%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU679^1 : 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 : n015.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 08:30:43 AM UTC 2026
% Result : Theorem 13.04s 2.32s
% Output : Refutation 13.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU679^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n015.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 14:11:19 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running higher-order theorem proving
% 0.21/0.30 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
% 0.28/0.46 % (3583392)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.46 % (3583397)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3417876924:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.28/0.46 % (3583399)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3586932726:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.28/0.46 % (3583402)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3436405834:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.28/0.46 % (3583399)Instruction limit reached!
% 0.28/0.46 % (3583399)------------------------------
% 0.28/0.46 % (3583399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.46 % (3583399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.46 % (3583399)CaDiCaL version: 2.1.3
% 0.28/0.46 % (3583399)Termination reason: Instruction limit
% 0.28/0.46 % (3583399)Termination phase: shuffling
% 0.28/0.46 % (3583399)Time elapsed: 0.002 s
% 0.28/0.46 % (3583399)Peak memory usage: 10 MB
% 0.28/0.46 % (3583399)Instructions burned: 3 (million)
% 0.28/0.46 % (3583400)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=1690810778:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.28/0.46 % (3583398)lrs+10_16_si=on:nwc=1.5:random_seed=2167007733:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.28/0.46 % (3583403)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.28/0.46 % (3583403)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.28/0.46 % (3583403)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=1576651576:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.28/0.46 % (3583401)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3829546264:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.28/0.46 % (3583398)Instruction limit reached!
% 0.28/0.46 % (3583398)------------------------------
% 0.28/0.46 % (3583398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.46 % (3583398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.46 % (3583398)CaDiCaL version: 2.1.3
% 0.28/0.46 % (3583398)Termination reason: Instruction limit
% 0.28/0.46 % (3583398)Termination phase: shuffling
% 0.28/0.46 % (3583398)Time elapsed: 0.009 s
% 0.28/0.46 % (3583398)Peak memory usage: 10 MB
% 0.28/0.46 % (3583398)Instructions burned: 19 (million)
% 0.28/0.46 % (3583407)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3642683602:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.28/0.46 % (3583407)Instruction limit reached!
% 0.28/0.46 % (3583407)------------------------------
% 0.28/0.46 % (3583407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.46 % (3583407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.46 % (3583407)CaDiCaL version: 2.1.3
% 0.28/0.46 % (3583407)Termination reason: Instruction limit
% 0.28/0.46 % (3583407)Termination phase: shuffling
% 0.28/0.46 % (3583407)Time elapsed: 0.002 s
% 0.28/0.46 % (3583407)Peak memory usage: 10 MB
% 0.28/0.46 % (3583407)Instructions burned: 3 (million)
% 0.28/0.46 % (3583401)Instruction limit reached!
% 0.28/0.46 % (3583401)------------------------------
% 0.28/0.46 % (3583401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.46 % (3583401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.46 % (3583401)CaDiCaL version: 2.1.3
% 0.28/0.46 % (3583401)Termination reason: Instruction limit
% 0.28/0.46 % (3583401)Termination phase: Property scanning
% 0.28/0.46 % (3583401)Time elapsed: 0.021 s
% 0.28/0.46 % (3583401)Peak memory usage: 10 MB
% 0.28/0.46 % (3583401)Instructions burned: 25 (million)
% 0.28/0.46 % (3583412)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=167686305:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.04/0.49 % (3583412)Instruction limit reached!
% 1.04/0.49 % (3583412)------------------------------
% 1.04/0.49 % (3583412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3583412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3583412)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3583412)Termination reason: Instruction limit
% 1.04/0.49 % (3583412)Termination phase: shuffling
% 1.04/0.49 % (3583412)Time elapsed: 0.003 s
% 1.04/0.49 % (3583412)Peak memory usage: 10 MB
% 1.04/0.49 % (3583412)Instructions burned: 5 (million)
% 1.04/0.49 % (3583414)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.04/0.49 % (3583397)Instruction limit reached!
% 1.04/0.49 % (3583397)------------------------------
% 1.04/0.49 % (3583397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3583397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3583397)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3583397)Termination reason: Instruction limit
% 1.04/0.49 % (3583397)Termination phase: Property scanning
% 1.04/0.49 % (3583397)Time elapsed: 0.042 s
% 1.04/0.49 % (3583397)Peak memory usage: 12 MB
% 1.04/0.49 % (3583397)Instructions burned: 89 (million)
% 1.04/0.49 % (3583414)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=819831406:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.04/0.49 % (3583402)Instruction limit reached!
% 1.04/0.49 % (3583402)------------------------------
% 1.04/0.49 % (3583402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3583402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3583402)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3583402)Termination reason: Instruction limit
% 1.04/0.49 % (3583402)Termination phase: Property scanning
% 1.04/0.49 % (3583402)Time elapsed: 0.045 s
% 1.04/0.49 % (3583402)Peak memory usage: 12 MB
% 1.04/0.49 % (3583402)Instructions burned: 76 (million)
% 1.04/0.49 % (3583403)Instruction limit reached!
% 1.04/0.49 % (3583403)------------------------------
% 1.04/0.49 % (3583403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3583403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3583403)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3583403)Termination reason: Instruction limit
% 1.04/0.49 % (3583403)Termination phase: Saturation
% 1.04/0.49 % (3583403)Time elapsed: 0.037 s
% 1.04/0.49 % (3583403)Peak memory usage: 13 MB
% 1.04/0.49 % (3583403)Instructions burned: 159 (million)
% 1.04/0.49 % (3583414)Instruction limit reached!
% 1.04/0.49 % (3583414)------------------------------
% 1.04/0.49 % (3583414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3583414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3583414)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3583414)Termination reason: Instruction limit
% 1.04/0.49 % (3583414)Termination phase: shuffling
% 1.04/0.49 % (3583414)Time elapsed: 0.004 s
% 1.04/0.49 % (3583414)Peak memory usage: 10 MB
% 1.04/0.49 % (3583414)Instructions burned: 9 (million)
% 1.04/0.49 % (3583415)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4214496196:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.04/0.49 % (3583417)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
% 1.04/0.49 % (3583417)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.04/0.49 % (3583421)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.04/0.49 % (3583417)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=803164726:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.04/0.49 % (3583421)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=3366728150:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.04/0.52 % (3583415)Instruction limit reached!
% 1.04/0.52 % (3583415)------------------------------
% 1.04/0.52 % (3583415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.52 % (3583415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.52 % (3583415)CaDiCaL version: 2.1.3
% 1.04/0.52 % (3583415)Termination reason: Instruction limit
% 1.04/0.52 % (3583415)Termination phase: shuffling
% 1.04/0.52 % (3583415)Time elapsed: 0.006 s
% 1.04/0.52 % (3583415)Peak memory usage: 10 MB
% 1.04/0.52 % (3583415)Instructions burned: 13 (million)
% 1.04/0.52 % (3583421)Instruction limit reached!
% 1.04/0.52 % (3583421)------------------------------
% 1.04/0.52 % (3583421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.52 % (3583421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.52 % (3583421)CaDiCaL version: 2.1.3
% 1.04/0.52 % (3583421)Termination reason: Instruction limit
% 1.04/0.52 % (3583421)Termination phase: shuffling
% 1.04/0.52 % (3583421)Time elapsed: 0.002 s
% 1.04/0.52 % (3583421)Peak memory usage: 10 MB
% 1.04/0.52 % (3583421)Instructions burned: 7 (million)
% 1.04/0.52 % (3583418)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=2393404619:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.04/0.52 % (3583420)lrs+10_1_si=on:cs=on:random_seed=265181027:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.04/0.52 % (3583427)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1012762331:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.04/0.52 % (3583417)Instruction limit reached!
% 1.04/0.52 % (3583417)------------------------------
% 1.04/0.52 % (3583417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.52 % (3583417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.52 % (3583417)CaDiCaL version: 2.1.3
% 1.04/0.52 % (3583417)Termination reason: Instruction limit
% 1.04/0.52 % (3583417)Termination phase: Property scanning
% 1.04/0.52 % (3583417)Time elapsed: 0.013 s
% 1.04/0.52 % (3583417)Peak memory usage: 10 MB
% 1.04/0.52 % (3583417)Instructions burned: 29 (million)
% 1.04/0.52 % (3583420)Instruction limit reached!
% 1.04/0.52 % (3583420)------------------------------
% 1.04/0.52 % (3583420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.52 % (3583420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.52 % (3583420)CaDiCaL version: 2.1.3
% 1.04/0.52 % (3583420)Termination reason: Instruction limit
% 1.04/0.52 % (3583420)Termination phase: shuffling
% 1.04/0.52 % (3583420)Time elapsed: 0.005 s
% 1.04/0.52 % (3583420)Peak memory usage: 10 MB
% 1.04/0.52 % (3583420)Instructions burned: 10 (million)
% 1.04/0.52 % (3583422)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=281233857:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.04/0.52 % (3583426)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1512429947:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.04/0.52 % (3583427)Instruction limit reached!
% 1.04/0.52 % (3583427)------------------------------
% 1.04/0.52 % (3583427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.52 % (3583427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.52 % (3583427)CaDiCaL version: 2.1.3
% 1.04/0.52 % (3583427)Termination reason: Instruction limit
% 1.04/0.52 % (3583427)Termination phase: Preprocessing 2
% 1.04/0.52 % (3583427)Time elapsed: 0.009 s
% 1.04/0.52 % (3583427)Peak memory usage: 11 MB
% 1.04/0.52 % (3583427)Instructions burned: 37 (million)
% 1.04/0.52 % (3583431)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1313292256:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.04/0.52 % (3583435)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2291737347:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.04/0.52 % (3583433)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2090999668:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.04/0.52 % (3583435)Instruction limit reached!
% 1.04/0.52 % (3583435)------------------------------
% 1.84/0.59 % (3583435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.59 % (3583435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.59 % (3583435)CaDiCaL version: 2.1.3
% 1.84/0.59 % (3583435)Termination reason: Instruction limit
% 1.84/0.59 % (3583435)Termination phase: shuffling
% 1.84/0.59 % (3583435)Time elapsed: 0.004 s
% 1.84/0.59 % (3583435)Peak memory usage: 10 MB
% 1.84/0.59 % (3583435)Instructions burned: 18 (million)
% 1.84/0.59 % (3583431)Instruction limit reached!
% 1.84/0.59 % (3583431)------------------------------
% 1.84/0.59 % (3583431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.59 % (3583431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.59 % (3583431)CaDiCaL version: 2.1.3
% 1.84/0.59 % (3583431)Termination reason: Instruction limit
% 1.84/0.59 % (3583431)Termination phase: shuffling
% 1.84/0.59 % (3583431)Time elapsed: 0.008 s
% 1.84/0.59 % (3583431)Peak memory usage: 10 MB
% 1.84/0.59 % (3583431)Instructions burned: 15 (million)
% 1.84/0.59 % (3583418)Instruction limit reached!
% 1.84/0.59 % (3583418)------------------------------
% 1.84/0.59 % (3583418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.59 % (3583418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.59 % (3583418)CaDiCaL version: 2.1.3
% 1.84/0.59 % (3583418)Termination reason: Instruction limit
% 1.84/0.59 % (3583418)Termination phase: Property scanning
% 1.84/0.59 % (3583418)Time elapsed: 0.036 s
% 1.84/0.59 % (3583418)Peak memory usage: 11 MB
% 1.84/0.59 % (3583418)Instructions burned: 88 (million)
% 1.84/0.59 % (3583422)Instruction limit reached!
% 1.84/0.59 % (3583422)------------------------------
% 1.84/0.59 % (3583422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.59 % (3583422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.59 % (3583422)CaDiCaL version: 2.1.3
% 1.84/0.59 % (3583422)Termination reason: Instruction limit
% 1.84/0.59 % (3583422)Termination phase: Preprocessing 3
% 1.84/0.59 % (3583422)Time elapsed: 0.034 s
% 1.84/0.59 % (3583422)Peak memory usage: 11 MB
% 1.84/0.59 % (3583422)Instructions burned: 39 (million)
% 1.84/0.59 % (3583439)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4264289079:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.84/0.59 % (3583439)Instruction limit reached!
% 1.84/0.59 % (3583439)------------------------------
% 1.84/0.59 % (3583439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.59 % (3583439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.59 % (3583439)CaDiCaL version: 2.1.3
% 1.84/0.59 % (3583439)Termination reason: Instruction limit
% 1.84/0.59 % (3583439)Termination phase: shuffling
% 1.84/0.59 % (3583439)Time elapsed: 0.001 s
% 1.84/0.59 % (3583439)Peak memory usage: 10 MB
% 1.84/0.59 % (3583439)Instructions burned: 6 (million)
% 1.84/0.59 % (3583440)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=518623526:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.84/0.59 % (3583444)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.84/0.59 % (3583444)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.84/0.59 % (3583441)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3893680872:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.84/0.59 % (3583444)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=1158332460:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.84/0.59 % (3583444)Instruction limit reached!
% 1.84/0.59 % (3583444)------------------------------
% 1.84/0.59 % (3583444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.84/0.59 % (3583444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/0.59 % (3583444)CaDiCaL version: 2.1.3
% 1.84/0.59 % (3583444)Termination reason: Instruction limit
% 1.84/0.59 % (3583444)Termination phase: shuffling
% 1.84/0.59 % (3583444)Time elapsed: 0.004 s
% 2.15/0.67 % (3583444)Peak memory usage: 10 MB
% 2.15/0.67 % (3583444)Instructions burned: 17 (million)
% 2.15/0.67 % (3583442)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=274494867:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.15/0.67 % (3583441)Instruction limit reached!
% 2.15/0.67 % (3583441)------------------------------
% 2.15/0.67 % (3583441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (3583441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (3583441)CaDiCaL version: 2.1.3
% 2.15/0.67 % (3583441)Termination reason: Instruction limit
% 2.15/0.67 % (3583441)Termination phase: shuffling
% 2.15/0.67 % (3583441)Time elapsed: 0.011 s
% 2.15/0.67 % (3583441)Peak memory usage: 11 MB
% 2.15/0.67 % (3583441)Instructions burned: 23 (million)
% 2.15/0.67 % (3583440)Instruction limit reached!
