050,plain,(
% 21.36/3.55 ((($true => sF227)) = sF228)),
% 21.36/3.55 inference(backward_demodulation,[],[f1535,f2046])).
% 21.36/3.55 thf(f2051,plain,(
% 21.36/3.55 (sF227 = sF228)),
% 21.36/3.55 inference(boolean_simplification,[],[f2050])).
% 21.36/3.55 thf(f2052,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => sF271)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2049,f1097])).
% 21.36/3.55 thf(f2053,plain,(
% 21.36/3.55 (sF228 = ((exuI3 => sF226)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1534,f2051])).
% 21.36/3.55 thf(f2054,plain,(
% 21.36/3.55 (sF228 = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => sF226)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2053,f1654])).
% 21.36/3.55 thf(f2063,plain,(
% 21.36/3.55 ($false = sF271) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f2052,f1165])).
% 21.36/3.55 thf(f2066,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF271)),
% 21.36/3.55 inference(boolean_simplification,[],[f2063])).
% 21.36/3.55 thf(f2067,plain,(
% 21.36/3.55 ($false = sF271)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2066])).
% 21.36/3.55 thf(f2071,plain,(
% 21.36/3.55 ($false = ((emptysetE => sF270)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1598,f2067])).
% 21.36/3.55 thf(f2078,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => sF270)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2071,f1023])).
% 21.36/3.55 thf(f2081,plain,(
% 21.36/3.55 ($false = sF270) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f2078,f1165])).
% 21.36/3.55 thf(f2084,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF270)),
% 21.36/3.55 inference(boolean_simplification,[],[f2081])).
% 21.36/3.55 thf(f2085,plain,(
% 21.36/3.55 ($false = sF270)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2084])).
% 21.36/3.55 thf(f2097,plain,(
% 21.36/3.55 ($false = sF266) | ($false = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f1888,f2085])).
% 21.36/3.55 thf(f2098,plain,(
% 21.36/3.55 ($false = sF266)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2097])).
% 21.36/3.55 thf(f2102,plain,(
% 21.36/3.55 ($false = ((emptyI => sF265)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1591,f2098])).
% 21.36/3.55 thf(f2113,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => sF265)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f2102,f1015])).
% 21.36/3.55 thf(f2125,plain,(
% 21.36/3.55 ($false = sF265)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2113])).
% 21.36/3.55 thf(f2126,plain,(
% 21.36/3.55 ($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2113])).
% 21.36/3.55 thf(f2136,plain,(
% 21.36/3.55 (noeltsimpempty = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f914,f2126])).
% 21.36/3.55 thf(f2138,plain,(
% 21.36/3.55 (((noeltsimpempty => sF264)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1589,f2125])).
% 21.36/3.55 thf(f2139,plain,(
% 21.36/3.55 ($false = (($true => sF264)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2138,f2136])).
% 21.36/3.55 thf(f2140,plain,(
% 21.36/3.55 ($false = sF264)),
% 21.36/3.55 inference(boolean_simplification,[],[f2139])).
% 21.36/3.55 thf(f2141,plain,(
% 21.36/3.55 ($false = ((setbeta => sF263)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1587,f2140])).
% 21.36/3.55 thf(f2142,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => sF263)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2141,f1690])).
% 21.36/3.55 thf(f2164,plain,(
% 21.36/3.55 ($false = sF263)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2142])).
% 21.36/3.55 thf(f2176,plain,(
% 21.36/3.55 ($false = ((nonemptyE1 => sF262)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1586,f2164])).
% 21.36/3.55 thf(f2179,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => sF262)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2176,f1648])).
% 21.36/3.55 thf(f2181,plain,(
% 21.36/3.55 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2179])).
% 21.36/3.55 thf(f2182,plain,(
% 21.36/3.55 ($false = sF262) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f2179,f1165])).
% 21.36/3.55 thf(f2186,plain,(
% 21.36/3.55 ($false = sF262) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f2182])).
% 21.36/3.55 thf(f2187,plain,(
% 21.36/3.55 ($false = sF262)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2186])).
% 21.36/3.55 thf(f2190,plain,(
% 21.36/3.55 ($false = ((nonemptyI => sF261)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1584,f2187])).
% 21.36/3.55 thf(f2192,plain,(
% 21.36/3.55 (nonemptyImpWitness = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f1662,f2181])).
% 21.36/3.55 thf(f2196,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => sF261)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2190,f1663])).
% 21.36/3.55 thf(f2197,plain,(
% 21.36/3.55 (sF246 = (($true => sF245)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1563,f2192])).
% 21.36/3.55 thf(f2198,plain,(
% 21.36/3.55 (sF246 = sF245)),
% 21.36/3.55 inference(boolean_simplification,[],[f2197])).
% 21.36/3.55 thf(f2199,plain,(
% 21.36/3.55 (((exuE2 => sF245)) = sF247)),
% 21.36/3.55 inference(backward_demodulation,[],[f1564,f2198])).
% 21.36/3.55 thf(f2208,plain,(
% 21.36/3.55 (sF247 = ((exuE2 => $true))) | ($false = sF245)),
% 21.36/3.55 inference(superposition,[],[f2199,f1165])).
% 21.36/3.55 thf(f2211,plain,(
% 21.36/3.55 ($false = sF245) | ($true = sF247)),
% 21.36/3.55 inference(boolean_simplification,[],[f2208])).
% 21.36/3.55 thf(f2216,plain,(
% 21.36/3.55 ($false = sF261)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2196])).
% 21.36/3.55 thf(f2226,plain,(
% 21.36/3.55 ($false = ((nonemptyI1 => sF260)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1582,f2216])).
% 21.36/3.55 thf(f2231,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => sF260)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2226,f1676])).
% 21.36/3.55 thf(f2236,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => $true)) = $false) | (sF260 = $false)),
% 21.36/3.55 inference(superposition,[],[f2231,f1165])).
% 21.36/3.55 thf(f2241,plain,(
% 21.36/3.55 ($false = $true) | (sF260 = $false)),
% 21.36/3.55 inference(boolean_simplification,[],[f2236])).
% 21.36/3.55 thf(f2242,plain,(
% 21.36/3.55 (sF260 = $false)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2241])).
% 21.36/3.55 thf(f2250,plain,(
% 21.36/3.55 ($false = ((setadjoinIL => sF259)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1580,f2242])).
% 21.36/3.55 thf(f2251,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => sF259)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2250,f1127])).
% 21.36/3.55 thf(f2252,plain,(
% 21.36/3.55 ($false = sF259)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2251])).
% 21.36/3.55 thf(f2262,plain,(
% 21.36/3.55 ($false = ((emptyinunitempty => sF258)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1579,f2252])).
% 21.36/3.55 thf(f2267,plain,(
% 21.36/3.55 ((((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => sF258)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f2262,f1025])).
% 21.36/3.55 thf(f2270,plain,(
% 21.36/3.55 (sF258 = $false)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2267])).
% 21.36/3.55 thf(f2280,plain,(
% 21.36/3.55 ($false = ((setadjoinIR => sF257)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1578,f2270])).
% 21.36/3.55 thf(f2287,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => sF257)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2280,f1044])).
% 21.36/3.55 thf(f2288,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => (setadjoinE => sF256))))),
% 21.36/3.55 inference(forward_demodulation,[],[f2287,f1577])).
% 21.36/3.55 thf(f2291,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => (setadjoinE => $true)))) | (sF256 = $false)),
% 21.36/3.55 inference(superposition,[],[f2288,f1165])).
% 21.36/3.55 thf(f2299,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => $true))) | (sF256 = $false)),
% 21.36/3.55 inference(boolean_simplification,[],[f2291])).
% 21.36/3.55 thf(f2300,plain,(
% 21.36/3.55 (sF256 = $false) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f2299])).
% 21.36/3.55 thf(f2301,plain,(
% 21.36/3.55 (sF256 = $false)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2300])).
% 21.36/3.55 thf(f2311,plain,(
% 21.36/3.55 ($false = ((setadjoinOr => sF255)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1576,f2301])).
% 21.36/3.55 thf(f2323,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0))))))))) => sF255)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2311,f887])).
% 21.36/3.55 thf(f2328,plain,(
% 21.36/3.55 ($false = sF255)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2323])).
% 21.36/3.55 thf(f2338,plain,(
% 21.36/3.55 ($false = ((setoftrueEq => sF254)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1575,f2328])).
% 21.36/3.55 thf(f2343,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => sF254)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2338,f948])).
% 21.36/3.55 thf(f2348,plain,(
% 21.36/3.55 (sF254 = $false)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2343])).
% 21.36/3.55 thf(f2358,plain,(
% 21.36/3.55 ($false = ((powersetI => sF253)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1574,f2348])).
% 21.36/3.55 thf(f2363,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => sF253)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2358,f1034])).
% 21.36/3.55 thf(f2368,plain,(
% 21.36/3.55 ($false = sF253)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2363])).
% 21.36/3.55 thf(f2378,plain,(
% 21.36/3.55 ($false = ((emptyinPowerset => sF252)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1573,f2368])).
% 21.36/3.55 thf(f2383,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => sF252)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f2378,f871])).
% 21.36/3.55 thf(f2384,plain,(
% 21.36/3.55 ($false = sF252)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2383])).
% 21.36/3.55 thf(f2385,plain,(
% 21.36/3.55 (((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))) = $true)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2383])).
% 21.36/3.55 thf(f2395,plain,(
% 21.36/3.55 (emptyInPowerset = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f941,f2385])).
% 21.36/3.55 thf(f2401,plain,(
% 21.36/3.55 ($false = ((emptyInPowerset => sF251)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1571,f2384])).
% 21.36/3.55 thf(f2402,plain,(
% 21.36/3.55 ($false = (($true => sF251)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2401,f2395])).
% 21.36/3.55 thf(f2403,plain,(
% 21.36/3.55 ($false = sF251)),
% 21.36/3.55 inference(boolean_simplification,[],[f2402])).
% 21.36/3.55 thf(f2404,plain,(
% 21.36/3.55 ($false = ((powersetE => sF250)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1570,f2403])).
% 21.36/3.55 thf(f2405,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => sF250)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2404,f886])).
% 21.36/3.55 thf(f2410,plain,(
% 21.36/3.55 ($false = sF250) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f2405,f1165])).
% 21.36/3.55 thf(f2413,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF250)),
% 21.36/3.55 inference(boolean_simplification,[],[f2410])).
% 21.36/3.55 thf(f2414,plain,(
% 21.36/3.55 ($false = sF250)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2413])).
% 21.36/3.55 thf(f2418,plain,(
% 21.36/3.55 ($false = ((setunionI => sF249)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1569,f2414])).
% 21.36/3.55 thf(f2425,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => (in @ Y1 @ (setunion @ Y0)))))))))) => sF249)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2418,f928])).
% 21.36/3.55 thf(f2428,plain,(
% 21.36/3.55 ($false = sF249)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2425])).
% 21.36/3.55 thf(f2438,plain,(
% 21.36/3.55 ($false = ((setunionE => sF248)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1567,f2428])).
% 21.36/3.55 thf(f2443,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => sF248)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2438,f1087])).
% 21.36/3.55 thf(f2444,plain,(
% 21.36/3.55 ($false = sF248)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2443])).
% 21.36/3.55 thf(f2454,plain,(
% 21.36/3.55 (((subPowSU => sF247)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1566,f2444])).
% 21.36/3.55 thf(f2461,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => sF247)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f2454,f1120])).
% 21.36/3.55 thf(f2466,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => $true)) = $false) | ($false = sF247)),
% 21.36/3.55 inference(superposition,[],[f2461,f1165])).
% 21.36/3.55 thf(f2470,plain,(
% 21.36/3.55 ($false = sF247) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f2466])).
% 21.36/3.55 thf(f2471,plain,(
% 21.36/3.55 ($false = sF247)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2470])).
% 21.36/3.55 thf(f2475,plain,(
% 21.36/3.55 ($false = sF245) | ($false = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f2211,f2471])).
% 21.36/3.55 thf(f2477,plain,(
% 21.36/3.55 ($false = sF245)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2475])).
% 21.36/3.55 thf(f2484,plain,(
% 21.36/3.55 ($false = ((uniqinunit => sF244)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1561,f2477])).
% 21.36/3.55 thf(f2488,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => sF244)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2484,f1050])).
% 21.36/3.55 thf(f2501,plain,(
% 21.36/3.55 ($false = sF244) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f2488,f1165])).
% 21.36/3.55 thf(f2504,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF244)),
% 21.36/3.55 inference(boolean_simplification,[],[f2501])).
% 21.36/3.55 thf(f2505,plain,(
% 21.36/3.55 ($false = sF244)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2504])).
% 21.36/3.55 thf(f2511,plain,(
% 21.36/3.55 ($false = ((notinsingleton => sF243)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1560,f2505])).
% 21.36/3.55 thf(f2514,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => sF243)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2511,f1082])).
% 21.36/3.55 thf(f2517,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => $true))) | ($false = sF243)),
% 21.36/3.55 inference(superposition,[],[f2514,f1165])).
% 21.36/3.55 thf(f2522,plain,(
% 21.36/3.55 ($false = sF243) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f2517])).
% 21.36/3.55 thf(f2523,plain,(
% 21.36/3.55 ($false = sF243)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2522])).
% 21.36/3.55 thf(f2531,plain,(
% 21.36/3.55 ($false = ((eqinunit => sF242)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1559,f2523])).
% 21.36/3.55 thf(f2532,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => sF242)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2531,f1049])).
% 21.36/3.55 thf(f2535,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true)) = $false) | ($false = sF242)),
% 21.36/3.55 inference(superposition,[],[f2532,f1165])).
% 21.36/3.55 thf(f2540,plain,(
% 21.36/3.55 ($false = sF242) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f2535])).
% 21.36/3.55 thf(f2541,plain,(
% 21.36/3.55 ($false = sF242)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2540])).
% 21.36/3.55 thf(f2543,plain,(
% 21.36/3.55 (((singletonsswitch => sF241)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1557,f2541])).
% 21.36/3.55 thf(f2548,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => sF241)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2543,f1074])).
% 21.36/3.55 thf(f2551,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true))) | ($false = sF241)),
% 21.36/3.55 inference(superposition,[],[f2548,f1165])).
% 21.36/3.55 thf(f2554,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF241)),
% 21.36/3.55 inference(boolean_simplification,[],[f2551])).
% 21.36/3.55 thf(f2555,plain,(
% 21.36/3.55 ($false = sF241)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2554])).
% 21.36/3.55 thf(f2559,plain,(
% 21.36/3.55 ($false = ((upairsetE => sF240)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1555,f2555])).
% 21.36/3.55 thf(f2566,plain,(
% 21.36/3.55 ($false = sF240)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2559])).
% 21.36/3.55 thf(f2578,plain,(
% 21.36/3.55 ($false = ((upairsetIL => sF239)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1553,f2566])).
% 21.36/3.55 thf(f2581,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => sF239)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f2578,f1116])).
% 21.36/3.55 thf(f2584,plain,(
% 21.36/3.55 ($false = sF239) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f2581,f1165])).
% 21.36/3.55 thf(f2587,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF239)),
% 21.36/3.55 inference(boolean_simplification,[],[f2584])).
% 21.36/3.55 thf(f2588,plain,(
% 21.36/3.55 ($false = sF239)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2587])).
% 21.36/3.55 thf(f2592,plain,(
% 21.36/3.55 ($false = ((upairsetIR => sF238)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1551,f2588])).
% 21.36/3.55 thf(f2601,plain,(
% 21.36/3.55 ($false = sF238)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2592])).
% 21.36/3.55 thf(f2602,plain,(
% 21.36/3.55 (upairsetIR = $true)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2592])).
% 21.36/3.55 thf(f2611,plain,(
% 21.36/3.55 (((emptyE1 => sF237)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1550,f2601])).
% 21.36/3.55 thf(f2615,plain,(
% 21.36/3.55 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 21.36/3.55 inference(backward_demodulation,[],[f971,f2602])).
% 21.36/3.55 thf(f2618,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset))))))) => sF237)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2611,f1653])).
% 21.36/3.55 thf(f2621,plain,(
% 21.36/3.55 (secondinupair = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f908,f2615])).
% 21.36/3.55 thf(f2622,plain,(
% 21.36/3.55 (upairset2IR = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f1042,f2615])).
% 21.36/3.55 thf(f2623,plain,(
% 21.36/3.55 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset))))))) => (vacuousDall => sF236))) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f2618,f1548])).
% 21.36/3.55 thf(f2624,plain,(
% 21.36/3.55 ((($true => sF188)) = sF189)),
% 21.36/3.55 inference(backward_demodulation,[],[f1471,f2622])).