% 2.15/0.67 % (3583440)------------------------------
% 2.15/0.67 % (3583440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (3583440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (3583440)CaDiCaL version: 2.1.3
% 2.15/0.67 % (3583440)Termination reason: Instruction limit
% 2.15/0.67 % (3583440)Termination phase: Property scanning
% 2.15/0.67 % (3583440)Time elapsed: 0.013 s
% 2.15/0.67 % (3583440)Peak memory usage: 11 MB
% 2.15/0.67 % (3583440)Instructions burned: 28 (million)
% 2.15/0.67 % (3583448)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.15/0.67 % (3583448)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=2392224194:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.15/0.67 % (3583448)Instruction limit reached!
% 2.15/0.67 % (3583448)------------------------------
% 2.15/0.67 % (3583448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (3583448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (3583448)CaDiCaL version: 2.1.3
% 2.15/0.67 % (3583448)Termination reason: Instruction limit
% 2.15/0.67 % (3583448)Termination phase: shuffling
% 2.15/0.67 % (3583448)Time elapsed: 0.003 s
% 2.15/0.67 % (3583448)Peak memory usage: 10 MB
% 2.15/0.67 % (3583448)Instructions burned: 12 (million)
% 2.15/0.67 % (3583453)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2651832634:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.15/0.67 % (3583451)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1864376584:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.15/0.67 % (3583451)Instruction limit reached!
% 2.15/0.67 % (3583451)------------------------------
% 2.15/0.67 % (3583451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (3583451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (3583451)CaDiCaL version: 2.1.3
% 2.15/0.67 % (3583451)Termination reason: Instruction limit
% 2.15/0.67 % (3583451)Termination phase: shuffling
% 2.15/0.67 % (3583451)Time elapsed: 0.004 s
% 2.15/0.67 % (3583451)Peak memory usage: 10 MB
% 2.15/0.67 % (3583451)Instructions burned: 7 (million)
% 2.15/0.67 % (3583442)Instruction limit reached!
% 2.15/0.67 % (3583442)------------------------------
% 2.15/0.67 % (3583442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (3583442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (3583442)CaDiCaL version: 2.1.3
% 2.15/0.67 % (3583442)Termination reason: Instruction limit
% 2.15/0.67 % (3583442)Termination phase: Preprocessing 3
% 2.15/0.67 % (3583442)Time elapsed: 0.028 s
% 2.15/0.67 % (3583442)Peak memory usage: 12 MB
% 2.15/0.67 % (3583442)Instructions burned: 61 (million)
% 2.15/0.67 % (3583453)Instruction limit reached!
% 2.15/0.67 % (3583453)------------------------------
% 2.15/0.67 % (3583453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.67 % (3583453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.67 % (3583453)CaDiCaL version: 2.1.3
% 2.15/0.67 % (3583453)Termination reason: Instruction limit
% 2.15/0.67 % (3583453)Termination phase: shuffling
% 2.15/0.67 % (3583453)Time elapsed: 0.006 s
% 2.15/0.67 % (3583453)Peak memory usage: 10 MB
% 2.15/0.67 % (3583453)Instructions burned: 25 (million)
% 2.56/0.72 % (3583450)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=2779393599:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.56/0.72 % (3583458)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=739397316:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.56/0.72 % (3583456)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3868998721:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.56/0.72 % (3583457)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3443999892:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.56/0.72 % (3583456)Instruction limit reached!
% 2.56/0.72 % (3583456)------------------------------
% 2.56/0.72 % (3583456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.72 % (3583456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.72 % (3583456)CaDiCaL version: 2.1.3
% 2.56/0.72 % (3583456)Termination reason: Instruction limit
% 2.56/0.72 % (3583456)Termination phase: shuffling
% 2.56/0.72 % (3583456)Time elapsed: 0.010 s
% 2.56/0.72 % (3583456)Peak memory usage: 10 MB
% 2.56/0.72 % (3583456)Instructions burned: 22 (million)
% 2.56/0.72 % (3583450)Instruction limit reached!
% 2.56/0.72 % (3583450)------------------------------
% 2.56/0.72 % (3583450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.72 % (3583450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.72 % (3583450)CaDiCaL version: 2.1.3
% 2.56/0.72 % (3583450)Termination reason: Instruction limit
% 2.56/0.72 % (3583450)Termination phase: Property scanning
% 2.56/0.72 % (3583450)Time elapsed: 0.026 s
% 2.56/0.72 % (3583450)Peak memory usage: 11 MB
% 2.56/0.72 % (3583450)Instructions burned: 31 (million)
% 2.56/0.72 % (3583426)Instruction limit reached!
% 2.56/0.72 % (3583426)------------------------------
% 2.56/0.72 % (3583426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.72 % (3583426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.72 % (3583426)CaDiCaL version: 2.1.3
% 2.56/0.72 % (3583426)Termination reason: Instruction limit
% 2.56/0.72 % (3583426)Termination phase: Saturation
% 2.56/0.72 % (3583426)Time elapsed: 0.120 s
% 2.56/0.72 % (3583426)Peak memory usage: 14 MB
% 2.56/0.72 % (3583426)Instructions burned: 249 (million)
% 2.56/0.72 % (3583463)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=783998938:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.56/0.72 % (3583465)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.56/0.72 % (3583458)Instruction limit reached!
% 2.56/0.72 % (3583458)------------------------------
% 2.56/0.72 % (3583458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.72 % (3583458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.72 % (3583458)CaDiCaL version: 2.1.3
% 2.56/0.72 % (3583458)Termination reason: Instruction limit
% 2.56/0.72 % (3583458)Termination phase: Saturation
% 2.56/0.72 % (3583458)Time elapsed: 0.049 s
% 2.56/0.72 % (3583458)Peak memory usage: 14 MB
% 2.56/0.72 % (3583458)Instructions burned: 148 (million)
% 2.56/0.72 % (3583465)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4270704824:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.56/0.72 % (3583465)Instruction limit reached!
% 2.56/0.72 % (3583465)------------------------------
% 2.56/0.72 % (3583465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.72 % (3583465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.72 % (3583465)CaDiCaL version: 2.1.3
% 2.56/0.72 % (3583465)Termination reason: Instruction limit
% 2.56/0.72 % (3583465)Termination phase: shuffling
% 2.56/0.72 % (3583465)Time elapsed: 0.003 s
% 2.56/0.72 % (3583465)Peak memory usage: 10 MB
% 2.56/0.72 % (3583465)Instructions burned: 7 (million)
% 2.56/0.72 % (3583464)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=34988394:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.56/0.72 % (3583467)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1498610530:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.56/0.79 % (3583470)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=436277307:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.56/0.79 % (3583464)Instruction limit reached!
% 2.56/0.79 % (3583464)------------------------------
% 2.56/0.79 % (3583464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.79 % (3583464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.79 % (3583464)CaDiCaL version: 2.1.3
% 2.56/0.79 % (3583464)Termination reason: Instruction limit
% 2.56/0.79 % (3583464)Termination phase: Naming
% 2.56/0.79 % (3583464)Time elapsed: 0.023 s
% 2.56/0.79 % (3583464)Peak memory usage: 11 MB
% 2.56/0.79 % (3583464)Instructions burned: 44 (million)
% 2.56/0.79 % (3583473)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.56/0.79 % (3583473)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=4093812265:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.56/0.79 % (3583473)Instruction limit reached!
% 2.56/0.79 % (3583473)------------------------------
% 2.56/0.79 % (3583473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.79 % (3583473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.79 % (3583473)CaDiCaL version: 2.1.3
% 2.56/0.79 % (3583473)Termination reason: Instruction limit
% 2.56/0.79 % (3583473)Termination phase: shuffling
% 2.56/0.79 % (3583473)Time elapsed: 0.004 s
% 2.56/0.79 % (3583473)Peak memory usage: 10 MB
% 2.56/0.79 % (3583473)Instructions burned: 8 (million)
% 2.56/0.79 % (3583433)Instruction limit reached!
% 2.56/0.79 % (3583433)------------------------------
% 2.56/0.79 % (3583433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.79 % (3583433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.79 % (3583433)CaDiCaL version: 2.1.3
% 2.56/0.79 % (3583433)Termination reason: Instruction limit
% 2.56/0.79 % (3583433)Termination phase: Saturation
% 2.56/0.79 % (3583433)Time elapsed: 0.177 s
% 2.56/0.79 % (3583433)Peak memory usage: 14 MB
% 2.56/0.79 % (3583433)Instructions burned: 328 (million)
% 2.56/0.79 % (3583467)Instruction limit reached!
% 2.56/0.79 % (3583467)------------------------------
% 2.56/0.79 % (3583467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.79 % (3583467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.79 % (3583467)CaDiCaL version: 2.1.3
% 2.56/0.79 % (3583467)Termination reason: Instruction limit
% 2.56/0.79 % (3583467)Termination phase: Saturation
% 2.56/0.79 % (3583467)Time elapsed: 0.047 s
% 2.56/0.79 % (3583467)Peak memory usage: 14 MB
% 2.56/0.79 % (3583467)Instructions burned: 184 (million)
% 2.56/0.79 % (3583477)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=2701976571:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.56/0.79 % (3583476)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1336524269:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.56/0.79 % (3583475)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3074650437:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.56/0.79 % (3583476)Instruction limit reached!
% 2.56/0.79 % (3583476)------------------------------
% 2.56/0.79 % (3583476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.79 % (3583476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.79 % (3583476)CaDiCaL version: 2.1.3
% 2.56/0.79 % (3583476)Termination reason: Instruction limit
% 2.56/0.79 % (3583476)Termination phase: shuffling
% 2.56/0.79 % (3583476)Time elapsed: 0.009 s
% 2.56/0.79 % (3583476)Peak memory usage: 10 MB
% 2.56/0.79 % (3583476)Instructions burned: 21 (million)
% 2.56/0.79 % (3583463)Instruction limit reached!
% 2.56/0.79 % (3583463)------------------------------
% 2.56/0.79 % (3583463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.91 % (3583463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.91 % (3583463)CaDiCaL version: 2.1.3
% 3.46/0.91 % (3583463)Termination reason: Instruction limit
% 3.46/0.91 % (3583463)Termination phase: Saturation
% 3.46/0.91 % (3583463)Time elapsed: 0.094 s
% 3.46/0.91 % (3583463)Peak memory usage: 14 MB
% 3.46/0.91 % (3583463)Instructions burned: 193 (million)
% 3.46/0.91 % (3583475)Instruction limit reached!
% 3.46/0.91 % (3583475)------------------------------
% 3.46/0.91 % (3583475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.91 % (3583475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.91 % (3583475)CaDiCaL version: 2.1.3
% 3.46/0.91 % (3583475)Termination reason: Instruction limit
% 3.46/0.91 % (3583475)Termination phase: shuffling
% 3.46/0.91 % (3583475)Time elapsed: 0.019 s
% 3.46/0.91 % (3583475)Peak memory usage: 11 MB
% 3.46/0.91 % (3583475)Instructions burned: 22 (million)
% 3.46/0.91 % (3583470)Instruction limit reached!
% 3.46/0.91 % (3583470)------------------------------
% 3.46/0.91 % (3583470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.91 % (3583470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.91 % (3583470)CaDiCaL version: 2.1.3
% 3.46/0.91 % (3583470)Termination reason: Instruction limit
% 3.46/0.91 % (3583470)Termination phase: Saturation
% 3.46/0.91 % (3583470)Time elapsed: 0.073 s
% 3.46/0.91 % (3583470)Peak memory usage: 14 MB
% 3.46/0.91 % (3583470)Instructions burned: 171 (million)
% 3.46/0.91 % (3583481)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=269268732:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.46/0.91 % (3583482)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=2372272782:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.46/0.91 % (3583483)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=52336443:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.46/0.91 % (3583484)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3468410353:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.46/0.91 % (3583400)Instruction limit reached!
% 3.46/0.91 % (3583400)------------------------------
% 3.46/0.91 % (3583400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.91 % (3583400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.91 % (3583400)CaDiCaL version: 2.1.3
% 3.46/0.91 % (3583400)Termination reason: Instruction limit
% 3.46/0.91 % (3583400)Termination phase: Saturation
% 3.46/0.91 % (3583400)Time elapsed: 0.336 s
% 3.46/0.91 % (3583400)Peak memory usage: 19 MB
% 3.46/0.91 % (3583400)Instructions burned: 634 (million)
% 3.46/0.91 % (3583484)Instruction limit reached!
% 3.46/0.91 % (3583484)------------------------------
% 3.46/0.91 % (3583484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.91 % (3583484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.91 % (3583484)CaDiCaL version: 2.1.3
% 3.46/0.91 % (3583484)Termination reason: Instruction limit
% 3.46/0.91 % (3583484)Termination phase: shuffling
% 3.46/0.91 % (3583484)Time elapsed: 0.010 s
% 3.46/0.91 % (3583484)Peak memory usage: 10 MB
% 3.46/0.91 % (3583484)Instructions burned: 21 (million)
% 3.46/0.91 % (3583482)Instruction limit reached!
% 3.46/0.91 % (3583482)------------------------------
% 3.46/0.91 % (3583482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.46/0.91 % (3583482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/0.91 % (3583482)CaDiCaL version: 2.1.3
% 3.46/0.91 % (3583482)Termination reason: Instruction limit
% 3.46/0.91 % (3583482)Termination phase: Preprocessing 3
% 3.46/0.91 % (3583482)Time elapsed: 0.022 s
% 3.46/0.91 % (3583482)Peak memory usage: 11 MB
% 3.46/0.91 % (3583482)Instructions burned: 46 (million)
% 3.46/0.91 % (3583489)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.46/0.91 % (3583489)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=4110834786:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 5.52/1.19 % (3583491)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=2242323149:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 5.52/1.19 % (3583490)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2140331327:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 5.52/1.19 % (3583477)Instruction limit reached!