% 21.36/3.55 thf(f2625,plain,(
% 21.36/3.55 (sF189 = sF188)),
% 21.36/3.55 inference(boolean_simplification,[],[f2624])).
% 21.36/3.55 thf(f2626,plain,(
% 21.36/3.55 (sF156 = (($true => sF155)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1422,f2621])).
% 21.36/3.55 thf(f2627,plain,(
% 21.36/3.55 (sF155 = sF156)),
% 21.36/3.55 inference(boolean_simplification,[],[f2626])).
% 21.36/3.55 thf(f2628,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => sF236))))),
% 21.36/3.55 inference(forward_demodulation,[],[f2623,f890])).
% 21.36/3.55 thf(f2629,plain,(
% 21.36/3.55 (((binunionIL => sF188)) = sF190)),
% 21.36/3.55 inference(backward_demodulation,[],[f1472,f2625])).
% 21.36/3.55 thf(f2630,plain,(
% 21.36/3.55 (((setukpairIL => sF154)) = sF156)),
% 21.36/3.55 inference(backward_demodulation,[],[f1421,f2627])).
% 21.36/3.55 thf(f2631,plain,(
% 21.36/3.55 (((sepSubset => (binunionIL => sF188))) = sF191)),
% 21.36/3.55 inference(backward_demodulation,[],[f1474,f2629])).
% 21.36/3.55 thf(f2632,plain,(
% 21.36/3.55 (sF156 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => sF154)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2630,f1004])).
% 21.36/3.55 thf(f2633,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => (binunionIL => sF188))) = sF191)),
% 21.36/3.55 inference(forward_demodulation,[],[f2631,f1680])).
% 21.36/3.55 thf(f2658,plain,(
% 21.36/3.55 ($false = sF188) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => (binunionIL => $true))) = sF191)),
% 21.36/3.55 inference(superposition,[],[f2633,f1165])).
% 21.36/3.55 thf(f2664,plain,(
% 21.36/3.55 ($false = sF188) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => $true)) = sF191)),
% 21.36/3.55 inference(boolean_simplification,[],[f2658])).
% 21.36/3.55 thf(f2665,plain,(
% 21.36/3.55 ($false = sF188) | ($true = sF191)),
% 21.36/3.55 inference(boolean_simplification,[],[f2664])).
% 21.36/3.55 thf(f2673,plain,(
% 21.36/3.55 ($false = sF154) | (sF156 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f2632,f1165])).
% 21.36/3.55 thf(f2677,plain,(
% 21.36/3.55 ($false = sF154) | ($true = sF156)),
% 21.36/3.55 inference(boolean_simplification,[],[f2673])).
% 21.36/3.55 thf(f2711,plain,(
% 21.36/3.55 ($false = sF236) | ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => $true))))),
% 21.36/3.55 inference(superposition,[],[f2628,f1165])).
% 21.36/3.55 thf(f2719,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset))))))) => $true))) | ($false = sF236)),
% 21.36/3.55 inference(boolean_simplification,[],[f2711])).
% 21.36/3.55 thf(f2720,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF236)),
% 21.36/3.55 inference(boolean_simplification,[],[f2719])).
% 21.36/3.55 thf(f2721,plain,(
% 21.36/3.55 ($false = sF236)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2720])).
% 21.36/3.55 thf(f2732,plain,(
% 21.36/3.55 ($false = ((quantDeMorgan1 => sF235)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1546,f2721])).
% 21.36/3.55 thf(f2742,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0))))))))) => sF235)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2732,f934])).
% 21.36/3.55 thf(f2749,plain,(
% 21.36/3.55 ($false = sF235)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2742])).
% 21.36/3.55 thf(f2759,plain,(
% 21.36/3.55 ($false = ((quantDeMorgan2 => sF234)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1544,f2749])).
% 21.36/3.55 thf(f2766,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => sF234)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2759,f1013])).
% 21.36/3.55 thf(f2767,plain,(
% 21.36/3.55 ($false = sF234)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2766])).
% 21.36/3.55 thf(f2781,plain,(
% 21.36/3.55 ($false = ((quantDeMorgan3 => sF233)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1542,f2767])).
% 21.36/3.55 thf(f2782,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => sF233)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2781,f1068])).
% 21.36/3.55 thf(f2783,plain,(
% 21.36/3.55 ($false = sF233)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2782])).
% 21.36/3.55 thf(f2793,plain,(
% 21.36/3.55 ($false = ((quantDeMorgan4 => sF232)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1541,f2783])).
% 21.36/3.55 thf(f2798,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => sF232)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2793,f1045])).
% 21.36/3.55 thf(f2803,plain,(
% 21.36/3.55 ($false = sF232)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2798])).
% 21.36/3.55 thf(f2813,plain,(
% 21.36/3.55 ($false = ((prop2setI => sF231)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1540,f2803])).
% 21.36/3.55 thf(f2818,plain,(
% 21.36/3.55 ($false = (((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => sF231)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2813,f938])).
% 21.36/3.55 thf(f2827,plain,(
% 21.36/3.55 ($false = (((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => $true))) | ($false = sF231)),
% 21.36/3.55 inference(superposition,[],[f2818,f1165])).
% 21.36/3.55 thf(f2830,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF231)),
% 21.36/3.55 inference(boolean_simplification,[],[f2827])).
% 21.36/3.55 thf(f2831,plain,(
% 21.36/3.55 ($false = sF231)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2830])).
% 21.36/3.55 thf(f2837,plain,(
% 21.36/3.55 ($false = ((prop2set2propI => sF230)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1539,f2831])).
% 21.36/3.55 thf(f2840,plain,(
% 21.36/3.55 ($false = sF230)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2837])).
% 21.36/3.55 thf(f2850,plain,(
% 21.36/3.55 ($false = ((notdexE => sF229)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1538,f2840])).
% 21.36/3.55 thf(f2855,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => sF229)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2850,f1072])).
% 21.36/3.55 thf(f2860,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => (notdallE => sF228))))),
% 21.36/3.55 inference(forward_demodulation,[],[f2855,f1537])).
% 21.36/3.55 thf(f2868,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => (notdallE => $true))) = $false) | ($false = sF228)),
% 21.36/3.55 inference(superposition,[],[f2860,f1165])).
% 21.36/3.55 thf(f2878,plain,(
% 21.36/3.55 ($false = sF228) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => $true)))),
% 21.36/3.55 inference(boolean_simplification,[],[f2868])).
% 21.36/3.55 thf(f2879,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF228)),
% 21.36/3.55 inference(boolean_simplification,[],[f2878])).
% 21.36/3.55 thf(f2880,plain,(
% 21.36/3.55 ($false = sF228)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2879])).
% 21.36/3.55 thf(f2888,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => sF226)))),
% 21.36/3.55 inference(backward_demodulation,[],[f2054,f2880])).
% 21.36/3.55 thf(f2899,plain,(
% 21.36/3.55 ($false = sF226)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2888])).
% 21.36/3.55 thf(f2909,plain,(
% 21.36/3.55 ($false = ((exuI2 => sF225)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1533,f2899])).
% 21.36/3.55 thf(f2914,plain,(
% 21.36/3.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => sF225)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2909,f1631])).
% 21.36/3.55 thf(f2917,plain,(
% 21.36/3.55 ($false = sF225)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2914])).
% 21.36/3.55 thf(f2927,plain,(
% 21.36/3.55 ($false = ((inCongP => sF224)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1532,f2917])).
% 21.36/3.55 thf(f2934,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) => (in @ Y3 @ Y1)))))))))))) => sF224)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2927,f913])).
% 21.36/3.55 thf(f2939,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) => (in @ Y3 @ Y1)))))))))))) => $true))) | ($false = sF224)),
% 21.36/3.55 inference(superposition,[],[f2934,f1165])).
% 21.36/3.55 thf(f2942,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF224)),
% 21.36/3.55 inference(boolean_simplification,[],[f2939])).
% 21.36/3.55 thf(f2943,plain,(
% 21.36/3.55 ($false = sF224)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f2942])).
% 21.36/3.55 thf(f2949,plain,(
% 21.36/3.55 ($false = ((in__Cong => sF223)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1530,f2943])).
% 21.36/3.55 thf(f2952,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => sF223)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f2949,f919])).
% 21.36/3.55 thf(f2953,plain,(
% 21.36/3.55 ($false = sF223)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2952])).
% 21.36/3.55 thf(f2965,plain,(
% 21.36/3.55 (((exuE3u => sF222)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1528,f2953])).
% 21.36/3.55 thf(f2968,plain,(
% 21.36/3.55 ($false = sF222)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2965])).
% 21.36/3.55 thf(f2969,plain,(
% 21.36/3.55 (exuE3u = $true)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f2965])).
% 21.36/3.55 thf(f2978,plain,(
% 21.36/3.55 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 21.36/3.55 inference(backward_demodulation,[],[f1686,f2969])).
% 21.36/3.55 thf(f2980,plain,(
% 21.36/3.55 ($false = ((exu__Cong => sF221)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1526,f2968])).
% 21.36/3.55 thf(f2981,plain,(
% 21.36/3.55 (exuEu = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f1678,f2978])).
% 21.36/3.55 thf(f2982,plain,(
% 21.36/3.55 ((($true => sF215)) = sF216)),
% 21.36/3.55 inference(backward_demodulation,[],[f1516,f2981])).
% 21.36/3.55 thf(f2983,plain,(
% 21.36/3.55 (sF215 = sF216)),
% 21.36/3.55 inference(boolean_simplification,[],[f2982])).
% 21.36/3.55 thf(f2984,plain,(
% 21.36/3.55 (((omega__Cong => sF215)) = sF217)),
% 21.36/3.55 inference(backward_demodulation,[],[f1518,f2983])).
% 21.36/3.55 thf(f2985,plain,(
% 21.36/3.55 ((($true => sF215)) = sF217)),
% 21.36/3.55 inference(forward_demodulation,[],[f2984,f1635])).
% 21.36/3.55 thf(f2986,plain,(
% 21.36/3.55 (sF215 = sF217)),
% 21.36/3.55 inference(boolean_simplification,[],[f2985])).
% 21.36/3.55 thf(f2987,plain,(
% 21.36/3.55 (((setunion__Cong => sF215)) = sF218)),
% 21.36/3.55 inference(backward_demodulation,[],[f1519,f2986])).
% 21.36/3.55 thf(f2988,plain,(
% 21.36/3.55 (sF218 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => sF215)))),
% 21.36/3.55 inference(forward_demodulation,[],[f2987,f1066])).
% 21.36/3.55 thf(f3003,plain,(
% 21.36/3.55 ($false = ((exu__Cong => $true))) | ($false = sF221)),
% 21.36/3.55 inference(superposition,[],[f2980,f1165])).
% 21.36/3.55 thf(f3006,plain,(
% 21.36/3.55 ($false = sF221) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f3003])).
% 21.36/3.55 thf(f3007,plain,(
% 21.36/3.55 ($false = sF221)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3006])).
% 21.36/3.55 thf(f3013,plain,(
% 21.36/3.55 (((emptyset__Cong => sF220)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1525,f3007])).
% 21.36/3.55 thf(f3016,plain,(
% 21.36/3.55 ($false = (($true => sF220)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3013,f1628])).
% 21.36/3.55 thf(f3017,plain,(
% 21.36/3.55 ($false = sF220)),
% 21.36/3.55 inference(boolean_simplification,[],[f3016])).
% 21.36/3.55 thf(f3018,plain,(
% 21.36/3.55 ($false = ((setadjoin__Cong => sF219)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1523,f3017])).
% 21.36/3.55 thf(f3019,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => sF219)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f3018,f1160])).
% 21.36/3.55 thf(f3024,plain,(
% 21.36/3.55 (sF218 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => $true))) | ($false = sF215)),
% 21.36/3.55 inference(superposition,[],[f2988,f1165])).
% 21.36/3.55 thf(f3028,plain,(
% 21.36/3.55 ($false = sF215) | (sF218 = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f3024])).
% 21.36/3.55 thf(f3034,plain,(
% 21.36/3.55 ($false = sF219) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f3019,f1165])).
% 21.36/3.55 thf(f3037,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF219)),
% 21.36/3.55 inference(boolean_simplification,[],[f3034])).
% 21.36/3.55 thf(f3038,plain,(
% 21.36/3.55 ($false = sF219)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3037])).
% 21.36/3.55 thf(f3044,plain,(
% 21.36/3.55 (((powerset__Cong => sF218)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1521,f3038])).
% 21.36/3.55 thf(f3047,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => sF218)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3044,f1091])).
% 21.36/3.55 thf(f3050,plain,(
% 21.36/3.55 (sF218 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f3047,f1165])).
% 21.36/3.55 thf(f3053,plain,(
% 21.36/3.55 ($false = $true) | (sF218 = $false)),
% 21.36/3.55 inference(boolean_simplification,[],[f3050])).
% 21.36/3.55 thf(f3054,plain,(
% 21.36/3.55 (sF218 = $false)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3053])).
% 21.36/3.55 thf(f3058,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF215)),
% 21.36/3.55 inference(backward_demodulation,[],[f3028,f3054])).
% 21.36/3.55 thf(f3062,plain,(
% 21.36/3.55 ($false = sF215)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3058])).
% 21.36/3.55 thf(f3071,plain,(
% 21.36/3.55 ($false = ((descr__Cong => sF214)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1514,f3062])).
% 21.36/3.55 thf(f3077,plain,(
% 21.36/3.55 ($false = sF214)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f3071])).
% 21.36/3.55 thf(f3087,plain,(
% 21.36/3.55 (((dsetconstr__Cong => sF213)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1513,f3077])).
% 21.36/3.55 thf(f3098,plain,(
% 21.36/3.55 ($false = sF213) | (((dsetconstr__Cong => $true)) = $false)),
% 21.36/3.55 inference(superposition,[],[f3087,f1165])).
% 21.36/3.55 thf(f3102,plain,(
% 21.36/3.55 ($false = $true) | ($false = sF213)),
% 21.36/3.55 inference(boolean_simplification,[],[f3098])).
% 21.36/3.55 thf(f3103,plain,(
% 21.36/3.55 ($false = sF213)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3102])).
% 21.36/3.55 thf(f3106,plain,(
% 21.36/3.55 ($false = ((subsetI1 => sF212)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1511,f3103])).
% 21.36/3.55 thf(f3111,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => sF212)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3106,f1041])).
% 21.36/3.55 thf(f3135,plain,(
% 21.36/3.55 ($false = sF212)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f3111])).
% 21.36/3.55 thf(f3136,plain,(
% 21.36/3.55 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f3111])).
% 21.36/3.55 thf(f3145,plain,(
% 21.36/3.55 (((eqimpsubset2 => sF211)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1510,f3135])).
% 21.36/3.55 thf(f3147,plain,(
% 21.36/3.55 (subsetI2 = $true)),
% 21.36/3.55 inference(backward_demodulation,[],[f923,f3136])).
% 21.36/3.55 thf(f3151,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => sF211)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3145,f1080])).
% 21.36/3.55 thf(f3152,plain,(
% 21.36/3.55 (sF210 = (($true => sF209)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1507,f3147])).
% 21.36/3.55 thf(f3153,plain,(
% 21.36/3.55 (sF210 = sF209)),
% 21.36/3.55 inference(boolean_simplification,[],[f3152])).
% 21.36/3.55 thf(f3154,plain,(
% 21.36/3.55 (sF211 = ((eqimpsubset1 => sF209)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1508,f3153])).
% 21.36/3.55 thf(f3155,plain,(
% 21.36/3.55 (sF211 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => sF209)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3154,f955])).
% 21.36/3.55 thf(f3156,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => sF209))))),
% 21.36/3.55 inference(backward_demodulation,[],[f3151,f3155])).
% 21.36/3.55 thf(f3173,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => $true))) = $false) | ($false = sF209)),
% 21.36/3.55 inference(superposition,[],[f3156,f1165])).
% 21.36/3.55 thf(f3178,plain,(
% 21.36/3.55 ($false = sF209) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => $true)))),
% 21.36/3.55 inference(boolean_simplification,[],[f3173])).
% 21.36/3.55 thf(f3179,plain,(
% 21.36/3.55 ($false = sF209) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f3178])).
% 21.36/3.55 thf(f3180,plain,(
% 21.36/3.55 ($false = sF209)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3179])).
% 21.36/3.55 thf(f3198,plain,(
% 21.36/3.55 (((emptysetsubset => sF208)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1505,f3180])).
% 21.36/3.55 thf(f3202,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (subset @ emptyset)) => sF208)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3198,f1683])).
% 21.36/3.55 thf(f3207,plain,(
% 21.36/3.55 ($false = sF208)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f3202])).
% 21.36/3.55 thf(f3217,plain,(
% 21.36/3.55 ($false = ((subsetE => sF207)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1503,f3207])).
% 21.36/3.55 thf(f3224,plain,(
% 21.36/3.55 (sF207 = $false) | ($false = ((subsetE => $true)))),
% 21.36/3.55 inference(superposition,[],[f3217,f1165])).
% 21.36/3.55 thf(f3227,plain,(
% 21.36/3.55 ($false = $true) | (sF207 = $false)),
% 21.36/3.55 inference(boolean_simplification,[],[f3224])).
% 21.36/3.55 thf(f3228,plain,(
% 21.36/3.55 (sF207 = $false)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3227])).
% 21.36/3.55 thf(f3232,plain,(
% 21.36/3.55 ($false = ((subsetE2 => sF206)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1501,f3228])).
% 21.36/3.55 thf(f3237,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => sF206)) = $false)),
% 21.36/3.55 inference(forward_demodulation,[],[f3232,f959])).
% 21.36/3.55 thf(f3265,plain,(
% 21.36/3.55 ($false = sF206)),
% 21.36/3.55 inference(imp_proxy_clausification,[],[f3237])).
% 21.36/3.55 thf(f3281,plain,(
% 21.36/3.55 (((notsubsetI => sF205)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1500,f3265])).
% 21.36/3.55 thf(f3282,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => sF205)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3281,f991])).
% 21.36/3.55 thf(f3285,plain,(
% 21.36/3.55 ($false = sF205) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => $true)))),
% 21.36/3.55 inference(superposition,[],[f3282,f1165])).
% 21.36/3.55 thf(f3290,plain,(
% 21.36/3.55 ($false = sF205) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f3285])).
% 21.36/3.55 thf(f3291,plain,(
% 21.36/3.55 ($false = sF205)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3290])).
% 21.36/3.55 thf(f3293,plain,(
% 21.36/3.55 (((notequalI1 => sF204)) = $false)),
% 21.36/3.55 inference(backward_demodulation,[],[f1498,f3291])).
% 21.36/3.55 thf(f3298,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => sF204)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3293,f1031])).
% 21.36/3.55 thf(f3301,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => $true)) = $false) | (sF204 = $false)),
% 21.36/3.55 inference(superposition,[],[f3298,f1165])).
% 21.36/3.55 thf(f3304,plain,(
% 21.36/3.55 ($false = $true) | (sF204 = $false)),
% 21.36/3.55 inference(boolean_simplification,[],[f3301])).
% 21.36/3.55 thf(f3305,plain,(
% 21.36/3.55 (sF204 = $false)),
% 21.36/3.55 inference(trivial_inequality_removal,[],[f3304])).
% 21.36/3.55 thf(f3309,plain,(
% 21.36/3.55 ($false = ((notequalI2 => sF203)))),
% 21.36/3.55 inference(backward_demodulation,[],[f1496,f3305])).
% 21.36/3.55 thf(f3316,plain,(
% 21.36/3.55 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => sF203)))),
% 21.36/3.55 inference(forward_demodulation,[],[f3309,f972])).
% 21.36/3.55 thf(f3321,plain,(
% 21.36/3.55 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => $true)) = $false) | ($false = sF203)),
% 21.36/3.55 inference(superposition,[],[f3316,f1165])).
% 21.36/3.55 thf(f3324,plain,(
% 21.36/3.55 ($false = sF203) | ($false = $true)),
% 21.36/3.55 inference(boolean_simplification,[],[f3321])).
% 21.36/3.56 thf(f3325,plain,(
% 21.36/3.56 ($false = sF203)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3324])).
% 21.36/3.56 thf(f3329,plain,(
% 21.36/3.56 ($false = ((subsetRefl => sF202)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1495,f3325])).
% 21.36/3.56 thf(f3334,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => sF202)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f3329,f976])).
% 21.36/3.56 thf(f3337,plain,(
% 21.36/3.56 ($false = sF202)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3334])).
% 21.36/3.56 thf(f3347,plain,(
% 21.36/3.56 (((subsetTrans => sF201)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1493,f3337])).
% 21.36/3.56 thf(f3350,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y2) => (subset @ Y1 @ Y2))))))))) => sF201)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3347,f922])).
% 21.36/3.56 thf(f3355,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y2) => (subset @ Y1 @ Y2))))))))) => $true))) | ($false = sF201)),
% 21.36/3.56 inference(superposition,[],[f3350,f1165])).
% 21.36/3.56 thf(f3358,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF201)),
% 21.36/3.56 inference(boolean_simplification,[],[f3355])).
% 21.36/3.56 thf(f3359,plain,(
% 21.36/3.56 ($false = sF201)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3358])).
% 21.36/3.56 thf(f3363,plain,(
% 21.36/3.56 ($false = ((setadjoinSub => sF200)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1491,f3359])).
% 21.36/3.56 thf(f3368,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => sF200)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3363,f1039])).
% 21.36/3.56 thf(f3377,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => $true))) | ($false = sF200)),
% 21.36/3.56 inference(superposition,[],[f3368,f1165])).
% 21.36/3.56 thf(f3381,plain,(
% 21.36/3.56 ($false = sF200) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f3377])).
% 21.36/3.56 thf(f3382,plain,(
% 21.36/3.56 ($false = sF200)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3381])).
% 21.36/3.56 thf(f3385,plain,(
% 21.36/3.56 (((setadjoinSub2 => sF199)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1490,f3382])).
% 21.36/3.56 thf(f3390,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => sF199)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3385,f911])).
% 21.36/3.56 thf(f3395,plain,(
% 21.36/3.56 ($false = sF199)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3390])).
% 21.36/3.56 thf(f3405,plain,(
% 21.36/3.56 ($false = ((subset2powerset => sF198)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1488,f3395])).
% 21.36/3.56 thf(f3410,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => sF198)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3405,f921])).
% 21.36/3.56 thf(f3413,plain,(
% 21.36/3.56 ($false = sF198)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3410])).
% 21.36/3.56 thf(f3423,plain,(
% 21.36/3.56 (((setextsub => sF197)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1486,f3413])).
% 21.36/3.56 thf(f3430,plain,(
% 21.36/3.56 ($false = sF197)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3423])).
% 21.36/3.56 thf(f3442,plain,(
% 21.36/3.56 ($false = ((subsetemptysetimpeq => sF196)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1484,f3430])).
% 21.36/3.56 thf(f3443,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => sF196)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3442,f954])).
% 21.36/3.56 thf(f3444,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => (powersetI1 => sF195))))),
% 21.36/3.56 inference(forward_demodulation,[],[f3443,f1482])).
% 21.36/3.56 thf(f3445,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => sF195))))),
% 21.36/3.56 inference(forward_demodulation,[],[f3444,f1122])).
% 21.36/3.56 thf(f3464,plain,(
% 21.36/3.56 ($false = sF195) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => $true))))),
% 21.36/3.56 inference(superposition,[],[f3445,f1165])).
% 21.36/3.56 thf(f3469,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => $true))) | ($false = sF195)),
% 21.36/3.56 inference(boolean_simplification,[],[f3464])).
% 21.36/3.56 thf(f3470,plain,(
% 21.36/3.56 ($false = sF195) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f3469])).
% 21.36/3.56 thf(f3471,plain,(
% 21.36/3.56 ($false = sF195)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3470])).
% 21.36/3.56 thf(f3480,plain,(
% 21.36/3.56 ($false = ((powersetE1 => sF194)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1480,f3471])).
% 21.36/3.56 thf(f3496,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => sF194)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f3480,f1098])).
% 21.36/3.56 thf(f3502,plain,(
% 21.36/3.56 ($false = sF194)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3496])).
% 21.36/3.56 thf(f3512,plain,(
% 21.36/3.56 (((inPowerset => sF193)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1479,f3502])).
% 21.36/3.56 thf(f3517,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => sF193)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3512,f1163])).
% 21.36/3.56 thf(f3520,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => $true))) | ($false = sF193)),
% 21.36/3.56 inference(superposition,[],[f3517,f1165])).
% 21.36/3.56 thf(f3523,plain,(
% 21.36/3.56 ($false = sF193) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f3520])).
% 21.36/3.56 thf(f3524,plain,(
% 21.36/3.56 ($false = sF193)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3523])).
% 21.36/3.56 thf(f3528,plain,(
% 21.36/3.56 ($false = ((powersetsubset => sF192)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1477,f3524])).
% 21.36/3.56 thf(f3535,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => sF192)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3528,f952])).
% 21.36/3.56 thf(f3538,plain,(
% 21.36/3.56 (sF192 = $false)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3535])).
% 21.36/3.56 thf(f3548,plain,(
% 21.36/3.56 ($false = ((sepInPowerset => sF191)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1475,f3538])).
% 21.36/3.56 thf(f3555,plain,(
% 21.36/3.56 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => sF191)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f3548,f1667])).
% 21.36/3.56 thf(f3556,plain,(
% 21.36/3.56 ($false = sF191)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3555])).
% 21.36/3.56 thf(f3574,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF188)),
% 21.36/3.56 inference(backward_demodulation,[],[f2665,f3556])).
% 21.36/3.56 thf(f3577,plain,(
% 21.36/3.56 ($false = sF188)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3574])).
% 21.36/3.56 thf(f3579,plain,(
% 21.36/3.56 ($false = ((binunionIR => sF187)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1470,f3577])).
% 21.36/3.56 thf(f3591,plain,(
% 21.36/3.56 ($false = ((binunionIR => (binunionEcases => sF186))))),
% 21.36/3.56 inference(forward_demodulation,[],[f3579,f1468])).
% 21.36/3.56 thf(f3601,plain,(
% 21.36/3.56 ($false = ((binunionIR => (binunionEcases => $true)))) | ($false = sF186)),
% 21.36/3.56 inference(superposition,[],[f3591,f1165])).
% 21.36/3.56 thf(f3611,plain,(
% 21.36/3.56 ($false = ((binunionIR => $true))) | ($false = sF186)),
% 21.36/3.56 inference(boolean_simplification,[],[f3601])).
% 21.36/3.56 thf(f3612,plain,(
% 21.36/3.56 ($false = sF186) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f3611])).
% 21.36/3.56 thf(f3613,plain,(
% 21.36/3.56 ($false = sF186)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3612])).
% 21.36/3.56 thf(f3623,plain,(
% 21.36/3.56 ($false = ((binunionE => sF185)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1466,f3613])).
% 21.36/3.56 thf(f3629,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y0) | (in @ Y2 @ Y1))))))))) => sF185)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3623,f1108])).
% 21.36/3.56 thf(f3673,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y0) | (in @ Y2 @ Y1))))))))) => $true))) | ($false = sF185)),
% 21.36/3.56 inference(superposition,[],[f3629,f1165])).
% 21.36/3.56 thf(f3677,plain,(
% 21.36/3.56 ($false = sF185) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f3673])).
% 21.36/3.56 thf(f3678,plain,(
% 21.36/3.56 ($false = sF185)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3677])).
% 21.36/3.56 thf(f3681,plain,(
% 21.36/3.56 ($false = ((binunionLsub => sF184)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1464,f3678])).
% 21.36/3.56 thf(f3688,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => sF184)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3681,f1029])).
% 21.36/3.56 thf(f3691,plain,(
% 21.36/3.56 ($false = sF184)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3688])).
% 21.36/3.56 thf(f3707,plain,(
% 21.36/3.56 ($false = ((binunionRsub => sF183)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1462,f3691])).
% 21.36/3.56 thf(f3708,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => sF183)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3707,f1107])).
% 21.36/3.56 thf(f3711,plain,(
% 21.36/3.56 ($false = sF183)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3708])).
% 21.36/3.56 thf(f3723,plain,(
% 21.36/3.56 ($false = ((binintersectI => sF182)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1461,f3711])).
% 21.36/3.56 thf(f3726,plain,(
% 21.36/3.56 ($false = sF182)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3723])).
% 21.36/3.56 thf(f3736,plain,(
% 21.36/3.56 (((binintersectSubset5 => sF181)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1460,f3726])).
% 21.36/3.56 thf(f3747,plain,(
% 21.36/3.56 ($false = sF181)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3736])).
% 21.36/3.56 thf(f3757,plain,(
% 21.36/3.56 ($false = ((binintersectEL => sF180)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1458,f3747])).
% 21.36/3.56 thf(f3762,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => sF180)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3757,f997])).
% 21.36/3.56 thf(f3763,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => (binintersectLsub => sF179))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f3762,f1457])).
% 21.36/3.56 thf(f3764,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => sF179))))),
% 21.36/3.56 inference(forward_demodulation,[],[f3763,f1002])).
% 21.36/3.56 thf(f3812,plain,(
% 21.36/3.56 ($false = sF179) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => $true))))),
% 21.36/3.56 inference(superposition,[],[f3764,f1165])).
% 21.36/3.56 thf(f3822,plain,(
% 21.36/3.56 ($false = sF179) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => $true)))),
% 21.36/3.56 inference(boolean_simplification,[],[f3812])).
% 21.36/3.56 thf(f3823,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF179)),
% 21.36/3.56 inference(boolean_simplification,[],[f3822])).
% 21.36/3.56 thf(f3824,plain,(
% 21.36/3.56 ($false = sF179)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3823])).
% 21.36/3.56 thf(f3833,plain,(
% 21.36/3.56 ($false = ((binintersectSubset2 => sF178)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1456,f3824])).
% 21.36/3.56 thf(f3844,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => sF178)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3833,f1139])).
% 21.36/3.56 thf(f3850,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => $true))) | (sF178 = $false)),
% 21.36/3.56 inference(superposition,[],[f3844,f1165])).
% 21.36/3.56 thf(f3855,plain,(
% 21.36/3.56 ($false = $true) | (sF178 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f3850])).
% 21.36/3.56 thf(f3856,plain,(
% 21.36/3.56 (sF178 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3855])).
% 21.36/3.56 thf(f3864,plain,(
% 21.36/3.56 ($false = ((binintersectSubset3 => sF177)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1455,f3856])).
% 21.36/3.56 thf(f3865,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => sF177)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3864,f1001])).
% 21.36/3.56 thf(f3866,plain,(
% 21.36/3.56 ($false = sF177)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3865])).
% 21.36/3.56 thf(f3876,plain,(
% 21.36/3.56 ($false = ((binintersectER => sF176)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1454,f3866])).
% 21.36/3.56 thf(f3881,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => sF176)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3876,f996])).
% 21.36/3.56 thf(f3888,plain,(
% 21.36/3.56 ($false = sF176)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3881])).
% 21.36/3.56 thf(f3902,plain,(
% 21.36/3.56 ($false = ((disjointsetsI1 => sF175)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1453,f3888])).
% 21.36/3.56 thf(f3905,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => sF175)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3902,f1061])).
% 21.36/3.56 thf(f3906,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => (binintersectRsub => sF174))))),
% 21.36/3.56 inference(forward_demodulation,[],[f3905,f1452])).
% 21.36/3.56 thf(f3907,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => sF174))))),
% 21.36/3.56 inference(forward_demodulation,[],[f3906,f1047])).
% 21.36/3.56 thf(f3917,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => $true)))) | ($false = sF174)),
% 21.36/3.56 inference(superposition,[],[f3907,f1165])).
% 21.36/3.56 thf(f3922,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => $true))) | ($false = sF174)),
% 21.36/3.56 inference(boolean_simplification,[],[f3917])).
% 21.36/3.56 thf(f3923,plain,(
% 21.36/3.56 ($false = sF174) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f3922])).
% 21.36/3.56 thf(f3924,plain,(
% 21.36/3.56 ($false = sF174)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f3923])).
% 21.36/3.56 thf(f3934,plain,(
% 21.36/3.56 ($false = ((binintersectSubset4 => sF173)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1450,f3924])).
% 21.36/3.56 thf(f3956,plain,(
% 21.36/3.56 ($false = sF173)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3934])).
% 21.36/3.56 thf(f3966,plain,(
% 21.36/3.56 (((binintersectSubset1 => sF172)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1448,f3956])).
% 21.36/3.56 thf(f3973,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => sF172)))),
% 21.36/3.56 inference(forward_demodulation,[],[f3966,f982])).
% 21.36/3.56 thf(f3989,plain,(
% 21.36/3.56 ($false = sF172)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f3973])).
% 21.36/3.56 thf(f3999,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1446,f3989])).
% 21.36/3.56 thf(f4010,plain,(
% 21.36/3.56 ($false = ((bs114d => $true))) | ($false = sF171)),
% 21.36/3.56 inference(superposition,[],[f3999,f1165])).
% 21.36/3.56 thf(f4013,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f4010])).
% 21.36/3.56 thf(f4014,plain,(
% 21.36/3.56 ($false = sF171)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4013])).
% 21.36/3.56 thf(f4018,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1444,f4014])).