% 5.52/1.19 % (3583477)------------------------------
% 5.52/1.19 % (3583477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.19 % (3583477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.19 % (3583477)CaDiCaL version: 2.1.3
% 5.52/1.19 % (3583477)Termination reason: Instruction limit
% 5.52/1.19 % (3583477)Termination phase: Saturation
% 5.52/1.19 % (3583477)Time elapsed: 0.084 s
% 5.52/1.19 % (3583477)Peak memory usage: 16 MB
% 5.52/1.19 % (3583477)Instructions burned: 319 (million)
% 5.52/1.19 % (3583490)Instruction limit reached!
% 5.52/1.19 % (3583490)------------------------------
% 5.52/1.19 % (3583490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.19 % (3583490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.19 % (3583490)CaDiCaL version: 2.1.3
% 5.52/1.19 % (3583490)Termination reason: Instruction limit
% 5.52/1.19 % (3583490)Termination phase: shuffling
% 5.52/1.19 % (3583490)Time elapsed: 0.006 s
% 5.52/1.19 % (3583490)Peak memory usage: 10 MB
% 5.52/1.19 % (3583490)Instructions burned: 14 (million)
% 5.52/1.19 % (3583495)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=101861256:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 5.52/1.19 % (3583496)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3164867752:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 5.52/1.19 % (3583491)Instruction limit reached!
% 5.52/1.19 % (3583491)------------------------------
% 5.52/1.19 % (3583491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.19 % (3583491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.19 % (3583491)CaDiCaL version: 2.1.3
% 5.52/1.19 % (3583491)Termination reason: Instruction limit
% 5.52/1.19 % (3583491)Termination phase: Property scanning
% 5.52/1.19 % (3583491)Time elapsed: 0.028 s
% 5.52/1.19 % (3583491)Peak memory usage: 11 MB
% 5.52/1.19 % (3583491)Instructions burned: 67 (million)
% 5.52/1.19 % (3583495)Instruction limit reached!
% 5.52/1.19 % (3583495)------------------------------
% 5.52/1.19 % (3583495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.19 % (3583495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.19 % (3583495)CaDiCaL version: 2.1.3
% 5.52/1.19 % (3583495)Termination reason: Instruction limit
% 5.52/1.19 % (3583495)Termination phase: Property scanning
% 5.52/1.19 % (3583495)Time elapsed: 0.014 s
% 5.52/1.19 % (3583495)Peak memory usage: 11 MB
% 5.52/1.19 % (3583495)Instructions burned: 52 (million)
% 5.52/1.19 % (3583496)Instruction limit reached!
% 5.52/1.19 % (3583496)------------------------------
% 5.52/1.19 % (3583496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.19 % (3583496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.19 % (3583496)CaDiCaL version: 2.1.3
% 5.52/1.19 % (3583496)Termination reason: Instruction limit
% 5.52/1.19 % (3583496)Termination phase: Property scanning
% 5.52/1.19 % (3583496)Time elapsed: 0.014 s
% 5.52/1.19 % (3583496)Peak memory usage: 10 MB
% 5.52/1.19 % (3583496)Instructions burned: 33 (million)
% 5.52/1.19 % (3583500)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=1058321990:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 5.52/1.19 % (3583499)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=4120507403:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 5.52/1.19 % (3583500)Instruction limit reached!
% 5.52/1.19 % (3583500)------------------------------
% 5.52/1.19 % (3583500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.19 % (3583500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.29 % (3583500)CaDiCaL version: 2.1.3
% 5.84/1.29 % (3583500)Termination reason: Instruction limit
% 5.84/1.29 % (3583500)Termination phase: Property scanning
% 5.84/1.29 % (3583500)Time elapsed: 0.011 s
% 5.84/1.29 % (3583500)Peak memory usage: 10 MB
% 5.84/1.29 % (3583500)Instructions burned: 36 (million)
% 5.84/1.29 % (3583501)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=340655207:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.84/1.29 % (3583504)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.84/1.29 % (3583504)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1486351567:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 5.84/1.29 % (3583489)Instruction limit reached!
% 5.84/1.29 % (3583489)------------------------------
% 5.84/1.29 % (3583489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.84/1.29 % (3583489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.29 % (3583489)CaDiCaL version: 2.1.3
% 5.84/1.29 % (3583489)Termination reason: Instruction limit
% 5.84/1.29 % (3583489)Termination phase: Saturation
% 5.84/1.29 % (3583489)Time elapsed: 0.090 s
% 5.84/1.29 % (3583489)Peak memory usage: 14 MB
% 5.84/1.29 % (3583489)Instructions burned: 201 (million)
% 5.84/1.29 % (3583501)Instruction limit reached!
% 5.84/1.29 % (3583501)------------------------------
% 5.84/1.29 % (3583501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.84/1.29 % (3583501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.29 % (3583501)CaDiCaL version: 2.1.3
% 5.84/1.29 % (3583501)Termination reason: Instruction limit
% 5.84/1.29 % (3583501)Termination phase: Function definition elimination
% 5.84/1.29 % (3583501)Time elapsed: 0.028 s
% 5.84/1.29 % (3583501)Peak memory usage: 11 MB
% 5.84/1.29 % (3583501)Instructions burned: 67 (million)
% 5.84/1.29 % (3583507)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3352903777:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 5.84/1.29 % (3583499)Instruction limit reached!
% 5.84/1.29 % (3583499)------------------------------
% 5.84/1.29 % (3583499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.84/1.29 % (3583499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.29 % (3583499)CaDiCaL version: 2.1.3
% 5.84/1.29 % (3583499)Termination reason: Instruction limit
% 5.84/1.29 % (3583499)Termination phase: Saturation
% 5.84/1.29 % (3583499)Time elapsed: 0.059 s
% 5.84/1.29 % (3583499)Peak memory usage: 13 MB
% 5.84/1.29 % (3583499)Instructions burned: 137 (million)
% 5.84/1.29 % (3583508)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3329014849:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 5.84/1.29 % (3583504)Instruction limit reached!
% 5.84/1.29 % (3583504)------------------------------
% 5.84/1.29 % (3583504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.84/1.29 % (3583504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.29 % (3583504)CaDiCaL version: 2.1.3
% 5.84/1.29 % (3583504)Termination reason: Instruction limit
% 5.84/1.29 % (3583504)Termination phase: Saturation
% 5.84/1.29 % (3583504)Time elapsed: 0.052 s
% 5.84/1.29 % (3583504)Peak memory usage: 13 MB
% 5.84/1.29 % (3583504)Instructions burned: 183 (million)
% 5.84/1.29 % (3583511)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2166181161:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 5.84/1.29 % (3583508)Instruction limit reached!
% 5.84/1.29 % (3583508)------------------------------
% 5.84/1.29 % (3583508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.84/1.29 % (3583508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.84/1.29 % (3583508)CaDiCaL version: 2.1.3
% 5.84/1.29 % (3583508)Termination reason: Instruction limit
% 5.84/1.29 % (3583508)Termination phase: Property scanning
% 5.84/1.29 % (3583508)Time elapsed: 0.040 s
% 5.84/1.29 % (3583508)Peak memory usage: 12 MB
% 5.84/1.29 % (3583508)Instructions burned: 97 (million)
% 5.84/1.29 % (3583512)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2738773225:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.84/1.29 % (3583514)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1756467051:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 6.88/1.45 % (3583507)Instruction limit reached!
% 6.88/1.45 % (3583507)------------------------------
% 6.88/1.45 % (3583507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.45 % (3583507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.45 % (3583507)CaDiCaL version: 2.1.3
% 6.88/1.45 % (3583507)Termination reason: Instruction limit
% 6.88/1.45 % (3583507)Termination phase: Saturation
% 6.88/1.45 % (3583507)Time elapsed: 0.112 s
% 6.88/1.45 % (3583507)Peak memory usage: 14 MB
% 6.88/1.45 % (3583507)Instructions burned: 247 (million)
% 6.88/1.45 % (3583483)Instruction limit reached!
% 6.88/1.45 % (3583483)------------------------------
% 6.88/1.45 % (3583483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.45 % (3583483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.45 % (3583483)CaDiCaL version: 2.1.3
% 6.88/1.45 % (3583483)Termination reason: Instruction limit
% 6.88/1.45 % (3583483)Termination phase: Saturation
% 6.88/1.45 % (3583483)Time elapsed: 0.250 s
% 6.88/1.45 % (3583483)Peak memory usage: 17 MB
% 6.88/1.45 % (3583483)Instructions burned: 480 (million)
% 6.88/1.45 % (3583518)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=642380362:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 6.88/1.45 % (3583517)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3161147932:st=1.5:i=130:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/130Mi)
% 6.88/1.45 % (3583518)Instruction limit reached!
% 6.88/1.45 % (3583518)------------------------------
% 6.88/1.45 % (3583518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.45 % (3583518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.45 % (3583518)CaDiCaL version: 2.1.3
% 6.88/1.45 % (3583518)Termination reason: Instruction limit
% 6.88/1.45 % (3583518)Termination phase: Property scanning
% 6.88/1.45 % (3583518)Time elapsed: 0.010 s
% 6.88/1.45 % (3583518)Peak memory usage: 10 MB
% 6.88/1.45 % (3583518)Instructions burned: 45 (million)
% 6.88/1.45 % (3583521)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=697014854:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 6.88/1.45 % (3583517)Instruction limit reached!
% 6.88/1.45 % (3583517)------------------------------
% 6.88/1.45 % (3583517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.45 % (3583517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.45 % (3583517)CaDiCaL version: 2.1.3
% 6.88/1.45 % (3583517)Termination reason: Instruction limit
% 6.88/1.45 % (3583517)Termination phase: Saturation
% 6.88/1.45 % (3583517)Time elapsed: 0.053 s
% 6.88/1.45 % (3583517)Peak memory usage: 12 MB
% 6.88/1.45 % (3583517)Instructions burned: 130 (million)
% 6.88/1.45 % (3583523)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=17784504:i=450:rtra=on:ixr=off:ntd=on_2992 on theBenchmark for (2992ds/450Mi)
% 6.88/1.45 % (3583511)Instruction limit reached!
% 6.88/1.45 % (3583511)------------------------------
% 6.88/1.45 % (3583511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.45 % (3583511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.45 % (3583511)CaDiCaL version: 2.1.3
% 6.88/1.45 % (3583511)Termination reason: Instruction limit
% 6.88/1.45 % (3583511)Termination phase: Saturation
% 6.88/1.45 % (3583511)Time elapsed: 0.273 s
% 6.88/1.45 % (3583511)Peak memory usage: 15 MB
% 6.88/1.45 % (3583511)Instructions burned: 428 (million)
% 6.88/1.45 % (3583525)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3196888316:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/95Mi)
% 6.88/1.45 % (3583481)Instruction limit reached!
% 6.88/1.45 % (3583481)------------------------------
% 6.88/1.45 % (3583481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.45 % (3583481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.45 % (3583481)CaDiCaL version: 2.1.3
% 6.88/1.45 % (3583481)Termination reason: Instruction limit
% 6.88/1.45 % (3583481)Termination phase: Saturation
% 6.88/1.45 % (3583481)Time elapsed: 0.506 s
% 6.88/1.45 % (3583481)Peak memory usage: 23 MB
% 6.88/1.45 % (3583481)Instructions burned: 853 (million)
% 7.45/1.64 % (3583512)Instruction limit reached!
% 7.45/1.64 % (3583512)------------------------------
% 7.45/1.64 % (3583512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (3583512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (3583512)CaDiCaL version: 2.1.3
% 7.45/1.64 % (3583512)Termination reason: Instruction limit
% 7.45/1.64 % (3583512)Termination phase: Saturation
% 7.45/1.64 % (3583512)Time elapsed: 0.309 s
% 7.45/1.64 % (3583512)Peak memory usage: 15 MB
% 7.45/1.64 % (3583512)Instructions burned: 881 (million)
% 7.45/1.64 % (3583525)Instruction limit reached!
% 7.45/1.64 % (3583525)------------------------------
% 7.45/1.64 % (3583525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (3583525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (3583525)CaDiCaL version: 2.1.3
% 7.45/1.64 % (3583525)Termination reason: Instruction limit
% 7.45/1.64 % (3583525)Termination phase: Saturation
% 7.45/1.64 % (3583525)Time elapsed: 0.058 s
% 7.45/1.64 % (3583525)Peak memory usage: 13 MB
% 7.45/1.64 % (3583525)Instructions burned: 95 (million)
% 7.45/1.64 % (3583528)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=2811199302: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_2991 on theBenchmark for (2991ds/105Mi)
% 7.45/1.64 % (3583527)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=2602046485:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2991 on theBenchmark for (2991ds/65Mi)
% 7.45/1.64 % (3583530)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=3619965997:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 7.45/1.64 % (3583527)Instruction limit reached!
% 7.45/1.64 % (3583527)------------------------------
% 7.45/1.64 % (3583527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (3583527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (3583527)CaDiCaL version: 2.1.3
% 7.45/1.64 % (3583527)Termination reason: Instruction limit
% 7.45/1.64 % (3583527)Termination phase: Property scanning
% 7.45/1.64 % (3583527)Time elapsed: 0.027 s
% 7.45/1.64 % (3583527)Peak memory usage: 11 MB
% 7.45/1.64 % (3583527)Instructions burned: 66 (million)
% 7.45/1.64 % (3583533)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3872691250:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/375Mi)
% 7.45/1.64 % (3583528)Instruction limit reached!
% 7.45/1.64 % (3583528)------------------------------
% 7.45/1.64 % (3583528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (3583528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (3583528)CaDiCaL version: 2.1.3
% 7.45/1.64 % (3583528)Termination reason: Instruction limit
% 7.45/1.64 % (3583528)Termination phase: Property scanning
% 7.45/1.64 % (3583528)Time elapsed: 0.059 s
% 7.45/1.64 % (3583528)Peak memory usage: 11 MB
% 7.45/1.64 % (3583528)Instructions burned: 107 (million)
% 7.45/1.64 % (3583514)Instruction limit reached!