% 21.36/3.56 thf(f4025,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => sF170)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4018,f1144])).
% 21.36/3.56 thf(f4055,plain,(
% 21.36/3.56 ($false = sF170)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4025])).
% 21.36/3.56 thf(f4065,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1442,f4055])).
% 21.36/3.56 thf(f4068,plain,(
% 21.36/3.56 (((setminusEL => (setminusER => sF168))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4065,f1440])).
% 21.36/3.56 thf(f4073,plain,(
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% 21.36/3.56 inference(superposition,[],[f4068,f1165])).
% 21.36/3.56 thf(f4078,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f4073])).
% 21.36/3.56 thf(f4079,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f4078])).
% 21.36/3.56 thf(f4080,plain,(
% 21.36/3.56 ($false = sF168)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4079])).
% 21.36/3.56 thf(f4090,plain,(
% 21.36/3.56 ($false = ((setminusSubset2 => sF167)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1438,f4080])).
% 21.36/3.56 thf(f4104,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => sF167)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4090,f876])).
% 21.36/3.56 thf(f4129,plain,(
% 21.36/3.56 ($false = sF167)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4104])).
% 21.36/3.56 thf(f4139,plain,(
% 21.36/3.56 ($false = ((setminusERneg => sF166)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1437,f4129])).
% 21.36/3.56 thf(f4144,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => sF166)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4139,f994])).
% 21.36/3.56 thf(f4149,plain,(
% 21.36/3.56 ($false = sF166)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4144])).
% 21.36/3.56 thf(f4163,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1435,f4149])).
% 21.36/3.56 thf(f4166,plain,(
% 21.36/3.56 ($false = sF165) | ($false = ((setminusELneg => $true)))),
% 21.36/3.56 inference(superposition,[],[f4163,f1165])).
% 21.36/3.56 thf(f4170,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f4166])).
% 21.36/3.56 thf(f4171,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f4170])).
% 21.36/3.56 thf(f4174,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1433,f4171])).
% 21.36/3.56 thf(f4181,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f4174,f1065])).
% 21.36/3.56 thf(f4188,plain,(
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% 21.36/3.56 inference(superposition,[],[f4181,f1165])).
% 21.36/3.56 thf(f4191,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f4188])).
% 21.36/3.56 thf(f4192,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f4191])).
% 21.36/3.56 thf(f4196,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1432,f4192])).
% 21.36/3.56 thf(f4201,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f4196,f1147])).
% 21.36/3.56 thf(f4206,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f4201,f1431])).
% 21.36/3.56 thf(f4207,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f4206,f903])).
% 21.36/3.56 thf(f4245,plain,(
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% 21.36/3.56 inference(superposition,[],[f4207,f1165])).
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% 21.36/3.56 inference(boolean_simplification,[],[f4245])).
% 21.36/3.56 thf(f4251,plain,(
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% 21.36/3.56 thf(f4252,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f4251])).
% 21.36/3.56 thf(f4260,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1430,f4252])).
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% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => sF161)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4260,f883])).
% 21.36/3.56 thf(f4287,plain,(
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% 21.36/3.56 inference(superposition,[],[f4276,f1165])).
% 21.36/3.56 thf(f4290,plain,(
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% 21.36/3.56 thf(f4291,plain,(
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% 21.36/3.56 thf(f4297,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1429,f4291])).
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% 21.36/3.56 inference(forward_demodulation,[],[f4297,f1145])).
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% 21.36/3.56 inference(forward_demodulation,[],[f4300,f1428])).
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% 21.36/3.56 inference(forward_demodulation,[],[f4301,f918])).
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% 21.36/3.56 inference(superposition,[],[f4302,f1165])).
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% 21.36/3.56 inference(boolean_simplification,[],[f4360])).
% 21.36/3.56 thf(f4367,plain,(
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% 21.36/3.56 thf(f4368,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f4367])).
% 21.36/3.56 thf(f4376,plain,(
% 21.36/3.56 (((symdiffI2 => sF158)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1426,f4368])).
% 21.36/3.56 thf(f4393,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ (symdiff @ Y0 @ Y2)))))))))) => sF158)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4376,f975])).
% 21.36/3.56 thf(f4400,plain,(
% 21.36/3.56 ($false = sF158)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4393])).
% 21.36/3.56 thf(f4410,plain,(
% 21.36/3.56 ($false = ((symdiffIneg1 => sF157)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1424,f4400])).
% 21.36/3.56 thf(f4415,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => sF157)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4410,f884])).
% 21.36/3.56 thf(f4418,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => (symdiffIneg2 => sF156))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4415,f1423])).
% 21.36/3.56 thf(f4421,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => (symdiffIneg2 => $true)))) | ($false = sF156)),
% 21.36/3.56 inference(superposition,[],[f4418,f1165])).
% 21.36/3.56 thf(f4428,plain,(
% 21.36/3.56 ($false = sF156) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => $true)))),
% 21.36/3.56 inference(boolean_simplification,[],[f4421])).
% 21.36/3.56 thf(f4429,plain,(
% 21.36/3.56 ($false = sF156) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f4428])).
% 21.36/3.56 thf(f4430,plain,(
% 21.36/3.56 ($false = sF156)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4429])).
% 21.36/3.56 thf(f4443,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF154)),
% 21.36/3.56 inference(backward_demodulation,[],[f2677,f4430])).
% 21.36/3.56 thf(f4448,plain,(
% 21.36/3.56 ($false = sF154)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4443])).
% 21.36/3.56 thf(f4458,plain,(
% 21.36/3.56 ($false = ((setukpairIR => sF153)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1420,f4448])).
% 21.36/3.56 thf(f4462,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => sF153)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4458,f872])).
% 21.36/3.56 thf(f4502,plain,(
% 21.36/3.56 ($false = sF153)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4462])).
% 21.36/3.56 thf(f4516,plain,(
% 21.36/3.56 ($false = ((kpairiskpair => sF152)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1419,f4502])).
% 21.36/3.56 thf(f4517,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => sF152)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4516,f1150])).
% 21.36/3.56 thf(f4520,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => $true))) | ($false = sF152)),
% 21.36/3.56 inference(superposition,[],[f4517,f1165])).
% 21.36/3.56 thf(f4523,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF152)),
% 21.36/3.56 inference(boolean_simplification,[],[f4520])).
% 21.36/3.56 thf(f4524,plain,(
% 21.36/3.56 ($false = sF152)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4523])).
% 21.36/3.56 thf(f4528,plain,(
% 21.36/3.56 ($false = ((kpairp => sF151)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1417,f4524])).
% 21.36/3.56 thf(f4535,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => sF151)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4528,f964])).
% 21.36/3.56 thf(f4538,plain,(
% 21.36/3.56 ($false = sF151) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f4535,f1165])).
% 21.36/3.56 thf(f4542,plain,(
% 21.36/3.56 ($false = sF151) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f4538])).
% 21.36/3.56 thf(f4543,plain,(
% 21.36/3.56 ($false = sF151)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4542])).
% 21.36/3.56 thf(f4546,plain,(
% 21.36/3.56 ($false = ((singletonsubset => sF150)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1415,f4543])).
% 21.36/3.56 thf(f4553,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => sF150)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4546,f995])).
% 21.36/3.56 thf(f4556,plain,(
% 21.36/3.56 ($false = sF150)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4553])).
% 21.36/3.56 thf(f4568,plain,(
% 21.36/3.56 ($false = ((singletoninpowerset => sF149)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1414,f4556])).
% 21.36/3.56 thf(f4571,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => sF149)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4568,f882])).
% 21.36/3.56 thf(f4572,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => (singletoninpowunion => sF148))))),
% 21.36/3.56 inference(forward_demodulation,[],[f4571,f1413])).
% 21.36/3.56 thf(f4575,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => (singletoninpowunion => $true)))) | (sF148 = $false)),
% 21.36/3.56 inference(superposition,[],[f4572,f1165])).
% 21.36/3.56 thf(f4585,plain,(
% 21.36/3.56 (sF148 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => $true)) = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f4575])).
% 21.36/3.56 thf(f4586,plain,(
% 21.36/3.56 (sF148 = $false) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f4585])).
% 21.36/3.56 thf(f4587,plain,(
% 21.36/3.56 (sF148 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4586])).
% 21.36/3.56 thf(f4597,plain,(
% 21.36/3.56 ($false = ((upairset2E => sF147)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1411,f4587])).
% 21.36/3.56 thf(f4603,plain,(
% 21.36/3.56 (((upairset2E => (upairsubunion => sF146))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4597,f1410])).
% 21.36/3.56 thf(f4604,plain,(
% 21.36/3.56 (((upairset2E => (upairsubunion => (upairinpowunion => sF145)))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4603,f1408])).
% 21.36/3.56 thf(f4609,plain,(
% 21.36/3.56 (sF145 = $false) | ($false = ((upairset2E => (upairsubunion => (upairinpowunion => $true)))))),
% 21.36/3.56 inference(superposition,[],[f4604,f1165])).
% 21.36/3.56 thf(f4621,plain,(
% 21.36/3.56 ($false = ((upairset2E => (upairsubunion => $true)))) | (sF145 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f4609])).
% 21.36/3.56 thf(f4622,plain,(
% 21.36/3.56 (sF145 = $false) | ($false = ((upairset2E => $true)))),
% 21.36/3.56 inference(boolean_simplification,[],[f4621])).
% 21.36/3.56 thf(f4623,plain,(
% 21.36/3.56 ($false = $true) | (sF145 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f4622])).
% 21.36/3.56 thf(f4624,plain,(
% 21.36/3.56 (sF145 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4623])).
% 21.36/3.56 thf(f4639,plain,(
% 21.36/3.56 ($false = ((ubforcartprodlem1 => sF144)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1407,f4624])).
% 21.36/3.56 thf(f4655,plain,(
% 21.36/3.56 (((ubforcartprodlem1 => (ubforcartprodlem2 => sF143))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4639,f1406])).
% 21.36/3.56 thf(f4675,plain,(
% 21.36/3.56 (((ubforcartprodlem1 => (ubforcartprodlem2 => $true))) = $false) | ($false = sF143)),
% 21.36/3.56 inference(superposition,[],[f4655,f1165])).
% 21.36/3.56 thf(f4680,plain,(
% 21.36/3.56 ($false = ((ubforcartprodlem1 => $true))) | ($false = sF143)),
% 21.36/3.56 inference(boolean_simplification,[],[f4675])).
% 21.36/3.56 thf(f4681,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF143)),
% 21.36/3.56 inference(boolean_simplification,[],[f4680])).
% 21.36/3.56 thf(f4682,plain,(
% 21.36/3.56 ($false = sF143)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4681])).
% 21.36/3.56 thf(f4690,plain,(
% 21.36/3.56 ($false = ((ubforcartprodlem3 => sF142)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1405,f4682])).
% 21.36/3.56 thf(f4706,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y0)))))))))))))) => sF142)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4690,f924])).
% 21.36/3.56 thf(f4735,plain,(
% 21.36/3.56 ($false = sF142)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4706])).
% 21.36/3.56 thf(f4745,plain,(
% 21.36/3.56 ($false = ((cartprodpairin => sF141)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1404,f4735])).
% 21.36/3.56 thf(f4750,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => sF141)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4745,f998])).
% 21.36/3.56 thf(f4757,plain,(
% 21.36/3.56 ($false = sF141)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4750])).
% 21.36/3.56 thf(f4771,plain,(
% 21.36/3.56 ($false = ((cartprodmempair1 => sF140)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1403,f4757])).
% 21.36/3.56 thf(f4774,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & ((kpair @ Y3 @ Y4) = Y1)))) & (in @ Y3 @ Y0))))))))))) => sF140)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4771,f1059])).
% 21.36/3.56 thf(f4775,plain,(
% 21.36/3.56 ($false = sF140)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4774])).
% 21.36/3.56 thf(f4785,plain,(
% 21.36/3.56 ($false = ((cartprodmempair => sF139)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1402,f4775])).
% 21.36/3.56 thf(f4790,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => sF139)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4785,f881])).
% 21.36/3.56 thf(f4795,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => $true))) | ($false = sF139)),
% 21.36/3.56 inference(superposition,[],[f4790,f1165])).
% 21.36/3.56 thf(f4799,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF139)),
% 21.36/3.56 inference(boolean_simplification,[],[f4795])).
% 21.36/3.56 thf(f4800,plain,(
% 21.36/3.56 ($false = sF139)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4799])).
% 21.36/3.56 thf(f4807,plain,(
% 21.36/3.56 ($false = ((setunionE2 => sF138)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1401,f4800])).
% 21.36/3.56 thf(f4810,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => sF138)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4807,f1106])).
% 21.36/3.56 thf(f4813,plain,(
% 21.36/3.56 (sF138 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f4810,f1165])).
% 21.36/3.56 thf(f4816,plain,(
% 21.36/3.56 ($false = $true) | (sF138 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f4813])).
% 21.36/3.56 thf(f4817,plain,(
% 21.36/3.56 (sF138 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4816])).
% 21.36/3.56 thf(f4821,plain,(
% 21.36/3.56 ($false = ((setunionsingleton1 => sF137)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1400,f4817])).
% 21.36/3.56 thf(f4828,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => sF137)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4821,f1155])).
% 21.36/3.56 thf(f4833,plain,(
% 21.36/3.56 ($false = sF137) | ($false = (((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f4828,f1165])).
% 21.36/3.56 thf(f4836,plain,(
% 21.36/3.56 ($false = sF137) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f4833])).
% 21.36/3.56 thf(f4837,plain,(
% 21.36/3.56 ($false = sF137)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4836])).
% 21.36/3.56 thf(f4841,plain,(
% 21.36/3.56 ($false = ((setunionsingleton2 => sF136)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1399,f4837])).
% 21.36/3.56 thf(f4846,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => sF136)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4841,f1000])).
% 21.36/3.56 thf(f4849,plain,(
% 21.36/3.56 ($false = sF136)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f4846])).
% 21.36/3.56 thf(f4865,plain,(
% 21.36/3.56 ($false = ((setunionsingleton => sF135)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1397,f4849])).
% 21.36/3.56 thf(f4866,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => sF135)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4865,f912])).
% 21.36/3.56 thf(f4867,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => (singletonprop => sF134))))),
% 21.36/3.56 inference(forward_demodulation,[],[f4866,f1395])).
% 21.36/3.56 thf(f4870,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => (singletonprop => $true))) = $false) | ($false = sF134)),
% 21.36/3.56 inference(superposition,[],[f4867,f1165])).
% 21.36/3.56 thf(f4880,plain,(
% 21.36/3.56 ($false = sF134) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => $true)))),
% 21.36/3.56 inference(boolean_simplification,[],[f4870])).
% 21.36/3.56 thf(f4881,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f4880])).
% 21.36/3.56 thf(f4882,plain,(
% 21.36/3.56 ($false = sF134)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4881])).
% 21.36/3.56 thf(f4892,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1394,f4882])).
% 21.36/3.56 thf(f4898,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => sF133)))),
% 21.36/3.56 inference(forward_demodulation,[],[f4892,f1679])).
% 21.36/3.56 thf(f4903,plain,(
% 21.36/3.56 ($false = sF133) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f4898,f1165])).
% 21.36/3.56 thf(f4906,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF133)),
% 21.36/3.56 inference(boolean_simplification,[],[f4903])).
% 21.36/3.56 thf(f4907,plain,(
% 21.36/3.56 ($false = sF133)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4906])).
% 21.36/3.56 thf(f4911,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1393,f4907])).
% 21.36/3.56 thf(f4922,plain,(
% 21.36/3.56 ($false = sF132) | ($false = ((ex1I => $true)))),
% 21.36/3.56 inference(superposition,[],[f4911,f1165])).
% 21.36/3.56 thf(f4925,plain,(
% 21.36/3.56 ($false = sF132) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f4922])).
% 21.36/3.56 thf(f4926,plain,(
% 21.36/3.56 ($false = sF132)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f4925])).
% 21.36/3.56 thf(f4930,plain,(
% 21.36/3.56 ($false = ((ex1I2 => sF131)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1392,f4926])).
% 21.36/3.56 thf(f4937,plain,(
% 21.36/3.56 ((((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ Y1))))))) => sF131)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4930,f1691])).
% 21.36/3.56 thf(f4940,plain,(
% 21.36/3.56 ((((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ Y1))))))) => (singletonsuniq => sF130))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f4937,f1391])).
% 21.36/3.56 thf(f4994,plain,(
% 21.36/3.56 ($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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ Y1))))))) => (singletonsuniq => $true)))) | ($false = sF130)),
% 21.36/3.56 inference(superposition,[],[f4940,f1165])).
% 21.36/3.56 thf(f5002,plain,(
% 21.36/3.56 ($false = sF130) | ($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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ Y1))))))) => $true)))),
% 21.36/3.56 inference(boolean_simplification,[],[f4994])).