% 7.45/1.64 % (3583514)------------------------------
% 7.45/1.64 % (3583514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (3583514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (3583514)CaDiCaL version: 2.1.3
% 7.45/1.64 % (3583514)Termination reason: Instruction limit
% 7.45/1.64 % (3583514)Termination phase: Saturation
% 7.45/1.64 % (3583514)Time elapsed: 0.368 s
% 7.45/1.64 % (3583514)Peak memory usage: 15 MB
% 7.45/1.64 % (3583514)Instructions burned: 516 (million)
% 7.45/1.64 % (3583523)Instruction limit reached!
% 7.45/1.64 % (3583523)------------------------------
% 7.45/1.64 % (3583523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (3583523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (3583523)CaDiCaL version: 2.1.3
% 7.45/1.64 % (3583523)Termination reason: Instruction limit
% 7.45/1.64 % (3583523)Termination phase: Saturation
% 7.45/1.64 % (3583523)Time elapsed: 0.242 s
% 8.41/1.78 % (3583523)Peak memory usage: 20 MB
% 8.41/1.78 % (3583523)Instructions burned: 450 (million)
% 8.41/1.78 % (3583535)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1483479000:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/495Mi)
% 8.41/1.78 % (3583536)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=2303184646:cond=on:i=34:hud=10:nm=10:rtra=on_2990 on theBenchmark for (2990ds/34Mi)
% 8.41/1.78 % (3583537)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2749276904:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/91Mi)
% 8.41/1.78 % (3583536)Instruction limit reached!
% 8.41/1.78 % (3583536)------------------------------
% 8.41/1.78 % (3583536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.41/1.78 % (3583536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.41/1.78 % (3583536)CaDiCaL version: 2.1.3
% 8.41/1.78 % (3583536)Termination reason: Instruction limit
% 8.41/1.78 % (3583536)Termination phase: Property scanning
% 8.41/1.78 % (3583536)Time elapsed: 0.021 s
% 8.41/1.78 % (3583536)Peak memory usage: 10 MB
% 8.41/1.78 % (3583536)Instructions burned: 34 (million)
% 8.41/1.78 % (3583541)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3401585197:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2989 on theBenchmark for (2989ds/66Mi)
% 8.41/1.78 % (3583537)Instruction limit reached!
% 8.41/1.78 % (3583537)------------------------------
% 8.41/1.78 % (3583537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.41/1.78 % (3583537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.41/1.78 % (3583537)CaDiCaL version: 2.1.3
% 8.41/1.78 % (3583537)Termination reason: Instruction limit
% 8.41/1.78 % (3583537)Termination phase: Twee Goal Transformation
% 8.41/1.78 % (3583537)Time elapsed: 0.068 s
% 8.41/1.78 % (3583537)Peak memory usage: 12 MB
% 8.41/1.78 % (3583537)Instructions burned: 92 (million)
% 8.41/1.78 % (3583521)Instruction limit reached!
% 8.41/1.78 % (3583521)------------------------------
% 8.41/1.78 % (3583521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.41/1.78 % (3583521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.41/1.78 % (3583521)CaDiCaL version: 2.1.3
% 8.41/1.78 % (3583521)Termination reason: Instruction limit
% 8.41/1.78 % (3583521)Termination phase: Saturation
% 8.41/1.78 % (3583521)Time elapsed: 0.406 s
% 8.41/1.78 % (3583521)Peak memory usage: 18 MB
% 8.41/1.78 % (3583521)Instructions burned: 571 (million)
% 8.41/1.78 % (3583543)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2831875213:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2989 on theBenchmark for (2989ds/22Mi)
% 8.41/1.78 % (3583541)Instruction limit reached!
% 8.41/1.78 % (3583541)------------------------------
% 8.41/1.78 % (3583541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.41/1.78 % (3583541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.41/1.78 % (3583541)CaDiCaL version: 2.1.3
% 8.41/1.78 % (3583541)Termination reason: Instruction limit
% 8.41/1.78 % (3583541)Termination phase: Preprocessing 3
% 8.41/1.78 % (3583541)Time elapsed: 0.049 s
% 8.41/1.78 % (3583541)Peak memory usage: 12 MB
% 8.41/1.78 % (3583541)Instructions burned: 66 (million)
% 8.41/1.78 % (3583543)Instruction limit reached!
% 8.41/1.78 % (3583543)------------------------------
% 8.41/1.78 % (3583543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.41/1.78 % (3583543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.41/1.78 % (3583543)CaDiCaL version: 2.1.3
% 8.41/1.78 % (3583543)Termination reason: Instruction limit
% 8.41/1.78 % (3583543)Termination phase: shuffling
% 8.41/1.78 % (3583543)Time elapsed: 0.016 s
% 8.41/1.78 % (3583543)Peak memory usage: 10 MB
% 8.41/1.78 % (3583543)Instructions burned: 22 (million)
% 8.41/1.78 % (3583544)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=4293500270:i=338:bd=all:ins=4:rtra=on_2989 on theBenchmark for (2989ds/338Mi)
% 8.41/1.78 % (3583553)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2307694145:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2988 on theBenchmark for (2988ds/28Mi)
% 8.41/1.78 % (3583555)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 9.39/1.94 % (3583533)Instruction limit reached!
% 9.39/1.94 % (3583533)------------------------------
% 9.39/1.94 % (3583533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.39/1.94 % (3583533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.39/1.94 % (3583533)CaDiCaL version: 2.1.3
% 9.39/1.94 % (3583533)Termination reason: Instruction limit
% 9.39/1.94 % (3583533)Termination phase: Saturation
% 9.39/1.94 % (3583533)Time elapsed: 0.185 s
% 9.39/1.94 % (3583533)Peak memory usage: 15 MB
% 9.39/1.94 % (3583533)Instructions burned: 376 (million)
% 9.39/1.94 % (3583555)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=3899229608:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2988 on theBenchmark for (2988ds/137Mi)
% 9.39/1.94 % (3583553)Instruction limit reached!
% 9.39/1.94 % (3583553)------------------------------
% 9.39/1.94 % (3583553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.39/1.94 % (3583553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.39/1.94 % (3583553)CaDiCaL version: 2.1.3
% 9.39/1.94 % (3583553)Termination reason: Instruction limit
% 9.39/1.94 % (3583553)Termination phase: Property scanning
% 9.39/1.94 % (3583553)Time elapsed: 0.013 s
% 9.39/1.94 % (3583553)Peak memory usage: 11 MB
% 9.39/1.94 % (3583553)Instructions burned: 28 (million)
% 9.39/1.94 % (3583558)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=2477948342:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2988 on theBenchmark for (2988ds/340Mi)
% 9.39/1.94 % (3583559)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=1134750404:i=227:sd=1:bd=all:rtra=on:ss=axioms_2988 on theBenchmark for (2988ds/227Mi)
% 9.39/1.94 % (3583457)Instruction limit reached!
% 9.39/1.94 % (3583457)------------------------------
% 9.39/1.94 % (3583457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.39/1.94 % (3583457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.39/1.94 % (3583457)CaDiCaL version: 2.1.3
% 9.39/1.94 % (3583457)Termination reason: Instruction limit
% 9.39/1.94 % (3583457)Termination phase: Saturation
% 9.39/1.94 % (3583457)Time elapsed: 0.948 s
% 9.39/1.94 % (3583457)Peak memory usage: 19 MB
% 9.39/1.94 % (3583457)Instructions burned: 1240 (million)
% 9.39/1.94 % (3583555)Instruction limit reached!
% 9.39/1.94 % (3583555)------------------------------
% 9.39/1.94 % (3583555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.39/1.94 % (3583555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.39/1.94 % (3583555)CaDiCaL version: 2.1.3
% 9.39/1.94 % (3583555)Termination reason: Instruction limit
% 9.39/1.94 % (3583555)Termination phase: Saturation
% 9.39/1.94 % (3583555)Time elapsed: 0.056 s
% 9.39/1.94 % (3583555)Peak memory usage: 13 MB
% 9.39/1.94 % (3583555)Instructions burned: 137 (million)
% 9.39/1.94 % (3583562)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 9.39/1.94 % (3583562)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3097694774:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/373Mi)
% 9.39/1.94 % (3583563)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=4294528641:i=116:ep=RSTC:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/116Mi)
% 9.39/1.94 % (3583563)Instruction limit reached!
% 9.39/1.94 % (3583563)------------------------------
% 9.39/1.94 % (3583563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.39/1.94 % (3583563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.39/1.94 % (3583563)CaDiCaL version: 2.1.3
% 9.39/1.94 % (3583563)Termination reason: Instruction limit
% 9.39/1.94 % (3583563)Termination phase: Property scanning
% 9.39/1.94 % (3583563)Time elapsed: 0.080 s
% 9.39/1.94 % (3583563)Peak memory usage: 13 MB
% 9.39/1.94 % (3583563)Instructions burned: 116 (million)
% 9.39/1.94 % (3583566)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1694224218:i=575:rtra=on_2987 on theBenchmark for (2987ds/575Mi)
% 9.39/1.94 % (3583558)Instruction limit reached!
% 9.39/1.94 % (3583558)------------------------------
% 9.39/1.94 % (3583558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.22/2.16 % (3583558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.16 % (3583558)CaDiCaL version: 2.1.3
% 12.22/2.16 % (3583558)Termination reason: Instruction limit
% 12.22/2.16 % (3583558)Termination phase: Saturation
% 12.22/2.16 % (3583558)Time elapsed: 0.162 s
% 12.22/2.16 % (3583558)Peak memory usage: 14 MB
% 12.22/2.16 % (3583558)Instructions burned: 341 (million)
% 12.22/2.16 % (3583559)Instruction limit reached!
% 12.22/2.16 % (3583559)------------------------------
% 12.22/2.16 % (3583559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.22/2.16 % (3583559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.16 % (3583559)CaDiCaL version: 2.1.3
% 12.22/2.16 % (3583559)Termination reason: Instruction limit
% 12.22/2.16 % (3583559)Termination phase: Saturation
% 12.22/2.16 % (3583559)Time elapsed: 0.179 s
% 12.22/2.16 % (3583559)Peak memory usage: 14 MB
% 12.22/2.16 % (3583559)Instructions burned: 227 (million)
% 12.22/2.16 % (3583568)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1324107129:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2986 on theBenchmark for (2986ds/270Mi)
% 12.22/2.16 % (3583562)Instruction limit reached!
% 12.22/2.16 % (3583562)------------------------------
% 12.22/2.16 % (3583562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.22/2.16 % (3583562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.16 % (3583562)CaDiCaL version: 2.1.3
% 12.22/2.16 % (3583562)Termination reason: Instruction limit
% 12.22/2.16 % (3583562)Termination phase: Saturation
% 12.22/2.16 % (3583562)Time elapsed: 0.162 s
% 12.22/2.16 % (3583562)Peak memory usage: 13 MB
% 12.22/2.16 % (3583562)Instructions burned: 374 (million)
% 12.22/2.16 % (3583544)Instruction limit reached!
% 12.22/2.16 % (3583544)------------------------------
% 12.22/2.16 % (3583544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.22/2.16 % (3583544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.16 % (3583544)CaDiCaL version: 2.1.3
% 12.22/2.16 % (3583544)Termination reason: Instruction limit
% 12.22/2.16 % (3583544)Termination phase: Saturation
% 12.22/2.16 % (3583544)Time elapsed: 0.253 s
% 12.22/2.16 % (3583544)Peak memory usage: 17 MB
% 12.22/2.16 % (3583544)Instructions burned: 346 (million)
% 12.22/2.16 % (3583569)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=2966361143: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_2986 on theBenchmark for (2986ds/9840Mi)
% 12.22/2.16 % (3583535)Instruction limit reached!
% 12.22/2.16 % (3583535)------------------------------
% 12.22/2.16 % (3583535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.22/2.16 % (3583535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.22/2.16 % (3583535)CaDiCaL version: 2.1.3
% 12.22/2.16 % (3583535)Termination reason: Instruction limit
% 12.22/2.16 % (3583535)Termination phase: Saturation
% 12.22/2.16 % (3583535)Time elapsed: 0.409 s
% 12.22/2.16 % (3583535)Peak memory usage: 17 MB
% 12.22/2.16 % (3583535)Instructions burned: 495 (million)
% 12.22/2.16 % (3583571)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=3399987131:i=421:rtra=on:ss=axioms_2986 on theBenchmark for (2986ds/421Mi)
% 12.22/2.16 % (3583572)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
% 12.22/2.16 % (3583572)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=1121499139:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/270Mi)
% 12.22/2.16 % (3583574)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=4007306189:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/31Mi)
% 12.22/2.16 % (3583574)Instruction limit reached!
% 12.22/2.16 % (3583574)------------------------------
% 12.22/2.16 % (3583574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.22/2.16 % (3583574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583574)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583574)Termination reason: Instruction limit
% 13.04/2.31 % (3583574)Termination phase: Property scanning
% 13.04/2.31 % (3583574)Time elapsed: 0.029 s
% 13.04/2.31 % (3583574)Peak memory usage: 10 MB
% 13.04/2.31 % (3583574)Instructions burned: 33 (million)
% 13.04/2.31 % (3583578)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 13.04/2.31 % (3583578)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
% 13.04/2.31 % (3583578)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=2412290949:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2985 on theBenchmark for (2985ds/1440Mi)
% 13.04/2.31 % (3583568)Instruction limit reached!
% 13.04/2.31 % (3583568)------------------------------
% 13.04/2.31 % (3583568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583568)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583568)Termination reason: Instruction limit
% 13.04/2.31 % (3583568)Termination phase: Saturation
% 13.04/2.31 % (3583568)Time elapsed: 0.162 s
% 13.04/2.31 % (3583568)Peak memory usage: 14 MB
% 13.04/2.31 % (3583568)Instructions burned: 272 (million)
% 13.04/2.31 % (3583572)Refutation not found, incomplete strategy
% 13.04/2.31 % (3583572)------------------------------
% 13.04/2.31 % (3583572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583572)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583572)Termination reason: Refutation not found, incomplete strategy
% 13.04/2.31 % (3583572)Time elapsed: 0.107 s
% 13.04/2.31 % (3583572)Peak memory usage: 14 MB
% 13.04/2.31 % (3583572)Instructions burned: 190 (million)
% 13.04/2.31 % (3583572)------------------------------
% 13.04/2.31 % (3583572)------------------------------
% 13.04/2.31 % (3583580)dis+10_2_sil=128000:si=on:random_seed=1666010434:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2984 on theBenchmark for (2984ds/339Mi)
% 13.04/2.31 % (3583581)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=638816294:i=111:add=on:fgj=on:rtra=on:fdi=1024_2984 on theBenchmark for (2984ds/111Mi)
% 13.04/2.31 % (3583566)Instruction limit reached!
% 13.04/2.31 % (3583566)------------------------------
% 13.04/2.31 % (3583566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583566)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583566)Termination reason: Instruction limit
% 13.04/2.31 % (3583566)Termination phase: Saturation
% 13.04/2.31 % (3583566)Time elapsed: 0.250 s
% 13.04/2.31 % (3583566)Peak memory usage: 16 MB
% 13.04/2.31 % (3583566)Instructions burned: 577 (million)
% 13.04/2.31 % (3583584)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=2980217098:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2984 on theBenchmark for (2984ds/122Mi)
% 13.04/2.31 % (3583581)Instruction limit reached!
% 13.04/2.31 % (3583581)------------------------------
% 13.04/2.31 % (3583581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583581)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583581)Termination reason: Instruction limit
% 13.04/2.31 % (3583581)Termination phase: Saturation
% 13.04/2.31 % (3583581)Time elapsed: 0.047 s
% 13.04/2.31 % (3583581)Peak memory usage: 13 MB
% 13.04/2.31 % (3583581)Instructions burned: 113 (million)
% 13.04/2.31 % (3583586)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=1944015590:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/136Mi)
% 13.04/2.31 % (3583571)Instruction limit reached!
% 13.04/2.31 % (3583571)------------------------------
% 13.04/2.31 % (3583571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583571)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583571)Termination reason: Instruction limit
% 13.04/2.31 % (3583571)Termination phase: Saturation
% 13.04/2.31 % (3583571)Time elapsed: 0.224 s
% 13.04/2.31 % (3583571)Peak memory usage: 15 MB
% 13.04/2.31 % (3583571)Instructions burned: 422 (million)
% 13.04/2.31 % (3583584)Instruction limit reached!
% 13.04/2.31 % (3583584)------------------------------
% 13.04/2.31 % (3583584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583584)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583584)Termination reason: Instruction limit
% 13.04/2.31 % (3583584)Termination phase: Saturation
% 13.04/2.31 % (3583584)Time elapsed: 0.052 s
% 13.04/2.31 % (3583584)Peak memory usage: 13 MB
% 13.04/2.31 % (3583584)Instructions burned: 124 (million)
% 13.04/2.31 % (3583588)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=744726221:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2983 on theBenchmark for (2983ds/232Mi)
% 13.04/2.31 % (3583589)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=853569649:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2983 on theBenchmark for (2983ds/1254Mi)
% 13.04/2.31 % (3583586)Instruction limit reached!
% 13.04/2.31 % (3583586)------------------------------
% 13.04/2.31 % (3583586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583586)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583586)Termination reason: Instruction limit
% 13.04/2.31 % (3583586)Termination phase: Saturation
% 13.04/2.31 % (3583586)Time elapsed: 0.058 s
% 13.04/2.31 % (3583586)Peak memory usage: 13 MB
% 13.04/2.31 % (3583586)Instructions burned: 137 (million)
% 13.04/2.31 % (3583592)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 13.04/2.31 % (3583592)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=1193012998:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2983 on theBenchmark for (2983ds/281Mi)
% 13.04/2.31 % (3583580)Instruction limit reached!
% 13.04/2.31 % (3583580)------------------------------
% 13.04/2.31 % (3583580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.31 % (3583580)CaDiCaL version: 2.1.3
% 13.04/2.31 % (3583580)Termination reason: Instruction limit
% 13.04/2.31 % (3583580)Termination phase: Saturation
% 13.04/2.31 % (3583580)Time elapsed: 0.190 s
% 13.04/2.31 % (3583580)Peak memory usage: 14 MB
% 13.04/2.31 % (3583580)Instructions burned: 339 (million)
% 13.04/2.31 % (3583594)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1883507527:i=619:add=on:rtra=on_2982 on theBenchmark for (2982ds/619Mi)
% 13.04/2.31 % (3583588)Instruction limit reached!
% 13.04/2.31 % (3583588)------------------------------
% 13.04/2.31 % (3583588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.31 % (3583588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.32 % (3583588)CaDiCaL version: 2.1.3
% 13.04/2.32 % (3583588)Termination reason: Instruction limit
% 13.04/2.32 % (3583588)Termination phase: Saturation
% 13.04/2.32 % (3583588)Time elapsed: 0.112 s
% 13.04/2.32 % (3583588)Peak memory usage: 16 MB
% 13.04/2.32 % (3583588)Instructions burned: 234 (million)
% 13.04/2.32 % (3583596)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=238832517:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/865Mi)
% 13.04/2.32 % (3583592)Instruction limit reached!
% 13.04/2.32 % (3583592)------------------------------
% 13.04/2.32 % (3583592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.32 % (3583592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.32 % (3583592)CaDiCaL version: 2.1.3
% 13.04/2.32 % (3583592)Termination reason: Instruction limit
% 13.04/2.32 % (3583592)Termination phase: Saturation
% 13.04/2.32 % (3583592)Time elapsed: 0.129 s
% 13.04/2.32 % (3583592)Peak memory usage: 14 MB
% 13.04/2.32 % (3583592)Instructions burned: 281 (million)
% 13.04/2.32 % (3583598)lrs+10_1_sil=128000:si=on:urr=on:random_seed=4076854401:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2981 on theBenchmark for (2981ds/212Mi)
% 13.04/2.32 % (3583598)Instruction limit reached!
% 13.04/2.32 % (3583598)------------------------------
% 13.04/2.32 % (3583598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.32 % (3583598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.32 % (3583598)CaDiCaL version: 2.1.3
% 13.04/2.32 % (3583598)Termination reason: Instruction limit
% 13.04/2.32 % (3583598)Termination phase: Saturation
% 13.04/2.32 % (3583598)Time elapsed: 0.099 s
% 13.04/2.32 % (3583598)Peak memory usage: 15 MB
% 13.04/2.32 % (3583598)Instructions burned: 212 (million)
% 13.04/2.32 % (3583589) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3583392-3583589"...
% 13.04/2.32 % (3583600)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=933578816:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2980 on theBenchmark for (2980ds/130Mi)
% 13.04/2.32 % (3583589)...printing done.
% 13.04/2.32 % (3583589)Refutation found. Thanks to Tanya!
% 13.04/2.32 % SZS status Theorem for theBenchmark
% 13.04/2.32 % SZS output start Proof for theBenchmark
% 13.04/2.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 13.04/2.32 thf(func_def_0, type, in: ($i > $i > $o)).
% 13.04/2.32 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 13.04/2.32 thf(func_def_3, type, setextAx: $o).
% 13.04/2.32 thf(func_def_5, type, emptysetAx: $o).
% 13.04/2.32 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 13.04/2.32 thf(func_def_7, type, setadjoinAx: $o).
% 13.04/2.32 thf(func_def_8, type, powerset: ($i > $i)).
% 13.04/2.32 thf(func_def_9, type, powersetAx: $o).
% 13.04/2.32 thf(func_def_10, type, setunion: ($i > $i)).
% 13.04/2.32 thf(func_def_11, type, setunionAx: $o).
% 13.04/2.32 thf(func_def_13, type, omega0Ax: $o).
% 13.04/2.32 thf(func_def_14, type, omegaSAx: $o).
% 13.04/2.32 thf(func_def_15, type, omegaIndAx: $o).
% 13.04/2.32 thf(func_def_16, type, replAx: $o).
% 13.04/2.32 thf(func_def_17, type, foundationAx: $o).
% 13.04/2.32 thf(func_def_18, type, wellorderingAx: $o).
% 13.04/2.32 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 13.04/2.32 thf(func_def_20, type, descrp: $o).
% 13.04/2.32 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 13.04/2.32 thf(func_def_22, type, dsetconstrI: $o).
% 13.04/2.32 thf(func_def_23, type, dsetconstrEL: $o).
% 13.04/2.32 thf(func_def_24, type, dsetconstrER: $o).
% 13.04/2.32 thf(func_def_25, type, exuE1: $o).
% 13.04/2.32 thf(func_def_26, type, prop2set: ($o > $i)).
% 13.04/2.32 thf(func_def_27, type, prop2setE: $o).
% 13.04/2.32 thf(func_def_28, type, emptysetE: $o).
% 13.04/2.32 thf(func_def_29, type, emptysetimpfalse: $o).
% 13.04/2.32 thf(func_def_30, type, notinemptyset: $o).
% 13.04/2.32 thf(func_def_31, type, exuE3e: $o).
% 13.04/2.32 thf(func_def_32, type, setext: $o).
% 13.04/2.32 thf(func_def_33, type, emptyI: $o).
% 13.04/2.32 thf(func_def_34, type, noeltsimpempty: $o).
% 13.04/2.32 thf(func_def_35, type, setbeta: $o).
% 13.04/2.32 thf(func_def_36, type, nonempty: ($i > $o)).
% 13.04/2.32 thf(func_def_37, type, nonemptyE1: $o).
% 13.04/2.32 thf(func_def_38, type, nonemptyI: $o).
% 13.04/2.32 thf(func_def_39, type, nonemptyI1: $o).
% 13.04/2.32 thf(func_def_40, type, setadjoinIL: $o).
% 13.04/2.32 thf(func_def_41, type, emptyinunitempty: $o).
% 13.04/2.32 thf(func_def_42, type, setadjoinIR: $o).
% 13.04/2.32 thf(func_def_43, type, setadjoinE: $o).
% 13.04/2.32 thf(func_def_44, type, setadjoinOr: $o).
% 13.04/2.32 thf(func_def_45, type, setoftrueEq: $o).
% 13.04/2.32 thf(func_def_46, type, powersetI: $o).
% 13.04/2.32 thf(func_def_47, type, emptyinPowerset: $o).
% 13.04/2.32 thf(func_def_48, type, emptyInPowerset: $o).
% 13.04/2.32 thf(func_def_49, type, powersetE: $o).
% 13.04/2.32 thf(func_def_50, type, setunionI: $o).
% 13.04/2.32 thf(func_def_51, type, setunionE: $o).
% 13.04/2.32 thf(func_def_52, type, subPowSU: $o).
% 13.04/2.32 thf(func_def_53, type, exuE2: $o).
% 13.04/2.32 thf(func_def_54, type, nonemptyImpWitness: $o).
% 13.04/2.32 thf(func_def_55, type, uniqinunit: $o).
% 13.04/2.32 thf(func_def_56, type, notinsingleton: $o).
% 13.04/2.32 thf(func_def_57, type, eqinunit: $o).
% 13.04/2.32 thf(func_def_58, type, singletonsswitch: $o).
% 13.04/2.32 thf(func_def_59, type, upairsetE: $o).
% 13.04/2.32 thf(func_def_60, type, upairsetIL: $o).
% 13.04/2.32 thf(func_def_61, type, upairsetIR: $o).
% 13.04/2.32 thf(func_def_62, type, emptyE1: $o).
% 13.04/2.32 thf(func_def_63, type, vacuousDall: $o).
% 13.04/2.32 thf(func_def_64, type, quantDeMorgan1: $o).
% 13.04/2.32 thf(func_def_65, type, quantDeMorgan2: $o).
% 13.04/2.32 thf(func_def_66, type, quantDeMorgan3: $o).
% 13.04/2.32 thf(func_def_67, type, quantDeMorgan4: $o).
% 13.04/2.32 thf(func_def_68, type, prop2setI: $o).
% 13.04/2.32 thf(func_def_69, type, set2prop: ($i > $o)).
% 13.04/2.32 thf(func_def_70, type, prop2set2propI: $o).
% 13.04/2.32 thf(func_def_71, type, notdexE: $o).
% 13.04/2.32 thf(func_def_72, type, notdallE: $o).
% 13.04/2.32 thf(func_def_73, type, exuI1: $o).
% 13.04/2.32 thf(func_def_74, type, exuI3: $o).
% 13.04/2.32 thf(func_def_75, type, exuI2: $o).
% 13.04/2.32 thf(func_def_76, type, inCongP: $o).
% 13.04/2.32 thf(func_def_77, type, in__Cong: $o).
% 13.04/2.32 thf(func_def_78, type, exuE3u: $o).
% 13.04/2.32 thf(func_def_79, type, exu__Cong: $o).
% 13.04/2.32 thf(func_def_80, type, emptyset__Cong: $o).
% 13.04/2.32 thf(func_def_81, type, setadjoin__Cong: $o).
% 13.04/2.32 thf(func_def_82, type, powerset__Cong: $o).
% 13.04/2.32 thf(func_def_83, type, setunion__Cong: $o).
% 13.04/2.32 thf(func_def_84, type, omega__Cong: $o).
% 13.04/2.32 thf(func_def_85, type, exuEu: $o).
% 13.04/2.32 thf(func_def_86, type, descr__Cong: $o).
% 13.04/2.32 thf(func_def_87, type, dsetconstr__Cong: $o).
% 13.04/2.32 thf(func_def_88, type, subset: ($i > $i > $o)).
% 13.04/2.32 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 13.04/2.32 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 13.04/2.32 thf(func_def_91, type, subsetI1: $o).
% 13.04/2.32 thf(func_def_92, type, eqimpsubset2: $o).
% 13.04/2.32 thf(func_def_93, type, eqimpsubset1: $o).
% 13.04/2.32 thf(func_def_94, type, subsetI2: $o).
% 13.04/2.32 thf(func_def_95, type, emptysetsubset: $o).