% 21.36/3.56 thf(f5003,plain,(
% 21.36/3.56 ($false = sF130) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5002])).
% 21.36/3.56 thf(f5004,plain,(
% 21.36/3.56 ($false = sF130)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5003])).
% 21.36/3.56 thf(f5012,plain,(
% 21.36/3.56 ($false = ((setukpairinjL1 => sF129)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1389,f5004])).
% 21.36/3.56 thf(f5030,plain,(
% 21.36/3.56 ($false = sF129)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5012])).
% 21.36/3.56 thf(f5040,plain,(
% 21.36/3.56 ($false = ((kfstsingleton => sF128)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1387,f5030])).
% 21.36/3.56 thf(f5047,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))) => sF128)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5040,f1089])).
% 21.36/3.56 thf(f5050,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))) => $true))) | ($false = sF128)),
% 21.36/3.56 inference(superposition,[],[f5047,f1165])).
% 21.36/3.56 thf(f5055,plain,(
% 21.36/3.56 ($false = sF128) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5050])).
% 21.36/3.56 thf(f5056,plain,(
% 21.36/3.56 ($false = sF128)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5055])).
% 21.36/3.56 thf(f5058,plain,(
% 21.36/3.56 ($false = ((theprop => sF127)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1385,f5056])).
% 21.36/3.56 thf(f5063,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))) => sF127)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5058,f1018])).
% 21.36/3.56 thf(f5066,plain,(
% 21.36/3.56 ($false = sF127) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f5063,f1165])).
% 21.36/3.56 thf(f5069,plain,(
% 21.36/3.56 ($false = sF127) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5066])).
% 21.36/3.56 thf(f5070,plain,(
% 21.36/3.56 ($false = sF127)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5069])).
% 21.36/3.56 thf(f5076,plain,(
% 21.36/3.56 ($false = ((kfstpairEq => sF126)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1383,f5070])).
% 21.36/3.56 thf(f5079,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))) => sF126)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5076,f936])).
% 21.36/3.56 thf(f5080,plain,(
% 21.36/3.56 ($false = sF126)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5079])).
% 21.36/3.56 thf(f5090,plain,(
% 21.36/3.56 (((cartprodfstin => sF125)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1381,f5080])).
% 21.36/3.56 thf(f5095,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => sF125)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5090,f1019])).
% 21.36/3.56 thf(f5100,plain,(
% 21.36/3.56 ($false = sF125) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f5095,f1165])).
% 21.36/3.56 thf(f5103,plain,(
% 21.36/3.56 ($false = sF125) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5100])).
% 21.36/3.56 thf(f5104,plain,(
% 21.36/3.56 ($false = sF125)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5103])).
% 21.36/3.56 thf(f5108,plain,(
% 21.36/3.56 ($false = ((setukpairinjL2 => sF124)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1379,f5104])).
% 21.36/3.56 thf(f5117,plain,(
% 21.36/3.56 ($false = ((setukpairinjL2 => $true))) | ($false = sF124)),
% 21.36/3.56 inference(superposition,[],[f5108,f1165])).
% 21.36/3.56 thf(f5122,plain,(
% 21.36/3.56 ($false = sF124) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5117])).
% 21.36/3.56 thf(f5123,plain,(
% 21.36/3.56 ($false = sF124)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5122])).
% 21.36/3.56 thf(f5125,plain,(
% 21.36/3.56 ($false = ((setukpairinjL => sF123)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1377,f5123])).
% 21.36/3.56 thf(f5128,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y0) = (kpair @ Y1 @ Y3)) => (Y2 = Y1)))))))))) => sF123)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5125,f1123])).
% 21.36/3.56 thf(f5133,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y0) = (kpair @ Y1 @ Y3)) => (Y2 = Y1)))))))))) => $true))) | ($false = sF123)),
% 21.36/3.56 inference(superposition,[],[f5128,f1165])).
% 21.36/3.56 thf(f5137,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF123)),
% 21.36/3.56 inference(boolean_simplification,[],[f5133])).
% 21.36/3.56 thf(f5138,plain,(
% 21.36/3.56 ($false = sF123)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5137])).
% 21.36/3.56 thf(f5141,plain,(
% 21.36/3.56 ($false = ((setukpairinjR11 => sF122)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1376,f5138])).
% 21.36/3.56 thf(f5148,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => sF122)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f5141,f1028])).
% 21.36/3.56 thf(f5149,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => (setukpairinjR12 => sF121))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f5148,f1374])).
% 21.36/3.56 thf(f5152,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => (setukpairinjR12 => $true))) = $false) | ($false = sF121)),
% 21.36/3.56 inference(superposition,[],[f5149,f1165])).
% 21.36/3.56 thf(f5159,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => $true))) | ($false = sF121)),
% 21.36/3.56 inference(boolean_simplification,[],[f5152])).
% 21.36/3.56 thf(f5160,plain,(
% 21.36/3.56 ($false = sF121) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5159])).
% 21.36/3.56 thf(f5161,plain,(
% 21.36/3.56 ($false = sF121)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5160])).
% 21.36/3.56 thf(f5170,plain,(
% 21.36/3.56 ($false = ((setukpairinjR1 => sF120)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1372,f5161])).
% 21.36/3.56 thf(f5186,plain,(
% 21.36/3.56 ($false = sF120)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5170])).
% 21.36/3.56 thf(f5196,plain,(
% 21.36/3.56 ($false = ((upairequniteq => sF119)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1371,f5186])).
% 21.36/3.56 thf(f5203,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => (Y2 = Y0)))))))) => sF119)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f5196,f1010])).
% 21.36/3.56 thf(f5204,plain,(
% 21.36/3.56 ($false = sF119)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5203])).
% 21.36/3.56 thf(f5214,plain,(
% 21.36/3.56 ($false = ((setukpairinjR2 => sF118)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1370,f5204])).
% 21.36/3.56 thf(f5221,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y3 = Y1)))))))))) => sF118)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5214,f1052])).
% 21.36/3.56 thf(f5248,plain,(
% 21.36/3.56 ($false = sF118)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5221])).
% 21.36/3.56 thf(f5260,plain,(
% 21.36/3.56 ($false = ((setukpairinjR => sF117)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1368,f5248])).
% 21.36/3.56 thf(f5261,plain,(
% 21.36/3.56 ($false = ((setukpairinjR => (ksndsingleton => sF116))))),
% 21.36/3.56 inference(forward_demodulation,[],[f5260,f1367])).
% 21.36/3.56 thf(f5264,plain,(
% 21.36/3.56 ($false = sF116) | ($false = ((setukpairinjR => (ksndsingleton => $true))))),
% 21.36/3.56 inference(superposition,[],[f5261,f1165])).
% 21.36/3.56 thf(f5271,plain,(
% 21.36/3.56 ($false = ((setukpairinjR => $true))) | ($false = sF116)),
% 21.36/3.56 inference(boolean_simplification,[],[f5264])).
% 21.36/3.56 thf(f5272,plain,(
% 21.36/3.56 ($false = sF116) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5271])).
% 21.36/3.56 thf(f5273,plain,(
% 21.36/3.56 ($false = sF116)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5272])).
% 21.36/3.56 thf(f5282,plain,(
% 21.36/3.56 ($false = ((ksndpairEq => sF115)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1366,f5273])).
% 21.36/3.56 thf(f5294,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1))))) => sF115)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5282,f1093])).
% 21.36/3.56 thf(f5299,plain,(
% 21.36/3.56 ($false = sF115)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5294])).
% 21.36/3.56 thf(f5309,plain,(
% 21.36/3.56 ($false = ((kpairsurjEq => sF114)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1365,f5299])).
% 21.36/3.56 thf(f5318,plain,(
% 21.36/3.56 ($false = sF114) | (((kpairsurjEq => $true)) = $false)),
% 21.36/3.56 inference(superposition,[],[f5309,f1165])).
% 21.36/3.56 thf(f5322,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF114)),
% 21.36/3.56 inference(boolean_simplification,[],[f5318])).
% 21.36/3.56 thf(f5323,plain,(
% 21.36/3.56 ($false = sF114)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5322])).
% 21.36/3.56 thf(f5326,plain,(
% 21.36/3.56 ($false = ((cartprodsndin => sF113)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1363,f5323])).
% 21.36/3.56 thf(f5331,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))) => sF113)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f5326,f1005])).
% 21.36/3.56 thf(f5339,plain,(
% 21.36/3.56 ($false = sF113)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5331])).
% 21.36/3.56 thf(f5349,plain,(
% 21.36/3.56 (((cartprodpairmemEL => sF112)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1362,f5339])).
% 21.36/3.56 thf(f5358,plain,(
% 21.36/3.56 ($false = ((cartprodpairmemEL => $true))) | ($false = sF112)),
% 21.36/3.56 inference(superposition,[],[f5349,f1165])).
% 21.36/3.56 thf(f5362,plain,(
% 21.36/3.56 ($false = sF112) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5358])).
% 21.36/3.56 thf(f5363,plain,(
% 21.36/3.56 ($false = sF112)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5362])).
% 21.36/3.56 thf(f5366,plain,(
% 21.36/3.56 ($false = ((cartprodpairmemER => sF111)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1360,f5363])).
% 21.36/3.56 thf(f5369,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y2) @ (cartprod @ Y3 @ Y0)) => (in @ Y2 @ Y0)))))))))) => sF111)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5366,f1110])).
% 21.36/3.56 thf(f5406,plain,(
% 21.36/3.56 (sF111 = $false)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5369])).
% 21.36/3.56 thf(f5416,plain,(
% 21.36/3.56 ($false = ((cartprodmempaircEq => sF110)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1358,f5406])).
% 21.36/3.56 thf(f5421,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF110)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5416,f1682])).
% 21.36/3.56 thf(f5424,plain,(
% 21.36/3.56 ($false = sF110)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5421])).
% 21.36/3.56 thf(f5438,plain,(
% 21.36/3.56 ($false = ((cartprodfstpairEq => sF109)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1357,f5424])).
% 21.36/3.56 thf(f5441,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => sF109)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f5438,f1149])).
% 21.36/3.56 thf(f5442,plain,(
% 21.36/3.56 ($false = sF109)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5441])).
% 21.36/3.56 thf(f5456,plain,(
% 21.36/3.56 ($false = ((cartprodsndpairEq => sF108)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1356,f5442])).
% 21.36/3.56 thf(f5459,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))) => sF108)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5456,f926])).
% 21.36/3.56 thf(f5464,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))) => $true))) | ($false = sF108)),
% 21.36/3.56 inference(superposition,[],[f5459,f1165])).
% 21.36/3.56 thf(f5467,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF108)),
% 21.36/3.56 inference(boolean_simplification,[],[f5464])).
% 21.36/3.56 thf(f5468,plain,(
% 21.36/3.56 ($false = sF108)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5467])).
% 21.36/3.56 thf(f5472,plain,(
% 21.36/3.56 ($false = ((cartprodpairsurjEq => sF107)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1355,f5468])).
% 21.36/3.56 thf(f5479,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))))) => sF107)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5472,f1100])).
% 21.36/3.56 thf(f5484,plain,(
% 21.36/3.56 ($false = sF107) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f5479,f1165])).
% 21.36/3.56 thf(f5488,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF107)),
% 21.36/3.56 inference(boolean_simplification,[],[f5484])).
% 21.36/3.56 thf(f5489,plain,(
% 21.36/3.56 ($false = sF107)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5488])).
% 21.36/3.56 thf(f5492,plain,(
% 21.36/3.56 (((dpsetconstrI => sF106)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1354,f5489])).
% 21.36/3.56 thf(f5497,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ Y1))))))))))))))) => sF106)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5492,f1685])).
% 21.36/3.56 thf(f5502,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ Y1))))))))))))))) => $true)) = $false) | ($false = sF106)),
% 21.36/3.56 inference(superposition,[],[f5497,f1165])).
% 21.36/3.56 thf(f5507,plain,(
% 21.36/3.56 ($false = sF106) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5502])).
% 21.36/3.56 thf(f5508,plain,(
% 21.36/3.56 ($false = sF106)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5507])).
% 21.36/3.56 thf(f5514,plain,(
% 21.36/3.56 (((dpsetconstrSub => sF105)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1352,f5508])).
% 21.36/3.56 thf(f5515,plain,(
% 21.36/3.56 ($false = sF105)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5514])).
% 21.36/3.56 thf(f5527,plain,(
% 21.36/3.56 ($false = ((setOfPairsIsBReln => sF104)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1350,f5515])).
% 21.36/3.56 thf(f5528,plain,(
% 21.36/3.56 ($false = ((setOfPairsIsBReln => (dpsetconstrERa => sF103))))),
% 21.36/3.56 inference(forward_demodulation,[],[f5527,f1348])).
% 21.36/3.56 thf(f5531,plain,(
% 21.36/3.56 ($false = sF103) | ($false = ((setOfPairsIsBReln => (dpsetconstrERa => $true))))),
% 21.36/3.56 inference(superposition,[],[f5528,f1165])).
% 21.36/3.56 thf(f5536,plain,(
% 21.36/3.56 ($false = sF103) | ($false = ((setOfPairsIsBReln => $true)))),
% 21.36/3.56 inference(boolean_simplification,[],[f5531])).
% 21.36/3.56 thf(f5537,plain,(
% 21.36/3.56 ($false = sF103) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5536])).
% 21.36/3.56 thf(f5538,plain,(
% 21.36/3.56 ($false = sF103)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5537])).
% 21.36/3.56 thf(f5546,plain,(
% 21.36/3.56 ($false = ((dpsetconstrEL1 => sF102)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1347,f5538])).
% 21.36/3.56 thf(f5562,plain,(
% 21.36/3.56 ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y3)))))))))))) => sF102)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5546,f1629])).
% 21.36/3.56 thf(f5598,plain,(
% 21.36/3.56 ($false = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y3)))))))))))) => $true))) | ($false = sF102)),
% 21.36/3.56 inference(superposition,[],[f5562,f1165])).
% 21.36/3.56 thf(f5603,plain,(
% 21.36/3.56 ($false = sF102) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5598])).
% 21.36/3.56 thf(f5604,plain,(
% 21.36/3.56 ($false = sF102)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5603])).
% 21.36/3.56 thf(f5612,plain,(
% 21.36/3.56 ($false = ((dpsetconstrEL2 => sF101)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1346,f5604])).
% 21.36/3.56 thf(f5613,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ Y1 @ Y3 @ Y4)) => (in @ Y2 @ Y3)))))))))))) => sF101)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5612,f1665])).
% 21.36/3.56 thf(f5614,plain,(
% 21.36/3.56 ($false = sF101)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5613])).
% 21.36/3.56 thf(f5624,plain,(
% 21.36/3.56 ($false = ((dpsetconstrER => sF100)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1345,f5614])).
% 21.36/3.56 thf(f5633,plain,(
% 21.36/3.56 ($false = sF100)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5624])).
% 21.36/3.56 thf(f5647,plain,(
% 21.36/3.56 (((funcImageSingleton => sF99)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1343,f5633])).
% 21.36/3.56 thf(f5650,plain,(
% 21.36/3.56 ($false = ((funcImageSingleton => $true))) | (sF99 = $false)),
% 21.36/3.56 inference(superposition,[],[f5647,f1165])).
% 21.36/3.56 thf(f5655,plain,(
% 21.36/3.56 ($false = $true) | (sF99 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f5650])).
% 21.36/3.56 thf(f5656,plain,(
% 21.36/3.56 (sF99 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5655])).
% 21.36/3.56 thf(f5664,plain,(
% 21.36/3.56 ($false = ((apProp => sF98)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1341,f5656])).
% 21.36/3.56 thf(f5665,plain,(
% 21.36/3.56 ($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 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2))))))))))) => sF98)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5664,f1157])).
% 21.36/3.56 thf(f5702,plain,(
% 21.36/3.56 ($false = sF98)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5665])).
% 21.36/3.56 thf(f5714,plain,(
% 21.36/3.56 (((app => sF97)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1340,f5702])).
% 21.36/3.56 thf(f5717,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y1 @ Y0 @ Y3) @ Y1))))))))))) => sF97)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5714,f1138])).
% 21.36/3.56 thf(f5720,plain,(
% 21.36/3.56 ($false = sF97)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5717])).
% 21.36/3.56 thf(f5730,plain,(
% 21.36/3.56 ($false = ((infuncsetfunc => sF96)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1338,f5720])).
% 21.36/3.56 thf(f5741,plain,(
% 21.36/3.56 ($false = sF96) | ($false = ((infuncsetfunc => $true)))),
% 21.36/3.56 inference(superposition,[],[f5730,f1165])).
% 21.36/3.56 thf(f5744,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF96)),
% 21.36/3.56 inference(boolean_simplification,[],[f5741])).