% 13.04/2.32 thf(func_def_96, type, subsetE: $o).
% 13.04/2.32 thf(func_def_97, type, subsetE2: $o).
% 13.04/2.32 thf(func_def_98, type, notsubsetI: $o).
% 13.04/2.32 thf(func_def_99, type, notequalI1: $o).
% 13.04/2.32 thf(func_def_100, type, notequalI2: $o).
% 13.04/2.32 thf(func_def_101, type, subsetRefl: $o).
% 13.04/2.32 thf(func_def_102, type, subsetTrans: $o).
% 13.04/2.32 thf(func_def_103, type, setadjoinSub: $o).
% 13.04/2.32 thf(func_def_104, type, setadjoinSub2: $o).
% 13.04/2.32 thf(func_def_105, type, subset2powerset: $o).
% 13.04/2.32 thf(func_def_106, type, setextsub: $o).
% 13.04/2.32 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 13.04/2.32 thf(func_def_108, type, powersetI1: $o).
% 13.04/2.32 thf(func_def_109, type, powersetE1: $o).
% 13.04/2.32 thf(func_def_110, type, inPowerset: $o).
% 13.04/2.32 thf(func_def_111, type, powersetsubset: $o).
% 13.04/2.32 thf(func_def_112, type, sepInPowerset: $o).
% 13.04/2.32 thf(func_def_113, type, sepSubset: $o).
% 13.04/2.32 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 13.04/2.32 thf(func_def_115, type, binunionIL: $o).
% 13.04/2.32 thf(func_def_116, type, upairset2IR: $o).
% 13.04/2.32 thf(func_def_117, type, binunionIR: $o).
% 13.04/2.32 thf(func_def_118, type, binunionEcases: $o).
% 13.04/2.32 thf(func_def_119, type, binunionE: $o).
% 13.04/2.32 thf(func_def_120, type, binunionLsub: $o).
% 13.04/2.32 thf(func_def_121, type, binunionRsub: $o).
% 13.04/2.32 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 13.04/2.32 thf(func_def_123, type, binintersectI: $o).
% 13.04/2.32 thf(func_def_124, type, binintersectSubset5: $o).
% 13.04/2.32 thf(func_def_125, type, binintersectEL: $o).
% 13.04/2.32 thf(func_def_126, type, binintersectLsub: $o).
% 13.04/2.32 thf(func_def_127, type, binintersectSubset2: $o).
% 13.04/2.32 thf(func_def_128, type, binintersectSubset3: $o).
% 13.04/2.32 thf(func_def_129, type, binintersectER: $o).
% 13.04/2.32 thf(func_def_130, type, disjointsetsI1: $o).
% 13.04/2.32 thf(func_def_131, type, binintersectRsub: $o).
% 13.04/2.32 thf(func_def_132, type, binintersectSubset4: $o).
% 13.04/2.32 thf(func_def_133, type, binintersectSubset1: $o).
% 13.04/2.32 thf(func_def_134, type, bs114d: $o).
% 13.04/2.32 thf(func_def_135, type, regular: ($i > $o)).
% 13.04/2.32 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 13.04/2.32 thf(func_def_137, type, setminusI: $o).
% 13.04/2.32 thf(func_def_138, type, setminusEL: $o).
% 13.04/2.32 thf(func_def_139, type, setminusER: $o).
% 13.04/2.32 thf(func_def_140, type, setminusSubset2: $o).
% 13.04/2.32 thf(func_def_141, type, setminusERneg: $o).
% 13.04/2.32 thf(func_def_142, type, setminusELneg: $o).
% 13.04/2.32 thf(func_def_143, type, setminusILneg: $o).
% 13.04/2.32 thf(func_def_144, type, setminusIRneg: $o).
% 13.04/2.32 thf(func_def_145, type, setminusLsub: $o).
% 13.04/2.32 thf(func_def_146, type, setminusSubset1: $o).
% 13.04/2.32 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 13.04/2.32 thf(func_def_148, type, symdiffE: $o).
% 13.04/2.32 thf(func_def_149, type, symdiffI1: $o).
% 13.04/2.32 thf(func_def_150, type, symdiffI2: $o).
% 13.04/2.32 thf(func_def_151, type, symdiffIneg1: $o).
% 13.04/2.32 thf(func_def_152, type, symdiffIneg2: $o).
% 13.04/2.32 thf(func_def_153, type, iskpair: ($i > $o)).
% 13.04/2.32 thf(func_def_154, type, secondinupair: $o).
% 13.04/2.32 thf(func_def_155, type, setukpairIL: $o).
% 13.04/2.32 thf(func_def_156, type, setukpairIR: $o).
% 13.04/2.32 thf(func_def_157, type, kpairiskpair: $o).
% 13.04/2.32 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 13.04/2.32 thf(func_def_159, type, kpairp: $o).
% 13.04/2.32 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 13.04/2.32 thf(func_def_161, type, singletonsubset: $o).
% 13.04/2.32 thf(func_def_162, type, singletoninpowerset: $o).
% 13.04/2.32 thf(func_def_163, type, singletoninpowunion: $o).
% 13.04/2.32 thf(func_def_164, type, upairset2E: $o).
% 13.04/2.32 thf(func_def_165, type, upairsubunion: $o).
% 13.04/2.32 thf(func_def_166, type, upairinpowunion: $o).
% 13.04/2.32 thf(func_def_167, type, ubforcartprodlem1: $o).
% 13.04/2.32 thf(func_def_168, type, ubforcartprodlem2: $o).
% 13.04/2.32 thf(func_def_169, type, ubforcartprodlem3: $o).
% 13.04/2.32 thf(func_def_170, type, cartprodpairin: $o).
% 13.04/2.32 thf(func_def_171, type, cartprodmempair1: $o).
% 13.04/2.32 thf(func_def_172, type, cartprodmempair: $o).
% 13.04/2.32 thf(func_def_173, type, setunionE2: $o).
% 13.04/2.32 thf(func_def_174, type, setunionsingleton1: $o).
% 13.04/2.32 thf(func_def_175, type, setunionsingleton2: $o).
% 13.04/2.32 thf(func_def_176, type, setunionsingleton: $o).
% 13.04/2.32 thf(func_def_177, type, singleton: ($i > $o)).
% 13.04/2.32 thf(func_def_178, type, singletonprop: $o).
% 13.04/2.32 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 13.04/2.32 thf(func_def_180, type, ex1E1: $o).
% 13.04/2.32 thf(func_def_181, type, ex1I: $o).
% 13.04/2.32 thf(func_def_182, type, ex1I2: $o).
% 13.04/2.32 thf(func_def_183, type, singletonsuniq: $o).
% 13.04/2.32 thf(func_def_184, type, atmost1p: ($i > $o)).
% 13.04/2.32 thf(func_def_185, type, atleast2p: ($i > $o)).
% 13.04/2.32 thf(func_def_186, type, atmost2p: ($i > $o)).
% 13.04/2.32 thf(func_def_187, type, upairsetp: ($i > $o)).
% 13.04/2.32 thf(func_def_188, type, setukpairinjL1: $o).
% 13.04/2.32 thf(func_def_189, type, kfstsingleton: $o).
% 13.04/2.32 thf(func_def_190, type, theprop: $o).
% 13.04/2.32 thf(func_def_191, type, kfst: ($i > $i)).
% 13.04/2.32 thf(func_def_192, type, kfstpairEq: $o).
% 13.04/2.32 thf(func_def_193, type, cartprodfstin: $o).
% 13.04/2.32 thf(func_def_194, type, setukpairinjL2: $o).
% 13.04/2.32 thf(func_def_195, type, setukpairinjL: $o).
% 13.04/2.32 thf(func_def_196, type, setukpairinjR11: $o).
% 13.04/2.32 thf(func_def_197, type, setukpairinjR12: $o).
% 13.04/2.32 thf(func_def_198, type, setukpairinjR1: $o).
% 13.04/2.32 thf(func_def_199, type, upairequniteq: $o).
% 13.04/2.32 thf(func_def_200, type, setukpairinjR2: $o).
% 13.04/2.32 thf(func_def_201, type, setukpairinjR: $o).
% 13.04/2.32 thf(func_def_202, type, ksndsingleton: $o).
% 13.04/2.32 thf(func_def_203, type, ksnd: ($i > $i)).
% 13.04/2.32 thf(func_def_204, type, ksndpairEq: $o).
% 13.04/2.32 thf(func_def_205, type, kpairsurjEq: $o).
% 13.04/2.32 thf(func_def_206, type, cartprodsndin: $o).
% 13.04/2.32 thf(func_def_207, type, cartprodpairmemEL: $o).
% 13.04/2.32 thf(func_def_208, type, cartprodpairmemER: $o).
% 13.04/2.32 thf(func_def_209, type, cartprodmempaircEq: $o).
% 13.04/2.32 thf(func_def_210, type, cartprodfstpairEq: $o).
% 13.04/2.32 thf(func_def_211, type, cartprodsndpairEq: $o).
% 13.04/2.32 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 13.04/2.32 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 13.04/2.32 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 13.04/2.32 thf(func_def_215, type, dpsetconstrI: $o).
% 13.04/2.32 thf(func_def_216, type, dpsetconstrSub: $o).
% 13.04/2.32 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 13.04/2.32 thf(func_def_218, type, dpsetconstrERa: $o).
% 13.04/2.32 thf(func_def_219, type, dpsetconstrEL1: $o).
% 13.04/2.32 thf(func_def_220, type, dpsetconstrEL2: $o).
% 13.04/2.32 thf(func_def_221, type, dpsetconstrER: $o).
% 13.04/2.32 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 13.04/2.32 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 13.04/2.32 thf(func_def_224, type, funcImageSingleton: $o).
% 13.04/2.32 thf(func_def_225, type, apProp: $o).
% 13.04/2.32 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 13.04/2.32 thf(func_def_227, type, app: $o).
% 13.04/2.32 thf(func_def_228, type, infuncsetfunc: $o).
% 13.04/2.32 thf(func_def_229, type, ap2p: $o).
% 13.04/2.32 thf(func_def_230, type, funcinfuncset: $o).
% 13.04/2.32 thf(func_def_231, type, lamProp: $o).
% 13.04/2.32 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 13.04/2.32 thf(func_def_233, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 13.04/2.32 thf(func_def_234, type, vIMP: ($o > $o > $o)).
% 13.04/2.32 thf(func_def_235, type, db2: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(func_def_236, type, db0: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(func_def_237, type, db1: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(func_def_238, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 13.04/2.32 thf(func_def_239, type, vNOT: ($o > $o)).
% 13.04/2.32 thf(func_def_240, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 13.04/2.32 thf(func_def_241, type, db3: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(func_def_242, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 13.04/2.32 thf(func_def_243, type, vAND: ($o > $o > $o)).
% 13.04/2.32 thf(func_def_244, type, vOR: ($o > $o > $o)).
% 13.04/2.32 thf(func_def_245, type, vIFF: ($o > $o > $o)).
% 13.04/2.32 thf(func_def_246, type, db4: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(func_def_249, type, db5: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(func_def_250, type, db6: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(func_def_251, type, sF0: $o).
% 13.04/2.32 thf(func_def_252, type, sF1: $o).
% 13.04/2.32 thf(func_def_253, type, sF2: $o).
% 13.04/2.32 thf(func_def_254, type, sF3: $o).
% 13.04/2.32 thf(func_def_255, type, sF4: $o).
% 13.04/2.32 thf(func_def_256, type, sF5: $o).
% 13.04/2.32 thf(func_def_257, type, sF6: $o).
% 13.04/2.32 thf(func_def_258, type, sF7: $o).
% 13.04/2.32 thf(func_def_259, type, sF8: $o).
% 13.04/2.32 thf(func_def_260, type, sF9: $o).
% 13.04/2.32 thf(func_def_261, type, sF10: $o).
% 13.04/2.32 thf(func_def_262, type, sF11: $o).
% 13.04/2.32 thf(func_def_263, type, sF12: $o).
% 13.04/2.32 thf(func_def_264, type, sF13: $o).
% 13.04/2.32 thf(func_def_265, type, sF14: $o).
% 13.04/2.32 thf(func_def_266, type, sF15: $o).
% 13.04/2.32 thf(func_def_267, type, sF16: $o).
% 13.04/2.32 thf(func_def_268, type, sF17: $o).
% 13.04/2.32 thf(func_def_269, type, sF18: $o).
% 13.04/2.32 thf(func_def_270, type, sF19: $o).
% 13.04/2.32 thf(func_def_271, type, sF20: $o).
% 13.04/2.32 thf(func_def_272, type, sF21: $o).
% 13.04/2.32 thf(func_def_273, type, sF22: $o).
% 13.04/2.32 thf(func_def_274, type, sF23: $o).
% 13.04/2.32 thf(func_def_275, type, sF24: $o).
% 13.04/2.32 thf(func_def_276, type, sF25: $o).
% 13.04/2.32 thf(func_def_277, type, sF26: $o).
% 13.04/2.32 thf(func_def_278, type, sF27: $o).
% 13.04/2.32 thf(func_def_279, type, sF28: $o).
% 13.04/2.32 thf(func_def_280, type, sF29: $o).
% 13.04/2.32 thf(func_def_281, type, sF30: $o).
% 13.04/2.32 thf(func_def_282, type, sF31: $o).
% 13.04/2.32 thf(func_def_283, type, sF32: $o).
% 13.04/2.32 thf(func_def_284, type, sF33: $o).
% 13.04/2.32 thf(func_def_285, type, sF34: $o).
% 13.04/2.32 thf(func_def_286, type, sF35: $o).
% 13.04/2.32 thf(func_def_287, type, sF36: $o).
% 13.04/2.32 thf(func_def_288, type, sF37: $o).
% 13.04/2.32 thf(func_def_289, type, sF38: $o).
% 13.04/2.32 thf(func_def_290, type, sF39: $o).
% 13.04/2.32 thf(func_def_291, type, sF40: $o).
% 13.04/2.32 thf(func_def_292, type, sF41: $o).
% 13.04/2.32 thf(func_def_293, type, sF42: $o).
% 13.04/2.32 thf(func_def_294, type, sF43: $o).
% 13.04/2.32 thf(func_def_295, type, sF44: $o).
% 13.04/2.32 thf(func_def_296, type, sF45: $o).
% 13.04/2.32 thf(func_def_297, type, sF46: $o).
% 13.04/2.32 thf(func_def_298, type, sF47: $o).
% 13.04/2.32 thf(func_def_299, type, sF48: $o).
% 13.04/2.32 thf(func_def_300, type, sF49: $o).
% 13.04/2.32 thf(func_def_301, type, sF50: $o).
% 13.04/2.32 thf(func_def_302, type, sF51: $o).
% 13.04/2.32 thf(func_def_303, type, sF52: $o).
% 13.04/2.32 thf(func_def_304, type, sF53: $o).
% 13.04/2.32 thf(func_def_305, type, sF54: $o).
% 13.04/2.32 thf(func_def_306, type, sF55: $o).
% 13.04/2.32 thf(func_def_307, type, sF56: $o).
% 13.04/2.32 thf(func_def_308, type, sF57: $o).
% 13.04/2.32 thf(func_def_309, type, sF58: $o).
% 13.04/2.32 thf(func_def_310, type, sF59: $o).
% 13.04/2.32 thf(func_def_311, type, sF60: $o).
% 13.04/2.32 thf(func_def_312, type, sF61: $o).
% 13.04/2.32 thf(func_def_313, type, sF62: $o).
% 13.04/2.32 thf(func_def_314, type, sF63: $o).
% 13.04/2.32 thf(func_def_315, type, sF64: $o).
% 13.04/2.32 thf(func_def_316, type, sF65: $o).
% 13.04/2.32 thf(func_def_317, type, sF66: $o).
% 13.04/2.32 thf(func_def_318, type, sF67: $o).
% 13.04/2.32 thf(func_def_319, type, sF68: $o).
% 13.04/2.32 thf(func_def_320, type, sF69: $o).
% 13.04/2.32 thf(func_def_321, type, sF70: $o).
% 13.04/2.32 thf(func_def_322, type, sF71: $o).
% 13.04/2.32 thf(func_def_323, type, sF72: $o).
% 13.04/2.32 thf(func_def_324, type, sF73: $o).
% 13.04/2.32 thf(func_def_325, type, sF74: $o).
% 13.04/2.32 thf(func_def_326, type, sF75: $o).
% 13.04/2.32 thf(func_def_327, type, sF76: $o).
% 13.04/2.32 thf(func_def_328, type, sF77: $o).
% 13.04/2.32 thf(func_def_329, type, sF78: $o).
% 13.04/2.32 thf(func_def_330, type, sF79: $o).
% 13.04/2.32 thf(func_def_331, type, sF80: $o).
% 13.04/2.32 thf(func_def_332, type, sF81: $o).
% 13.04/2.32 thf(func_def_333, type, sF82: $o).
% 13.04/2.32 thf(func_def_334, type, sF83: $o).
% 13.04/2.32 thf(func_def_335, type, sF84: $o).
% 13.04/2.32 thf(func_def_336, type, sF85: $o).
% 13.04/2.32 thf(func_def_337, type, sF86: $o).
% 13.04/2.32 thf(func_def_338, type, sF87: $o).
% 13.04/2.32 thf(func_def_339, type, sF88: $o).
% 13.04/2.32 thf(func_def_340, type, sF89: $o).
% 13.04/2.32 thf(func_def_341, type, sF90: $o).
% 13.04/2.32 thf(func_def_342, type, sF91: $o).
% 13.04/2.32 thf(func_def_343, type, sF92: $o).
% 13.04/2.32 thf(func_def_344, type, sF93: $o).
% 13.04/2.32 thf(func_def_345, type, sF94: $o).
% 13.04/2.32 thf(func_def_346, type, sF95: $o).
% 13.04/2.32 thf(func_def_347, type, sF96: $o).
% 13.04/2.32 thf(func_def_348, type, sF97: $o).
% 13.04/2.32 thf(func_def_349, type, sF98: $o).
% 13.04/2.32 thf(func_def_350, type, sF99: $o).
% 13.04/2.32 thf(func_def_351, type, sF100: $o).
% 13.04/2.32 thf(func_def_352, type, sF101: $o).
% 13.04/2.32 thf(func_def_353, type, sF102: $o).
% 13.04/2.32 thf(func_def_354, type, sF103: $o).
% 13.04/2.32 thf(func_def_355, type, sF104: $o).
% 13.04/2.32 thf(func_def_356, type, sF105: $o).
% 13.04/2.32 thf(func_def_357, type, sF106: $o).
% 13.04/2.32 thf(func_def_358, type, sF107: $o).
% 13.04/2.32 thf(func_def_359, type, sF108: $o).
% 13.04/2.32 thf(func_def_360, type, sF109: $o).
% 13.04/2.32 thf(func_def_361, type, sF110: $o).
% 13.04/2.32 thf(func_def_362, type, sF111: $o).
% 13.04/2.32 thf(func_def_363, type, sF112: $o).
% 13.04/2.32 thf(func_def_364, type, sF113: $o).
% 13.04/2.32 thf(func_def_365, type, sF114: $o).
% 13.04/2.32 thf(func_def_366, type, sF115: $o).
% 13.04/2.32 thf(func_def_367, type, sF116: $o).
% 13.04/2.32 thf(func_def_368, type, sF117: $o).
% 13.04/2.32 thf(func_def_369, type, sF118: $o).
% 13.04/2.32 thf(func_def_370, type, sF119: $o).
% 13.04/2.32 thf(func_def_371, type, sF120: $o).
% 13.04/2.32 thf(func_def_372, type, sF121: $o).
% 13.04/2.32 thf(func_def_373, type, sF122: $o).
% 13.04/2.32 thf(func_def_374, type, sF123: $o).
% 13.04/2.32 thf(func_def_375, type, sF124: $o).
% 13.04/2.32 thf(func_def_376, type, sF125: $o).
% 13.04/2.32 thf(func_def_377, type, sF126: $o).
% 13.04/2.32 thf(func_def_378, type, sF127: $o).
% 13.04/2.32 thf(func_def_379, type, sF128: $o).
% 13.04/2.32 thf(func_def_380, type, sF129: $o).
% 13.04/2.32 thf(func_def_381, type, sF130: $o).
% 13.04/2.32 thf(func_def_382, type, sF131: $o).
% 13.04/2.32 thf(func_def_383, type, sF132: $o).
% 13.04/2.32 thf(func_def_384, type, sF133: $o).
% 13.04/2.32 thf(func_def_385, type, sF134: $o).
% 13.04/2.32 thf(func_def_386, type, sF135: $o).
% 13.04/2.32 thf(func_def_387, type, sF136: $o).
% 13.04/2.32 thf(func_def_388, type, sF137: $o).
% 13.04/2.32 thf(func_def_389, type, sF138: $o).
% 13.04/2.32 thf(func_def_390, type, sF139: $o).
% 13.04/2.32 thf(func_def_391, type, sF140: $o).
% 13.04/2.32 thf(func_def_392, type, sF141: $o).
% 13.04/2.32 thf(func_def_393, type, sF142: $o).
% 13.04/2.32 thf(func_def_394, type, sF143: $o).
% 13.04/2.32 thf(func_def_395, type, sF144: $o).
% 13.04/2.32 thf(func_def_396, type, sF145: $o).
% 13.04/2.32 thf(func_def_397, type, sF146: $o).
% 13.04/2.32 thf(func_def_398, type, sF147: $o).
% 13.04/2.32 thf(func_def_399, type, sF148: $o).
% 13.04/2.32 thf(func_def_400, type, sF149: $o).
% 13.04/2.32 thf(func_def_401, type, sF150: $o).
% 13.04/2.32 thf(func_def_402, type, sF151: $o).
% 13.04/2.32 thf(func_def_403, type, sF152: $o).
% 13.04/2.32 thf(func_def_404, type, sF153: $o).
% 13.04/2.32 thf(func_def_405, type, sF154: $o).
% 13.04/2.32 thf(func_def_406, type, sF155: $o).
% 13.04/2.32 thf(func_def_407, type, sF156: $o).
% 13.04/2.32 thf(func_def_408, type, sF157: $o).
% 13.04/2.32 thf(func_def_409, type, sF158: $o).
% 13.04/2.32 thf(func_def_410, type, sF159: $o).
% 13.04/2.32 thf(func_def_411, type, sF160: $o).
% 13.04/2.32 thf(func_def_412, type, sF161: $o).
% 13.04/2.32 thf(func_def_413, type, sF162: $o).
% 13.04/2.32 thf(func_def_414, type, sF163: $o).
% 13.04/2.32 thf(func_def_415, type, sF164: $o).
% 13.04/2.32 thf(func_def_416, type, sF165: $o).
% 13.04/2.32 thf(func_def_417, type, sF166: $o).
% 13.04/2.32 thf(func_def_418, type, sF167: $o).
% 13.04/2.32 thf(func_def_419, type, sF168: $o).
% 13.04/2.32 thf(func_def_420, type, sF169: $o).
% 13.04/2.32 thf(func_def_421, type, sF170: $o).
% 13.04/2.32 thf(func_def_422, type, sF171: $o).
% 13.04/2.32 thf(func_def_423, type, sF172: $o).
% 13.04/2.32 thf(func_def_424, type, sF173: $o).
% 13.04/2.32 thf(func_def_425, type, sF174: $o).
% 13.04/2.32 thf(func_def_426, type, sF175: $o).
% 13.04/2.32 thf(func_def_427, type, sF176: $o).
% 13.04/2.32 thf(func_def_428, type, sF177: $o).
% 13.04/2.32 thf(func_def_429, type, sF178: $o).
% 13.04/2.32 thf(func_def_430, type, sF179: $o).
% 13.04/2.32 thf(func_def_431, type, sF180: $o).
% 13.04/2.32 thf(func_def_432, type, sF181: $o).
% 13.04/2.32 thf(func_def_433, type, sF182: $o).
% 13.04/2.32 thf(func_def_434, type, sF183: $o).
% 13.04/2.32 thf(func_def_435, type, sF184: $o).
% 13.04/2.32 thf(func_def_436, type, sF185: $o).
% 13.04/2.32 thf(func_def_437, type, sF186: $o).
% 13.04/2.32 thf(func_def_438, type, sF187: $o).
% 13.04/2.32 thf(func_def_439, type, sF188: $o).
% 13.04/2.32 thf(func_def_440, type, sF189: $o).
% 13.04/2.32 thf(func_def_441, type, sF190: $o).
% 13.04/2.32 thf(func_def_442, type, sF191: $o).
% 13.04/2.32 thf(func_def_443, type, sF192: $o).
% 13.04/2.32 thf(func_def_444, type, sF193: $o).
% 13.04/2.32 thf(func_def_445, type, sF194: $o).
% 13.04/2.32 thf(func_def_446, type, sF195: $o).
% 13.04/2.32 thf(func_def_447, type, sF196: $o).
% 13.04/2.32 thf(func_def_448, type, db7: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(func_def_449, type, db8: !>[X0: $tType]:(X0)).
% 13.04/2.32 thf(f1,axiom,(
% 13.04/2.32 ((^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu)).
% 13.04/2.32 thf(f3,axiom,(
% 13.04/2.32 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx)).
% 13.04/2.32 thf(f4,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) <=> ((X2 = X0) | (in @ X2 @ X1))) = setadjoinAx)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx)).
% 13.04/2.32 thf(f5,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetAx)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx)).
% 13.04/2.32 thf(f6,axiom,(
% 13.04/2.32 (setunionAx = ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2)) <=> (in @ X1 @ (setunion @ X0))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx)).
% 13.04/2.32 thf(f7,axiom,(
% 13.04/2.32 (omega0Ax = ((in @ emptyset @ omega)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax)).
% 13.04/2.32 thf(f13,axiom,(
% 13.04/2.32 (descrp = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => (X0 @ (descr @ (^[X1 : $i] : ((X0 @ X1)))))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp)).
% 13.04/2.32 thf(f14,axiom,(
% 13.04/2.32 (! [X1 : ($i > $o),X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))) = dsetconstrI)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI)).
% 13.04/2.32 thf(f15,axiom,(
% 13.04/2.32 (! [X1 : ($i > $o),X0 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL)).
% 13.04/2.32 thf(f16,axiom,(
% 13.04/2.32 (! [X1 : ($i > $o),X2 : $i,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (X1 @ X2)) = dsetconstrER)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 13.04/2.32 thf(f17,axiom,(
% 13.04/2.32 (exuE1 = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1)).
% 13.04/2.32 thf(f18,axiom,(
% 13.04/2.32 (prop2setE = ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE)).
% 13.04/2.32 thf(f19,axiom,(
% 13.04/2.32 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 13.04/2.32 thf(f20,axiom,(
% 13.04/2.32 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse)).
% 13.04/2.32 thf(f21,axiom,(
% 13.04/2.32 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset)).
% 13.04/2.32 thf(f22,axiom,(
% 13.04/2.32 (exuE3e = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (X0 @ X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e)).
% 13.04/2.32 thf(f23,axiom,(
% 13.04/2.32 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 13.04/2.32 thf(f24,axiom,(
% 13.04/2.32 (emptyI = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI)).
% 13.04/2.32 thf(f25,axiom,(
% 13.04/2.32 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = noeltsimpempty)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty)).
% 13.04/2.32 thf(f26,axiom,(
% 13.04/2.32 (! [X1 : ($i > $o),X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) <=> (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))) = setbeta)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta)).
% 13.04/2.32 thf(f27,axiom,(
% 13.04/2.32 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty)).
% 13.04/2.32 thf(f28,axiom,(
% 13.04/2.32 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1)).
% 13.04/2.32 thf(f30,axiom,(
% 13.04/2.32 (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)) = nonemptyI1)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1)).
% 13.04/2.32 thf(f31,axiom,(
% 13.04/2.32 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL)).