% 21.36/3.56 thf(f5745,plain,(
% 21.36/3.56 ($false = sF96)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5744])).
% 21.36/3.56 thf(f5749,plain,(
% 21.36/3.56 ($false = ((ap2p => sF95)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1337,f5745])).
% 21.36/3.56 thf(f5754,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y2 @ Y1 @ Y3) @ Y2))))))))))) => sF95)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5749,f945])).
% 21.36/3.56 thf(f5770,plain,(
% 21.36/3.56 ($false = sF95)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5754])).
% 21.36/3.56 thf(f5782,plain,(
% 21.36/3.56 ($false = ((funcinfuncset => sF94)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1335,f5770])).
% 21.36/3.56 thf(f5785,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (in @ Y1 @ (funcSet @ Y2 @ Y0))))))))) => sF94)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5782,f943])).
% 21.36/3.56 thf(f5822,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (in @ Y1 @ (funcSet @ Y2 @ Y0))))))))) => $true))) | ($false = sF94)),
% 21.36/3.56 inference(superposition,[],[f5785,f1165])).
% 21.36/3.56 thf(f5825,plain,(
% 21.36/3.56 ($false = sF94) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5822])).
% 21.36/3.56 thf(f5826,plain,(
% 21.36/3.56 ($false = sF94)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5825])).
% 21.36/3.56 thf(f5830,plain,(
% 21.36/3.56 ($false = ((lamProp => sF93)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1334,f5826])).
% 21.36/3.56 thf(f5835,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (func @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (Y2 @ Y3)))))))))))) => sF93)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5830,f1675])).
% 21.36/3.56 thf(f5840,plain,(
% 21.36/3.56 ($false = sF93)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5835])).
% 21.36/3.56 thf(f5850,plain,(
% 21.36/3.56 ($false = ((lamp => sF92)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1333,f5840])).
% 21.36/3.56 thf(f5857,plain,(
% 21.36/3.56 ((((!! @ $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))))))))) => sF92)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f5850,f1651])).
% 21.36/3.56 thf(f5862,plain,(
% 21.36/3.56 ($false = sF92) | ((((!! @ $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)) = $false)),
% 21.36/3.56 inference(superposition,[],[f5857,f1165])).
% 21.36/3.56 thf(f5865,plain,(
% 21.36/3.56 ($false = sF92) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5862])).
% 21.36/3.56 thf(f5866,plain,(
% 21.36/3.56 ($false = sF92)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5865])).
% 21.36/3.56 thf(f5870,plain,(
% 21.36/3.56 ($false = ((lam2p => sF91)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1332,f5866])).
% 21.36/3.56 thf(f5875,plain,(
% 21.36/3.56 (((lam2p => (brelnall1 => sF90))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f5870,f1330])).
% 21.36/3.56 thf(f5882,plain,(
% 21.36/3.56 (((lam2p => (brelnall1 => $true))) = $false) | (sF90 = $false)),
% 21.36/3.56 inference(superposition,[],[f5875,f1165])).
% 21.36/3.56 thf(f5888,plain,(
% 21.36/3.56 (sF90 = $false) | ($false = ((lam2p => $true)))),
% 21.36/3.56 inference(boolean_simplification,[],[f5882])).
% 21.36/3.56 thf(f5889,plain,(
% 21.36/3.56 ($false = $true) | (sF90 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f5888])).
% 21.36/3.56 thf(f5890,plain,(
% 21.36/3.56 (sF90 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5889])).
% 21.36/3.56 thf(f5898,plain,(
% 21.36/3.56 ($false = ((brelnall2 => sF89)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1328,f5890])).
% 21.36/3.56 thf(f5911,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y1 @ Y0)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))) => sF89)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5898,f1659])).
% 21.36/3.56 thf(f5967,plain,(
% 21.36/3.56 ($false = sF89) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y1 @ Y0)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))) => $true)) = $false)),
% 21.36/3.56 inference(superposition,[],[f5911,f1165])).
% 21.36/3.56 thf(f5970,plain,(
% 21.36/3.56 ($false = sF89) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5967])).
% 21.36/3.56 thf(f5971,plain,(
% 21.36/3.56 ($false = sF89)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5970])).
% 21.36/3.56 thf(f5977,plain,(
% 21.36/3.56 ($false = ((ex1E2 => sF88)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1327,f5971])).
% 21.36/3.56 thf(f5980,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => sF88)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f5977,f1638])).
% 21.36/3.56 thf(f5983,plain,(
% 21.36/3.56 ($false = sF88) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f5980,f1165])).
% 21.36/3.56 thf(f5986,plain,(
% 21.36/3.56 ($false = sF88) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f5983])).
% 21.36/3.56 thf(f5987,plain,(
% 21.36/3.56 ($false = sF88)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f5986])).
% 21.36/3.56 thf(f5991,plain,(
% 21.36/3.56 ($false = ((funcGraphProp1 => sF87)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1326,f5987])).
% 21.36/3.56 thf(f5998,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y2 @ Y1 @ Y3)) @ Y1))))))))))) => sF87)))),
% 21.36/3.56 inference(forward_demodulation,[],[f5991,f933])).
% 21.36/3.56 thf(f6001,plain,(
% 21.36/3.56 ($false = sF87)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f5998])).
% 21.36/3.56 thf(f6011,plain,(
% 21.36/3.56 ($false = ((funcGraphProp3 => sF86)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1324,f6001])).
% 21.36/3.56 thf(f6018,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0))))))))))) => sF86)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6011,f1036])).
% 21.36/3.56 thf(f6021,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0))))))))))) => (funcGraphProp2 => sF85))))),
% 21.36/3.56 inference(forward_demodulation,[],[f6018,f1323])).
% 21.36/3.56 thf(f6024,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0))))))))))) => (funcGraphProp2 => $true)))) | (sF85 = $false)),
% 21.36/3.56 inference(superposition,[],[f6021,f1165])).
% 21.36/3.56 thf(f6030,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0))))))))))) => $true))) | (sF85 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f6024])).
% 21.36/3.56 thf(f6031,plain,(
% 21.36/3.56 ($false = $true) | (sF85 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f6030])).
% 21.36/3.56 thf(f6032,plain,(
% 21.36/3.56 (sF85 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6031])).
% 21.36/3.56 thf(f6044,plain,(
% 21.36/3.56 ($false = ((funcextLem => sF84)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1322,f6032])).
% 21.36/3.56 thf(f6062,plain,(
% 21.36/3.56 ($false = ((funcextLem => $true))) | ($false = sF84)),
% 21.36/3.56 inference(superposition,[],[f6044,f1165])).
% 21.36/3.56 thf(f6065,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF84)),
% 21.36/3.56 inference(boolean_simplification,[],[f6062])).
% 21.36/3.56 thf(f6066,plain,(
% 21.36/3.56 ($false = sF84)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6065])).
% 21.36/3.56 thf(f6070,plain,(
% 21.36/3.56 (((funcGraphProp4 => sF83)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1321,f6066])).
% 21.36/3.56 thf(f6075,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))) => sF83)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6070,f1125])).
% 21.36/3.56 thf(f6078,plain,(
% 21.36/3.56 ($false = sF83)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6075])).
% 21.36/3.56 thf(f6088,plain,(
% 21.36/3.56 ($false = ((subbreln => sF82)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1319,f6078])).
% 21.36/3.56 thf(f6093,plain,(
% 21.36/3.56 (sF82 = $false)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6088])).
% 21.36/3.56 thf(f6105,plain,(
% 21.36/3.56 ($false = ((eqbreln => sF81)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1317,f6093])).
% 21.36/3.56 thf(f6110,plain,(
% 21.36/3.56 ($false = sF81) | ($false = ((eqbreln => $true)))),
% 21.36/3.56 inference(superposition,[],[f6105,f1165])).
% 21.36/3.56 thf(f6113,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF81)),
% 21.36/3.56 inference(boolean_simplification,[],[f6110])).
% 21.36/3.56 thf(f6114,plain,(
% 21.36/3.56 ($false = sF81)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6113])).
% 21.36/3.56 thf(f6120,plain,(
% 21.36/3.56 ($false = ((funcext => sF80)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1316,f6114])).
% 21.36/3.56 thf(f6123,plain,(
% 21.36/3.56 ($false = sF80)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6120])).
% 21.36/3.56 thf(f6133,plain,(
% 21.36/3.56 ($false = ((funcext2 => sF79)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1314,f6123])).
% 21.36/3.56 thf(f6142,plain,(
% 21.36/3.56 ($false = sF79)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6133])).
% 21.36/3.56 thf(f6158,plain,(
% 21.36/3.56 ($false = ((ap2apEq1 => sF78)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1313,f6142])).
% 21.36/3.56 thf(f6159,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (funcSet @ Y1 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF78)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6158,f1693])).
% 21.36/3.56 thf(f6162,plain,(
% 21.36/3.56 ($false = sF78)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6159])).
% 21.36/3.56 thf(f6172,plain,(
% 21.36/3.56 (((ap2apEq2 => sF77)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1312,f6162])).
% 21.36/3.56 thf(f6177,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF77)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6172,f1670])).
% 21.36/3.56 thf(f6184,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => $true))) | ($false = sF77)),
% 21.36/3.56 inference(superposition,[],[f6177,f1165])).
% 21.36/3.56 thf(f6189,plain,(
% 21.36/3.56 ($false = sF77) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f6184])).
% 21.36/3.56 thf(f6190,plain,(
% 21.36/3.56 ($false = sF77)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6189])).
% 21.36/3.56 thf(f6192,plain,(
% 21.36/3.56 ($false = ((beta1 => sF76)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1310,f6190])).
% 21.36/3.56 thf(f6197,plain,(
% 21.36/3.56 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3) = (Y2 @ Y3)))))))))))) => sF76)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f6192,f1641])).
% 21.36/3.56 thf(f6200,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ Y2) @ Y3) = (Y2 @ Y3)))))))))))) => $true))) | ($false = sF76)),
% 21.36/3.56 inference(superposition,[],[f6197,f1165])).
% 21.36/3.56 thf(f6205,plain,(
% 21.36/3.56 ($false = sF76) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f6200])).
% 21.36/3.56 thf(f6206,plain,(
% 21.36/3.56 ($false = sF76)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6205])).
% 21.36/3.56 thf(f6212,plain,(
% 21.36/3.56 ($false = ((eta1 => sF75)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1309,f6206])).
% 21.36/3.56 thf(f6213,plain,(
% 21.36/3.56 ($false = ((eta1 => (lam2lamEq => sF74))))),
% 21.36/3.56 inference(forward_demodulation,[],[f6212,f1307])).
% 21.36/3.56 thf(f6214,plain,(
% 21.36/3.56 (((eta1 => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ($true))))))) => sF74))) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f6213,f1658])).
% 21.36/3.56 thf(f6217,plain,(
% 21.36/3.56 ($false = ((eta1 => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ($true))))))) => $true)))) | (sF74 = $false)),
% 21.36/3.56 inference(superposition,[],[f6214,f1165])).
% 21.36/3.56 thf(f6224,plain,(
% 21.36/3.56 (sF74 = $false) | ($false = ((eta1 => $true)))),
% 21.36/3.56 inference(boolean_simplification,[],[f6217])).
% 21.36/3.56 thf(f6225,plain,(
% 21.36/3.56 ($false = $true) | (sF74 = $false)),
% 21.36/3.56 inference(boolean_simplification,[],[f6224])).
% 21.36/3.56 thf(f6226,plain,(
% 21.36/3.56 (sF74 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6225])).
% 21.36/3.56 thf(f6234,plain,(
% 21.36/3.56 ($false = ((beta2 => sF73)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1306,f6226])).
% 21.36/3.56 thf(f6246,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) = (ap @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ Y2) @ Y3)))))))))))) => sF73)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6234,f1640])).
% 21.36/3.56 thf(f6274,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) = (ap @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ Y2) @ Y3)))))))))))) => $true))) | ($false = sF73)),
% 21.36/3.56 inference(superposition,[],[f6246,f1165])).
% 21.36/3.56 thf(f6278,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF73)),
% 21.36/3.56 inference(boolean_simplification,[],[f6274])).
% 21.36/3.56 thf(f6279,plain,(
% 21.36/3.56 ($false = sF73)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6278])).
% 21.36/3.56 thf(f6282,plain,(
% 21.36/3.56 ($false = ((eta2 => sF72)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1305,f6279])).
% 21.36/3.56 thf(f6289,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => ((lam @ Y2 @ Y0 @ (ap @ Y2 @ Y0 @ Y1)) = Y1)))))))) => sF72)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6282,f1634])).
% 21.36/3.56 thf(f6290,plain,(
% 21.36/3.56 ($false = sF72)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6289])).
% 21.36/3.56 thf(f6302,plain,(
% 21.36/3.56 (((iffalseProp1 => sF71)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1304,f6290])).
% 21.36/3.56 thf(f6303,plain,(
% 21.36/3.56 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y0) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((~ Y0) & (Y3 = Y4)) | ((Y1 = Y4) & Y0)))))))))))))))) => sF71)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6302,f1133])).
% 21.36/3.56 thf(f6306,plain,(
% 21.36/3.56 ($false = sF71)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6303])).
% 21.36/3.56 thf(f6320,plain,(
% 21.36/3.56 ($false = ((iffalseProp2 => sF70)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1302,f6306])).
% 21.36/3.56 thf(f6323,plain,(
% 21.36/3.56 ($false = sF70)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6320])).
% 21.36/3.56 thf(f6333,plain,(
% 21.36/3.56 (((iftrueProp1 => sF69)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1300,f6323])).
% 21.36/3.56 thf(f6344,plain,(
% 21.36/3.56 ($false = sF69) | ($false = ((iftrueProp1 => $true)))),
% 21.36/3.56 inference(superposition,[],[f6333,f1165])).
% 21.36/3.56 thf(f6349,plain,(
% 21.36/3.56 ($false = sF69) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f6344])).
% 21.36/3.56 thf(f6350,plain,(
% 21.36/3.56 ($false = sF69)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6349])).
% 21.36/3.56 thf(f6356,plain,(
% 21.36/3.56 ($false = ((iftrueProp2 => sF68)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1298,f6350])).
% 21.36/3.56 thf(f6357,plain,(
% 21.36/3.56 ($false = sF68)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6356])).
% 21.36/3.56 thf(f6367,plain,(
% 21.36/3.56 ($false = ((ifSingleton => sF67)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1297,f6357])).
% 21.36/3.56 thf(f6374,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2)))))))))))))))) => sF67)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6367,f1064])).
% 21.36/3.56 thf(f6379,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y1 = Y4) & Y2) | ((Y3 = Y4) & (~ Y2)))))))))))))))) => $true))) | ($false = sF67)),
% 21.36/3.56 inference(superposition,[],[f6374,f1165])).
% 21.36/3.56 thf(f6383,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF67)),
% 21.36/3.56 inference(boolean_simplification,[],[f6379])).
% 21.36/3.56 thf(f6384,plain,(
% 21.36/3.56 ($false = sF67)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6383])).
% 21.36/3.56 thf(f6387,plain,(
% 21.36/3.56 ($false = ((ifp => sF66)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1295,f6384])).
% 21.36/3.56 thf(f6394,plain,(
% 21.36/3.56 ($false = sF66)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6387])).
% 21.36/3.56 thf(f6404,plain,(
% 21.36/3.56 ($false = ((theeq => sF65)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1293,f6394])).
% 21.36/3.56 thf(f6409,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1))))))) => sF65)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6404,f1109])).
% 21.36/3.56 thf(f6418,plain,(
% 21.36/3.56 (sF65 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1))))))) => $true)))),
% 21.36/3.56 inference(superposition,[],[f6409,f1165])).
% 21.36/3.56 thf(f6421,plain,(
% 21.36/3.56 (sF65 = $false) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f6418])).
% 21.36/3.56 thf(f6422,plain,(
% 21.36/3.56 (sF65 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6421])).
% 21.36/3.56 thf(f6426,plain,(
% 21.36/3.56 ($false = ((iftrue => sF64)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1292,f6422])).
% 21.36/3.56 thf(f6431,plain,(
% 21.36/3.56 ((((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y0 => ((if @ Y1 @ Y0 @ Y2 @ Y3) = Y2)))))))))))) => sF64)) = $false)),
% 21.36/3.56 inference(forward_demodulation,[],[f6426,f1079])).
% 21.36/3.56 thf(f6451,plain,(
% 21.36/3.56 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y0 => ((if @ Y1 @ Y0 @ Y2 @ Y3) = Y2)))))))))))) => $true))) | (sF64 = $false)),
% 21.36/3.56 inference(superposition,[],[f6431,f1165])).
% 21.36/3.56 thf(f6455,plain,(
% 21.36/3.56 (sF64 = $false) | ($false = $true)),
% 21.36/3.56 inference(boolean_simplification,[],[f6451])).
% 21.36/3.56 thf(f6456,plain,(
% 21.36/3.56 (sF64 = $false)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6455])).
% 21.36/3.56 thf(f6463,plain,(
% 21.36/3.56 ($false = ((iffalse => sF63)))),
% 21.36/3.56 inference(backward_demodulation,[],[f1291,f6456])).
% 21.36/3.56 thf(f6470,plain,(
% 21.36/3.56 ($false = sF63) | ($false = ((iffalse => $true)))),
% 21.36/3.56 inference(superposition,[],[f6463,f1165])).
% 21.36/3.56 thf(f6473,plain,(
% 21.36/3.56 ($false = $true) | ($false = sF63)),
% 21.36/3.56 inference(boolean_simplification,[],[f6470])).
% 21.36/3.56 thf(f6474,plain,(
% 21.36/3.56 ($false = sF63)),
% 21.36/3.56 inference(trivial_inequality_removal,[],[f6473])).
% 21.36/3.56 thf(f6478,plain,(
% 21.36/3.56 (((iftrueorfalse => sF62)) = $false)),
% 21.36/3.56 inference(backward_demodulation,[],[f1290,f6474])).
% 21.36/3.56 thf(f6485,plain,(
% 21.36/3.56 ($false = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (if @ Y1 @ Y0 @ Y2 @ Y3) @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset))))))))))))) => sF62)))),
% 21.36/3.56 inference(forward_demodulation,[],[f6478,f1009])).
% 21.36/3.56 thf(f6503,plain,(
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% 21.36/3.56 inference(superposition,[],[f6485,f1165])).
% 21.36/3.56 thf(f6507,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f6503])).
% 21.36/3.56 thf(f6508,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f6507])).
% 21.36/3.56 thf(f6511,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1288,f6508])).
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% 21.36/3.56 inference(forward_demodulation,[],[f6511,f1162])).
% 21.36/3.56 thf(f6519,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f6518,f1286])).
% 21.36/3.56 thf(f6522,plain,(
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% 21.36/3.56 inference(superposition,[],[f6519,f1165])).
% 21.36/3.56 thf(f6528,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ Y1)))))))))) => $true))) | ($false = sF60)),
% 21.36/3.56 inference(boolean_simplification,[],[f6522])).
% 21.36/3.56 thf(f6529,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f6528])).
% 21.36/3.56 thf(f6530,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f6529])).
% 21.36/3.56 thf(f6537,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1284,f6530])).
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% 21.36/3.56 inference(forward_demodulation,[],[f6537,f1073])).
% 21.36/3.56 thf(f6557,plain,(
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% 21.36/3.56 inference(imp_proxy_clausification,[],[f6551])).
% 21.36/3.56 thf(f6573,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1283,f6557])).
% 21.36/3.56 thf(f6574,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f6573,f929])).
% 21.36/3.56 thf(f6575,plain,(
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% 21.36/3.56 inference(imp_proxy_clausification,[],[f6574])).
% 21.36/3.56 thf(f6587,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1281,f6575])).
% 21.36/3.56 thf(f6590,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f6587,f1142])).
% 21.36/3.56 thf(f6593,plain,(
% 21.36/3.56 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ Y0))))))) => $true))) | ($false = sF57)),
% 21.36/3.56 inference(superposition,[],[f6590,f1165])).
% 21.36/3.56 thf(f6597,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f6593])).
% 21.36/3.56 thf(f6598,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f6597])).
% 21.36/3.56 thf(f6605,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1280,f6598])).
% 21.36/3.56 thf(f6608,plain,(
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% 21.36/3.56 inference(superposition,[],[f6605,f1165])).
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% 21.36/3.56 thf(f6612,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f6611])).
% 21.36/3.56 thf(f6616,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1278,f6612])).
% 21.36/3.56 thf(f6621,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f6616,f1276])).
% 21.36/3.56 thf(f6628,plain,(
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% 21.36/3.56 inference(superposition,[],[f6621,f1165])).
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% 21.36/3.56 inference(boolean_simplification,[],[f6628])).
% 21.36/3.56 thf(f6637,plain,(
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% 21.36/3.56 inference(boolean_simplification,[],[f6636])).
% 21.36/3.56 thf(f6638,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f6637])).
% 21.36/3.56 thf(f6649,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1275,f6638])).
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% 21.36/3.56 inference(forward_demodulation,[],[f6649,f974])).
% 21.36/3.56 thf(f6672,plain,(
% 21.36/3.56 (sF53 = $false)),
% 21.36/3.56 inference(imp_proxy_clausification,[],[f6659])).
% 21.36/3.56 thf(f6686,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1273,f6672])).
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% 21.36/3.56 inference(forward_demodulation,[],[f6686,f932])).
% 21.36/3.56 thf(f6688,plain,(
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% 21.36/3.56 inference(imp_proxy_clausification,[],[f6687])).
% 21.36/3.56 thf(f6698,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1272,f6688])).
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% 21.36/3.56 inference(forward_demodulation,[],[f6698,f1270])).
% 21.36/3.56 thf(f6708,plain,(
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% 21.36/3.56 inference(superposition,[],[f6703,f1165])).
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% 21.36/3.56 inference(boolean_simplification,[],[f6708])).
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% 21.36/3.56 thf(f6716,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f6715])).
% 21.36/3.56 thf(f6724,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1269,f6716])).
% 21.36/3.56 thf(f6737,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f6724,f1268])).
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% 21.36/3.56 inference(superposition,[],[f6737,f1165])).
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% 21.36/3.56 inference(boolean_simplification,[],[f6751])).
% 21.36/3.56 thf(f6761,plain,(
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% 21.36/3.56 thf(f6762,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f6761])).
% 21.36/3.56 thf(f6773,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1266,f6762])).
% 21.36/3.56 thf(f6783,plain,(
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% 21.36/3.56 inference(imp_proxy_clausification,[],[f6773])).
% 21.36/3.56 thf(f6795,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1265,f6783])).
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% 21.36/3.56 inference(forward_demodulation,[],[f6795,f937])).
% 21.36/3.56 thf(f6808,plain,(
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% 21.36/3.56 inference(imp_proxy_clausification,[],[f6798])).
% 21.36/3.56 thf(f6818,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1263,f6808])).
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% 21.36/3.56 inference(superposition,[],[f6818,f1165])).
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% 21.36/3.56 thf(f6829,plain,(
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% 21.36/3.56 inference(trivial_inequality_removal,[],[f6828])).
% 21.36/3.56 thf(f6833,plain,(
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% 21.36/3.56 inference(backward_demodulation,[],[f1261,f6829])).
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% 21.36/3.56 inference(forward_demodulation,[],[f6833,f1024])).
% 21.36/3.56 thf(f6852,plain,(
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% 21.36/3.56 inference(imp_proxy_clausification,[],[f6838])).
% 21.36/3.56 thf(f6862,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f6862,f950])).
% 21.36/3.56 thf(f6868,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f6865,f1259])).
% 21.36/3.56 thf(f6873,plain,(
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% 21.36/3.56 inference(superposition,[],[f6868,f1165])).
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% 21.36/3.56 inference(boolean_simplification,[],[f6873])).
% 21.36/3.56 thf(f6880,plain,(
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% 21.36/3.56 inference(forward_demodulation,[],[f6887,f944])).
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% 21.36/3.56 inference(superposition,[],[f6902,f1165])).
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% 21.36/3.56 inference(forward_demodulation,[],[f6918,f1046])).
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% 21.36/3.57 inference(forward_demodulation,[],[f6934,f951])).
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% 21.36/3.57 inference(backward_demodulation,[],[f1252,f6981])).
% 21.36/3.57 thf(f6990,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))) => sF37)))),
% 21.36/3.57 inference(forward_demodulation,[],[f6987,f1017])).
% 21.36/3.57 thf(f6991,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))) => (complementInPowersetComplementIntersect => sF36))))),
% 21.36/3.57 inference(forward_demodulation,[],[f6990,f1251])).
% 21.36/3.57 thf(f6992,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))) => ((!! @ $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)))))))))))) => sF36))))),
% 21.36/3.57 inference(forward_demodulation,[],[f6991,f1038])).
% 21.36/3.57 thf(f7101,plain,(
% 21.36/3.57 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))) => ((!! @ $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))) = $false) | ($false = sF36)),
% 21.36/3.57 inference(superposition,[],[f6992,f1165])).
% 21.36/3.57 thf(f7107,plain,(
% 21.36/3.57 ($false = sF36) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))) => $true)))),
% 21.36/3.57 inference(boolean_simplification,[],[f7101])).
% 21.36/3.57 thf(f7108,plain,(
% 21.36/3.57 ($false = $true) | ($false = sF36)),
% 21.36/3.57 inference(boolean_simplification,[],[f7107])).
% 21.36/3.57 thf(f7109,plain,(
% 21.36/3.57 ($false = sF36)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7108])).
% 21.36/3.57 thf(f7119,plain,(
% 21.36/3.57 ($false = ((contraSubsetComplement => sF35)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1250,f7109])).
% 21.36/3.57 thf(f7135,plain,(
% 21.36/3.57 ($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 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y2) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))))) => sF35)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7119,f885])).
% 21.36/3.57 thf(f7143,plain,(
% 21.36/3.57 ($false = sF35) | ($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))))))))))))))) => $true)))),
% 21.36/3.57 inference(superposition,[],[f7135,f1165])).
% 21.36/3.57 thf(f7146,plain,(
% 21.36/3.57 ($false = sF35) | ($false = $true)),
% 21.36/3.57 inference(boolean_simplification,[],[f7143])).
% 21.36/3.57 thf(f7147,plain,(
% 21.36/3.57 ($false = sF35)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7146])).
% 21.36/3.57 thf(f7151,plain,(
% 21.36/3.57 ($false = ((complementTcontraSubset => sF34)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1249,f7147])).
% 21.36/3.57 thf(f7156,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((subset @ Y0 @ (setminus @ Y1 @ Y2)) => (subset @ Y2 @ (setminus @ Y1 @ Y0))))))))))) => sF34)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7151,f1159])).
% 21.36/3.57 thf(f7161,plain,(
% 21.36/3.57 ($false = ((woz1_4 => sF34)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7156,f942])).
% 21.36/3.57 thf(f7162,plain,(
% 21.36/3.57 ($false = sF34)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7161])).
% 21.36/3.57 thf(f7163,plain,(
% 21.36/3.57 (woz1_4 = $true)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7161])).
% 21.36/3.57 thf(f7172,plain,(
% 21.36/3.57 ($false = ((binunionTILcontra => sF33)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1248,f7162])).
% 21.36/3.57 thf(f7176,plain,(
% 21.36/3.57 ((($true => sF5)) = sF6)),
% 21.36/3.57 inference(backward_demodulation,[],[f1201,f7163])).
% 21.36/3.57 thf(f7178,plain,(
% 21.36/3.57 (sF5 = sF6)),
% 21.36/3.57 inference(boolean_simplification,[],[f7176])).
% 21.36/3.57 thf(f7181,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((~ (in @ Y3 @ (binunion @ Y1 @ Y2))) => (~ (in @ Y3 @ Y1)))))))))))))) => sF33)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7172,f969])).
% 21.36/3.57 thf(f7184,plain,(
% 21.36/3.57 (((woz1_5 => sF4)) = sF6)),
% 21.36/3.57 inference(backward_demodulation,[],[f1199,f7178])).
% 21.36/3.57 thf(f7186,plain,(
% 21.36/3.57 ($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)))))))))))))) => (binunionTIRcontra => sF32))))),
% 21.36/3.57 inference(forward_demodulation,[],[f7181,f1246])).
% 21.36/3.57 thf(f7187,plain,(
% 21.36/3.57 (sF6 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ (binunion @ Y1 @ Y2)) @ (powerset @ (setminus @ Y0 @ Y1))))))))))) => sF4)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7184,f1020])).
% 21.36/3.57 thf(f7188,plain,(
% 21.36/3.57 (sF6 = ((complementUnionInPowersetComplement => sF4)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7187,f1146])).
% 21.36/3.57 thf(f7198,plain,(
% 21.36/3.57 ((($true => sF4)) = sF6) | (complementUnionInPowersetComplement = $false)),
% 21.36/3.57 inference(superposition,[],[f7188,f1165])).
% 21.36/3.57 thf(f7201,plain,(
% 21.36/3.57 (sF4 = sF6) | (complementUnionInPowersetComplement = $false)),
% 21.36/3.57 inference(boolean_simplification,[],[f7198])).
% 21.36/3.57 thf(f7218,plain,(
% 21.36/3.57 ($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)))))))))))))) => (binunionTIRcontra => $true)))) | ($false = sF32)),
% 21.36/3.57 inference(superposition,[],[f7186,f1165])).
% 21.36/3.57 thf(f7224,plain,(
% 21.36/3.57 ($false = sF32) | ($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)))))))))))))) => $true)))),
% 21.36/3.57 inference(boolean_simplification,[],[f7218])).
% 21.36/3.57 thf(f7225,plain,(
% 21.36/3.57 ($false = sF32) | ($false = $true)),
% 21.36/3.57 inference(boolean_simplification,[],[f7224])).
% 21.36/3.57 thf(f7226,plain,(
% 21.36/3.57 ($false = sF32)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7225])).
% 21.36/3.57 thf(f7234,plain,(
% 21.36/3.57 ($false = ((inIntersectImpInUnion => sF31)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1244,f7226])).
% 21.36/3.57 thf(f7258,plain,(
% 21.36/3.57 ($false = sF31)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7234])).
% 21.36/3.57 thf(f7268,plain,(
% 21.36/3.57 ($false = ((inIntersectImpInUnion2 => sF30)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1242,f7258])).
% 21.36/3.57 thf(f7279,plain,(
% 21.36/3.57 ($false = sF30) | ($false = ((inIntersectImpInUnion2 => $true)))),
% 21.36/3.57 inference(superposition,[],[f7268,f1165])).
% 21.36/3.57 thf(f7283,plain,(
% 21.36/3.57 ($false = sF30) | ($false = $true)),
% 21.36/3.57 inference(boolean_simplification,[],[f7279])).
% 21.36/3.57 thf(f7284,plain,(
% 21.36/3.57 ($false = sF30)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7283])).
% 21.36/3.57 thf(f7287,plain,(
% 21.36/3.57 ($false = ((inIntersectImpInIntersectUnions => sF29)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1240,f7284])).
% 21.36/3.57 thf(f7296,plain,(
% 21.36/3.57 ($false = sF29)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7287])).
% 21.36/3.57 thf(f7310,plain,(
% 21.36/3.57 ($false = ((intersectInPowersetIntersectUnions => sF28)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1238,f7296])).
% 21.36/3.57 thf(f7312,plain,(
% 21.36/3.57 (intersectInPowersetIntersectUnions = $true)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7310])).
% 21.36/3.57 thf(f7313,plain,(
% 21.36/3.57 ($false = sF28) | (((intersectInPowersetIntersectUnions => $true)) = $false)),
% 21.36/3.57 inference(superposition,[],[f7310,f1165])).
% 21.36/3.57 thf(f7316,plain,(
% 21.36/3.57 ($false = $true) | ($false = sF28)),
% 21.36/3.57 inference(boolean_simplification,[],[f7313])).
% 21.36/3.57 thf(f7317,plain,(
% 21.36/3.57 ($false = sF28)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7316])).
% 21.36/3.57 thf(f7321,plain,(
% 21.36/3.57 ($false = ((inComplementUnionImpNotIn1 => sF27)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1236,f7317])).
% 21.36/3.57 thf(f7325,plain,(
% 21.36/3.57 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3)))))))))))))))))),
% 21.36/3.57 inference(backward_demodulation,[],[f1153,f7312])).
% 21.36/3.57 thf(f7328,plain,(
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% 21.36/3.57 inference(forward_demodulation,[],[f7321,f920])).
% 21.36/3.57 thf(f7331,plain,(
% 21.36/3.57 (woz1_3 = $true)),
% 21.36/3.57 inference(backward_demodulation,[],[f1062,f7325])).
% 21.36/3.57 thf(f7332,plain,(
% 21.36/3.57 (sF7 = (($true => sF6)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1202,f7331])).
% 21.36/3.57 thf(f7333,plain,(
% 21.36/3.57 (sF6 = sF7)),
% 21.36/3.57 inference(boolean_simplification,[],[f7332])).
% 21.36/3.57 thf(f7334,plain,(
% 21.36/3.57 (sF4 = sF7) | (complementUnionInPowersetComplement = $false)),
% 21.36/3.57 inference(backward_demodulation,[],[f7201,f7333])).
% 21.36/3.57 thf(f7371,plain,(
% 21.36/3.57 (sF27 = $false) | ($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 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0)))))))))))))) => $true)))),
% 21.36/3.57 inference(superposition,[],[f7328,f1165])).
% 21.36/3.57 thf(f7375,plain,(
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% 21.36/3.57 inference(boolean_simplification,[],[f7371])).
% 21.36/3.57 thf(f7376,plain,(
% 21.36/3.57 (sF27 = $false)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7375])).
% 21.36/3.57 thf(f7379,plain,(
% 21.36/3.57 ($false = ((inComplementUnionImpInComplement1 => sF26)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1235,f7376])).
% 21.36/3.57 thf(f7382,plain,(
% 21.36/3.57 ($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 @ (binunion @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ Y0)))))))))))))) => sF26)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7379,f1035])).
% 21.36/3.57 thf(f7385,plain,(
% 21.36/3.57 (((demorgan2a1 => sF26)) = $false)),
% 21.36/3.57 inference(forward_demodulation,[],[f7382,f877])).
% 21.36/3.57 thf(f7389,plain,(
% 21.36/3.57 (demorgan2a1 = $true)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7385])).
% 21.36/3.57 thf(f7390,plain,(
% 21.36/3.57 ($false = ((demorgan2a1 => $true))) | ($false = sF26)),
% 21.36/3.57 inference(superposition,[],[f7385,f1165])).
% 21.36/3.57 thf(f7394,plain,(
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% 21.36/3.57 inference(boolean_simplification,[],[f7390])).
% 21.36/3.57 thf(f7395,plain,(
% 21.36/3.57 ($false = sF26)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7394])).
% 21.36/3.57 thf(f7398,plain,(
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% 21.36/3.57 inference(backward_demodulation,[],[f1234,f7395])).
% 21.36/3.57 thf(f7401,plain,(
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% 21.36/3.57 inference(backward_demodulation,[],[f1230,f7389])).
% 21.36/3.57 thf(f7402,plain,(
% 21.36/3.57 (sF24 = sF23)),
% 21.36/3.57 inference(boolean_simplification,[],[f7401])).
% 21.36/3.57 thf(f7403,plain,(
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% 21.36/3.57 inference(forward_demodulation,[],[f7398,f1232])).
% 21.36/3.57 thf(f7406,plain,(
% 21.36/3.57 (sF24 = ((complementUnionInPowersetComplement => sF22)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1228,f7402])).
% 21.36/3.57 thf(f7416,plain,(
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% 21.36/3.57 inference(superposition,[],[f7406,f1165])).
% 21.36/3.57 thf(f7419,plain,(
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% 21.36/3.57 inference(boolean_simplification,[],[f7416])).
% 21.36/3.57 thf(f7426,plain,(
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% 21.36/3.57 inference(superposition,[],[f7403,f1165])).
% 21.36/3.57 thf(f7432,plain,(
% 21.36/3.57 (sF24 = $false) | (((binunionTE => $true)) = $false)),
% 21.36/3.57 inference(boolean_simplification,[],[f7426])).
% 21.36/3.57 thf(f7433,plain,(
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% 21.36/3.57 inference(boolean_simplification,[],[f7432])).
% 21.36/3.57 thf(f7434,plain,(
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% 21.36/3.57 inference(trivial_inequality_removal,[],[f7433])).
% 21.36/3.57 thf(f7443,plain,(
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% 21.36/3.57 inference(backward_demodulation,[],[f7406,f7434])).
% 21.36/3.57 thf(f7444,plain,(
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% 21.36/3.57 inference(backward_demodulation,[],[f7419,f7434])).
% 21.36/3.57 thf(f7448,plain,(
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% 21.36/3.57 inference(trivial_inequality_removal,[],[f7444])).
% 21.36/3.57 thf(f7458,plain,(
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% 21.36/3.57 inference(backward_demodulation,[],[f7443,f7448])).
% 21.36/3.57 thf(f7459,plain,(
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% 21.36/3.57 inference(backward_demodulation,[],[f1226,f7448])).
% 21.36/3.57 thf(f7460,plain,(
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% 21.36/3.57 inference(boolean_simplification,[],[f7458])).
% 21.36/3.57 thf(f7467,plain,(
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% 21.36/3.57 thf(f7473,plain,(
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% 21.36/3.57 inference(backward_demodulation,[],[f7334,f7467])).
% 21.36/3.57 thf(f7477,plain,(
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% 21.36/3.57 inference(trivial_inequality_removal,[],[f7473])).
% 21.36/3.57 thf(f7482,plain,(
% 21.36/3.57 (sF7 = ((breln1all2 => sF3)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1198,f7477])).
% 21.36/3.57 thf(f7484,plain,(
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% 21.36/3.57 inference(imp_proxy_clausification,[],[f7459])).
% 21.36/3.57 thf(f7494,plain,(
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% 21.36/3.57 inference(backward_demodulation,[],[f1224,f7484])).
% 21.36/3.57 thf(f7503,plain,(
% 21.36/3.57 ($false = sF3) | (sF7 = ((breln1all2 => $true)))),
% 21.36/3.57 inference(superposition,[],[f7482,f1165])).
% 21.36/3.57 thf(f7507,plain,(
% 21.36/3.57 ($false = sF3) | ($true = sF7)),
% 21.36/3.57 inference(boolean_simplification,[],[f7503])).
% 21.36/3.57 thf(f7511,plain,(
% 21.36/3.57 (sF20 = $false)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7494])).
% 21.36/3.57 thf(f7525,plain,(
% 21.36/3.57 ($false = ((demorgan1b => sF19)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1222,f7511])).
% 21.36/3.57 thf(f7528,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (binunion @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))))) => sF19)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7525,f966])).
% 21.36/3.57 thf(f7587,plain,(
% 21.36/3.57 ($false = sF19)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7528])).
% 21.36/3.57 thf(f7601,plain,(
% 21.36/3.57 ($false = ((demorgan1 => sF18)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1221,f7587])).
% 21.36/3.57 thf(f7606,plain,(
% 21.36/3.57 ($false = sF18) | ($false = ((demorgan1 => $true)))),
% 21.36/3.57 inference(superposition,[],[f7601,f1165])).
% 21.36/3.57 thf(f7610,plain,(
% 21.36/3.57 ($false = $true) | ($false = sF18)),
% 21.36/3.57 inference(boolean_simplification,[],[f7606])).
% 21.36/3.57 thf(f7611,plain,(
% 21.36/3.57 ($false = sF18)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7610])).
% 21.36/3.57 thf(f7614,plain,(
% 21.36/3.57 ($false = ((demorgan2a => sF17)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1220,f7611])).
% 21.36/3.57 thf(f7623,plain,(
% 21.36/3.57 ($false = sF17)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7614])).
% 21.36/3.57 thf(f7633,plain,(
% 21.36/3.57 ($false = ((demorgan2b2 => sF16)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1218,f7623])).
% 21.36/3.57 thf(f7642,plain,(
% 21.36/3.57 ($false = sF16)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7633])).
% 21.36/3.57 thf(f7652,plain,(
% 21.36/3.57 (((demorgan2b => sF15)) = $false)),
% 21.36/3.57 inference(backward_demodulation,[],[f1216,f7642])).
% 21.36/3.57 thf(f7661,plain,(
% 21.36/3.57 ($false = sF15)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7652])).
% 21.36/3.57 thf(f7671,plain,(
% 21.36/3.57 ($false = ((demorgan2 => sF14)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1214,f7661])).
% 21.36/3.57 thf(f7676,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((setminus @ Y0 @ (binunion @ Y1 @ Y2)) = (binintersect @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))) => sF14)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7671,f1156])).
% 21.36/3.57 thf(f7690,plain,(
% 21.36/3.57 ($false = sF14)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7676])).
% 21.36/3.57 thf(f7702,plain,(
% 21.36/3.57 ($false = ((woz13rule0 => sF13)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1212,f7690])).
% 21.36/3.57 thf(f7705,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y1 @ Y2)) => (in @ Y3 @ Y0)))))))))))) => sF13)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7702,f1006])).
% 21.36/3.57 thf(f7708,plain,(
% 21.36/3.57 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y1 @ Y2)) => (in @ Y3 @ Y0)))))))))))) => $true)) = $false) | ($false = sF13)),
% 21.36/3.57 inference(superposition,[],[f7705,f1165])).
% 21.36/3.57 thf(f7711,plain,(
% 21.36/3.57 ($false = sF13) | ($false = $true)),
% 21.36/3.57 inference(boolean_simplification,[],[f7708])).
% 21.36/3.57 thf(f7712,plain,(
% 21.36/3.57 ($false = sF13)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7711])).
% 21.36/3.57 thf(f7716,plain,(
% 21.36/3.57 ($false = ((woz13rule1 => sF12)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1210,f7712])).
% 21.36/3.57 thf(f7721,plain,(
% 21.36/3.57 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3))))))))))))) => sF12)) = $false)),
% 21.36/3.57 inference(forward_demodulation,[],[f7716,f1105])).
% 21.36/3.57 thf(f7728,plain,(
% 21.36/3.57 ($false = sF12) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3))))))))))))) => $true)))),
% 21.36/3.57 inference(superposition,[],[f7721,f1165])).
% 21.36/3.57 thf(f7732,plain,(
% 21.36/3.57 ($false = sF12) | ($false = $true)),
% 21.36/3.57 inference(boolean_simplification,[],[f7728])).
% 21.36/3.57 thf(f7733,plain,(
% 21.36/3.57 ($false = sF12)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7732])).
% 21.36/3.57 thf(f7736,plain,(
% 21.36/3.57 ($false = ((woz13rule2 => sF11)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1208,f7733])).
% 21.36/3.57 thf(f7741,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3))))))))))))) => sF11)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7736,f957])).
% 21.36/3.57 thf(f7748,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3))))))))))))) => $true))) | ($false = sF11)),
% 21.36/3.57 inference(superposition,[],[f7741,f1165])).
% 21.36/3.57 thf(f7751,plain,(
% 21.36/3.57 ($false = $true) | ($false = sF11)),
% 21.36/3.57 inference(boolean_simplification,[],[f7748])).
% 21.36/3.57 thf(f7752,plain,(
% 21.36/3.57 ($false = sF11)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7751])).
% 21.36/3.57 thf(f7756,plain,(
% 21.36/3.57 ($false = ((woz13rule3 => sF10)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1207,f7752])).
% 21.36/3.57 thf(f7761,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => ((subset @ Y1 @ Y3) => (subset @ Y1 @ (binintersect @ Y2 @ Y3))))))))))))))) => sF10)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7756,f981])).
% 21.36/3.57 thf(f7766,plain,(
% 21.36/3.57 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => ((subset @ Y1 @ Y3) => (subset @ Y1 @ (binintersect @ Y2 @ Y3))))))))))))))) => (woz13rule4 => sF9))) = $false)),
% 21.36/3.57 inference(forward_demodulation,[],[f7761,f1206])).
% 21.36/3.57 thf(f7858,plain,(
% 21.36/3.57 ($false = sF9) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => ((subset @ Y1 @ Y3) => (subset @ Y1 @ (binintersect @ Y2 @ Y3))))))))))))))) => (woz13rule4 => $true))))),
% 21.36/3.57 inference(superposition,[],[f7766,f1165])).
% 21.36/3.57 thf(f7866,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y1 @ Y2) => ((subset @ Y1 @ Y3) => (subset @ Y1 @ (binintersect @ Y2 @ Y3))))))))))))))) => $true))) | ($false = sF9)),
% 21.36/3.57 inference(boolean_simplification,[],[f7858])).
% 21.36/3.57 thf(f7867,plain,(
% 21.36/3.57 ($false = $true) | ($false = sF9)),
% 21.36/3.57 inference(boolean_simplification,[],[f7866])).
% 21.36/3.57 thf(f7868,plain,(
% 21.36/3.57 ($false = sF9)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7867])).
% 21.36/3.57 thf(f7882,plain,(
% 21.36/3.57 ($false = ((woz1_1 => sF8)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1205,f7868])).
% 21.36/3.57 thf(f7896,plain,(
% 21.36/3.57 (sF8 = $false)),
% 21.36/3.57 inference(imp_proxy_clausification,[],[f7882])).
% 21.36/3.57 thf(f7912,plain,(
% 21.36/3.57 ($false = ((woz1_2 => sF7)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1203,f7896])).
% 21.36/3.57 thf(f7915,plain,(
% 21.36/3.57 ($false = ((woz1_2 => $true))) | ($false = sF7)),
% 21.36/3.57 inference(superposition,[],[f7912,f1165])).
% 21.36/3.57 thf(f7918,plain,(
% 21.36/3.57 ($false = sF7) | ($false = $true)),
% 21.36/3.57 inference(boolean_simplification,[],[f7915])).
% 21.36/3.57 thf(f7919,plain,(
% 21.36/3.57 ($false = sF7)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7918])).
% 21.36/3.57 thf(f7925,plain,(
% 21.36/3.57 ($false = ((breln1all2 => sF3)))),
% 21.36/3.57 inference(backward_demodulation,[],[f7482,f7919])).
% 21.36/3.57 thf(f7927,plain,(
% 21.36/3.57 ($false = sF3) | ($false = $true)),
% 21.36/3.57 inference(backward_demodulation,[],[f7507,f7919])).
% 21.36/3.57 thf(f7929,plain,(
% 21.36/3.57 ($false = sF3)),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7927])).
% 21.36/3.57 thf(f7934,plain,(
% 21.36/3.57 ($false = ((breln1SetBreln1 => sF2)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1197,f7929])).
% 21.36/3.57 thf(f7935,plain,(
% 21.36/3.57 (((breln1all2 => $false)) = $false)),
% 21.36/3.57 inference(forward_demodulation,[],[f7925,f7929])).
% 21.36/3.57 thf(f7936,plain,(
% 21.36/3.57 (((~ breln1all2)) = $false)),
% 21.36/3.57 inference(boolean_simplification,[],[f7935])).
% 21.36/3.57 thf(f7939,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (breln1Set @ Y1)) => (subset @ Y0 @ (cartprod @ Y1 @ Y1))))))) => sF2)))),
% 21.36/3.57 inference(forward_demodulation,[],[f7934,f1639])).
% 21.36/3.57 thf(f7944,plain,(
% 21.36/3.57 (breln1all2 = $true)),
% 21.36/3.57 inference(not_proxy_clausification,[],[f7936])).
% 21.36/3.57 thf(f7950,plain,(
% 21.36/3.57 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))))) = $true)),
% 21.36/3.57 inference(backward_demodulation,[],[f1660,f7944])).
% 21.36/3.57 thf(f7952,plain,(
% 21.36/3.57 (sF0 = $true)),
% 21.36/3.57 inference(backward_demodulation,[],[f1677,f7950])).
% 21.36/3.57 thf(f7953,plain,(
% 21.36/3.57 (((setOfPairsIsBReln1 => $true)) = sF1)),
% 21.36/3.57 inference(backward_demodulation,[],[f1194,f7952])).
% 21.36/3.57 thf(f7954,plain,(
% 21.36/3.57 ($true = sF1)),
% 21.36/3.57 inference(boolean_simplification,[],[f7953])).
% 21.36/3.57 thf(f7955,plain,(
% 21.36/3.57 (sF2 = ((choice2fnsingleton => $true)))),
% 21.36/3.57 inference(backward_demodulation,[],[f1196,f7954])).
% 21.36/3.57 thf(f7956,plain,(
% 21.36/3.57 ($true = sF2)),
% 21.36/3.57 inference(boolean_simplification,[],[f7955])).
% 21.36/3.57 thf(f7957,plain,(
% 21.36/3.57 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (breln1Set @ Y1)) => (subset @ Y0 @ (cartprod @ Y1 @ Y1))))))) => $true)))),
% 21.36/3.57 inference(backward_demodulation,[],[f7939,f7956])).
% 21.36/3.57 thf(f7958,plain,(
% 21.36/3.57 ($false = $true)),
% 21.36/3.57 inference(boolean_simplification,[],[f7957])).
% 21.36/3.57 thf(f7959,plain,(
% 21.36/3.57 $false),
% 21.36/3.57 inference(trivial_inequality_removal,[],[f7958])).
% 21.36/3.57 % SZS output end Proof for theBenchmark
% 21.36/3.57 % (1741685)------------------------------
% 21.36/3.57 % (1741685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.36/3.57 % (1741685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.36/3.57 % (1741685)CaDiCaL version: 2.1.3
% 21.36/3.57 % (1741685)Termination reason: Refutation
% 21.36/3.57 % (1741685)Time elapsed: 0.900 s
% 21.36/3.57 % (1741685)Peak memory usage: 20 MB
% 21.36/3.57 % (1741685)Instructions burned: 1010 (million)
% 21.36/3.57 % (1741486)Success in time 3.105 s
% 21.36/3.57 % Vampire exiting
%------------------------------------------------------------------------------