% 13.04/2.32 thf(f32,axiom,(
% 13.04/2.32 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty)).
% 13.04/2.32 thf(f33,axiom,(
% 13.04/2.32 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))) = setadjoinIR)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR)).
% 13.04/2.32 thf(f35,axiom,(
% 13.04/2.32 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ((in @ X2 @ X1) | (X2 = X0))) = setadjoinOr)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr)).
% 13.04/2.32 thf(f36,axiom,(
% 13.04/2.32 (setoftrueEq = ! [X0 : $i] : (((dsetconstr @ X0 @ (^[X1 : $i] : ($true)))) = X0))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq)).
% 13.04/2.32 thf(f37,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 13.04/2.32 thf(f38,axiom,(
% 13.04/2.32 (! [X0 : $i] : (in @ emptyset @ (powerset @ X0)) = emptyinPowerset)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset)).
% 13.04/2.32 thf(f39,axiom,(
% 13.04/2.32 (! [X0 : $i] : (in @ emptyset @ (powerset @ X0)) = emptyInPowerset)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset)).
% 13.04/2.32 thf(f43,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0)))) = subPowSU)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU)).
% 13.04/2.32 thf(f45,axiom,(
% 13.04/2.32 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & $true)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 13.04/2.32 thf(f46,axiom,(
% 13.04/2.32 (uniqinunit = ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 13.04/2.32 thf(f47,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))) = notinsingleton)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton)).
% 13.04/2.32 thf(f48,axiom,(
% 13.04/2.32 (eqinunit = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit)).
% 13.04/2.32 thf(f49,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = singletonsswitch)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch)).
% 13.04/2.32 thf(f51,axiom,(
% 13.04/2.32 (upairsetIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL)).
% 13.04/2.32 thf(f52,axiom,(
% 13.04/2.32 (upairsetIR = ! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR)).
% 13.04/2.32 thf(f54,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : ($i > $o)] : ((in @ X1 @ emptyset) => (X0 @ X1)) = vacuousDall)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall)).
% 13.04/2.32 thf(f56,axiom,(
% 13.04/2.32 (quantDeMorgan2 = ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2)) => ~ ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2)).
% 13.04/2.32 thf(f57,axiom,(
% 13.04/2.32 (! [X1 : ($i > $o),X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2))) = quantDeMorgan3)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3)).
% 13.04/2.32 thf(f59,axiom,(
% 13.04/2.32 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI)).
% 13.04/2.32 thf(f61,axiom,(
% 13.04/2.32 (! [X1 : ($i > $o),X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2))) = notdexE)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE)).
% 13.04/2.32 thf(f63,axiom,(
% 13.04/2.32 (exuI1 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1))))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1)).
% 13.04/2.32 thf(f64,axiom,(
% 13.04/2.32 (exuI3 = ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1)))))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3)).
% 13.04/2.32 thf(f65,axiom,(
% 13.04/2.32 (exuI2 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X2 = X1)) => (exu @ (^[X1 : $i] : ((X0 @ X1))))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2)).
% 13.04/2.32 thf(f66,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1)))) = inCongP)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP)).
% 13.04/2.32 thf(f68,axiom,(
% 13.04/2.32 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuE3u)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u)).
% 13.04/2.32 thf(f70,axiom,(
% 13.04/2.32 (emptyset__Cong = (emptyset = emptyset))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong)).
% 13.04/2.32 thf(f71,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => (((setadjoin @ X0 @ X2)) = ((setadjoin @ X1 @ X3))))) = setadjoin__Cong)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong)).
% 13.04/2.32 thf(f73,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : ((X0 = X1) => (((setunion @ X0)) = ((setunion @ X1)))) = setunion__Cong)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong)).
% 13.04/2.32 thf(f74,axiom,(
% 13.04/2.32 ((omega = omega) = omega__Cong)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong)).
% 13.04/2.32 thf(f75,axiom,(
% 13.04/2.32 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuEu)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu)).
% 13.04/2.32 thf(f78,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 13.04/2.32 thf(f79,axiom,(
% 13.04/2.32 (eqimpsubset2 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2)).
% 13.04/2.32 thf(f80,axiom,(
% 13.04/2.32 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1)).
% 13.04/2.32 thf(f81,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 13.04/2.32 thf(f82,axiom,(
% 13.04/2.32 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset)).
% 13.04/2.32 thf(f84,axiom,(
% 13.04/2.32 (subsetE2 = ! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X0 @ X1) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2)).
% 13.04/2.32 thf(f85,axiom,(
% 13.04/2.32 (notsubsetI = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI)).
% 13.04/2.32 thf(f86,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)) = notequalI1)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1)).
% 13.04/2.32 thf(f88,axiom,(
% 13.04/2.32 (subsetRefl = ! [X0 : $i] : (subset @ X0 @ X0))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl)).
% 13.04/2.32 thf(f90,axiom,(
% 13.04/2.32 (setadjoinSub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub)).
% 13.04/2.32 thf(f91,axiom,(
% 13.04/2.32 (setadjoinSub2 = ! [X2 : $i,X1 : $i,X0 : $i] : ((subset @ X0 @ X2) => (subset @ X0 @ (setadjoin @ X1 @ X2))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2)).
% 13.04/2.32 thf(f93,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub)).
% 13.04/2.32 thf(f94,axiom,(
% 13.04/2.32 (subsetemptysetimpeq = ! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq)).
% 13.04/2.32 thf(f95,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1)).
% 13.04/2.32 thf(f96,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)) = powersetE1)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1)).
% 13.04/2.32 thf(f97,axiom,(
% 13.04/2.32 (! [X0 : $i] : (in @ X0 @ (powerset @ X0)) = inPowerset)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset)).
% 13.04/2.32 thf(f98,axiom,(
% 13.04/2.32 (powersetsubset = ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset)).
% 13.04/2.32 thf(f99,axiom,(
% 13.04/2.32 (sepInPowerset = ! [X1 : ($i > $o),X0 : $i] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ (powerset @ X0)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset)).
% 13.04/2.32 thf(f100,axiom,(
% 13.04/2.32 (! [X1 : ($i > $o),X0 : $i] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ X0) = sepSubset)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset)).
% 13.04/2.32 thf(f101,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))) = binunionIL)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL)).
% 13.04/2.32 thf(f102,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = upairset2IR)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR)).
% 13.04/2.32 thf(f103,axiom,(
% 13.04/2.32 (binunionIR = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR)).
% 13.04/2.32 thf(f104,axiom,(
% 13.04/2.32 (! [X0 : $i,X3 : $o,X1 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => (((in @ X2 @ X0) => X3) => (((in @ X2 @ X1) => X3) => X3))) = binunionEcases)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases)).
% 13.04/2.32 thf(f106,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)) = binunionLsub)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub)).
% 13.04/2.32 thf(f108,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI)).
% 13.04/2.32 thf(f111,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0) = binintersectLsub)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub)).
% 13.04/2.32 thf(f112,axiom,(
% 13.04/2.32 (binintersectSubset2 = ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2)).
% 13.04/2.32 thf(f114,axiom,(
% 13.04/2.32 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)).
% 13.04/2.32 thf(f115,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (((binintersect @ X0 @ X1)) = emptyset)) = disjointsetsI1)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1)).
% 13.04/2.32 thf(f116,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1) = binintersectRsub)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub)).
% 13.04/2.32 thf(f118,axiom,(
% 13.04/2.32 (binintersectSubset1 = ! [X1 : $i,X0 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1)).
% 13.04/2.32 thf(f119,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i,X2 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X2))) = ((binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2)))) = bs114d)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d)).
% 13.04/2.32 thf(f120,axiom,(
% 13.04/2.32 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI)).
% 13.04/2.32 thf(f122,axiom,(
% 13.04/2.32 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER)).
% 13.04/2.32 thf(f123,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((setminus @ X0 @ X1)) = emptyset)) = setminusSubset2)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2)).
% 13.04/2.32 thf(f126,axiom,(
% 13.04/2.32 (! [X2 : $i,X1 : $i,X0 : $i] : (~(in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X0 @ X1))) = setminusILneg)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg)).
% 13.04/2.32 thf(f127,axiom,(
% 13.04/2.32 (setminusIRneg = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg)).
% 13.04/2.32 thf(f128,axiom,(
% 13.04/2.32 (setminusLsub = ! [X1 : $i,X0 : $i] : (subset @ (setminus @ X0 @ X1) @ X0))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub)).
% 13.04/2.32 thf(f129,axiom,(
% 13.04/2.32 (setminusSubset1 = ! [X1 : $i,X0 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1)).
% 13.04/2.32 thf(f132,axiom,(
% 13.04/2.32 (! [X2 : $i,X0 : $i,X1 : $i] : (~(in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (symdiff @ X0 @ X1)))) = symdiffI2)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2)).
% 13.04/2.32 thf(f135,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair)).
% 13.04/2.32 thf(f136,axiom,(
% 13.04/2.32 (setukpairIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL)).
% 13.04/2.32 thf(f137,axiom,(
% 13.04/2.32 (setukpairIR = ! [X1 : $i,X0 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR)).
% 13.04/2.32 thf(f138,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair)).
% 13.04/2.32 thf(f139,axiom,(
% 13.04/2.32 (kpairp = ! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp)).
% 13.04/2.32 thf(f142,axiom,(
% 13.04/2.32 (singletoninpowunion = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion)).
% 13.04/2.32 thf(f143,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X2 = X0) | (X2 = X1))) = upairset2E)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E)).
% 13.04/2.32 thf(f149,axiom,(
% 13.04/2.32 (cartprodpairin = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin)).
% 13.04/2.32 thf(f151,axiom,(
% 13.04/2.32 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (iskpair @ X2)) = cartprodmempair)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair)).
% 13.04/2.32 thf(f152,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0))) = setunionE2)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2)).
% 13.04/2.32 thf(f154,axiom,(
% 13.04/2.32 (setunionsingleton2 = ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2)).
% 13.04/2.32 thf(f155,axiom,(
% 13.04/2.32 (! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset))) = X0) = setunionsingleton)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton)).
% 13.04/2.32 thf(f156,axiom,(
% 13.04/2.32 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((X0 = ((setadjoin @ X1 @ emptyset))) & (in @ X1 @ X0)))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 13.04/2.32 thf(f158,axiom,(
% 13.04/2.32 ((^[X0 : $i, X1 : ($i > $o)] : ((singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))) = ex1)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1)).
% 13.04/2.32 thf(f162,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X1 @ emptyset))) => (X0 = X1)) = singletonsuniq)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq)).
% 13.04/2.32 thf(f165,axiom,(
% 13.04/2.32 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop)).
% 13.04/2.32 thf(f166,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i] : (((kfst @ (kpair @ X0 @ X1))) = X0) = kfstpairEq)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq)).
% 13.04/2.32 thf(f167,axiom,(
% 13.04/2.32 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (kfst @ X2) @ X0)) = cartprodfstin)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin)).
% 13.04/2.32 thf(f168,axiom,(
% 13.04/2.32 (! [X2 : $i,X0 : $i,X1 : $i,X3 : $i] : ((((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = ((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) => (X0 = X2)) = setukpairinjL2)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2)).
% 13.04/2.32 thf(f169,axiom,(
% 13.04/2.32 (setukpairinjL = ! [X0 : $i,X3 : $i,X1 : $i,X2 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X0 = X2)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL)).
% 13.04/2.32 thf(f170,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset)))) = setukpairinjR11)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11)).
% 13.04/2.32 thf(f171,axiom,(
% 13.04/2.32 (setukpairinjR12 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = ((setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12)).
% 13.04/2.32 thf(f175,axiom,(
% 13.04/2.32 (setukpairinjR = ! [X2 : $i,X0 : $i,X1 : $i,X3 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X1 = X3)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR)).
% 13.04/2.32 thf(f177,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1) = ksndpairEq)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq)).
% 13.04/2.32 thf(f182,axiom,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kpair @ X2 @ X3)) = ((kpair @ X2 @ X3))))) = cartprodmempaircEq)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq)).
% 13.04/2.32 thf(f183,axiom,(
% 13.04/2.32 (cartprodfstpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kfst @ (kpair @ X2 @ X3))) = X2))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq)).
% 13.04/2.32 thf(f185,axiom,(
% 13.04/2.32 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (((kpair @ (kfst @ X2) @ (ksnd @ X2))) = X2)) = cartprodpairsurjEq)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq)).
% 13.04/2.32 thf(f186,axiom,(
% 13.04/2.32 ((^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))) = breln)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 13.04/2.32 thf(f189,axiom,(
% 13.04/2.32 (! [X1 : $i,X2 : ($i > $i > $o),X0 : $i] : (breln @ X0 @ X1 @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((X2 @ X3 @ X4))))) = setOfPairsIsBReln)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln)).
% 13.04/2.32 thf(f191,axiom,(
% 13.04/2.32 (dpsetconstrEL1 = ! [X2 : ($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 @ X3 @ X0)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL1)).
% 13.04/2.32 thf(f192,axiom,(
% 13.04/2.32 (dpsetconstrEL2 = ! [X3 : $i,X2 : ($i > $i > $o),X0 : $i,X4 : $i,X1 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X4 @ X1)))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL2)).
% 13.04/2.32 thf(f194,axiom,(
% 13.04/2.32 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) & (breln @ X0 @ X1 @ X2))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func)).
% 13.04/2.32 thf(f202,axiom,(
% 13.04/2.32 (! [X1 : $i,X0 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((((X2 @ X3)) = X4)))))) = lamProp)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamProp)).
% 13.04/2.32 thf(f203,axiom,(
% 13.04/2.32 ((^[X0 : $i, X1 : $i, X2 : ($i > $i)] : ((dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((((X2 @ X3)) = X4)))))) = lam)),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam)).
% 13.04/2.32 thf(f204,conjecture,(
% 13.04/2.32 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 => ! [X1 : $i,X0 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.04/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp)).
% 13.04/2.32 thf(f205,negated_conjecture,(
% 13.04/2.32 ~(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 => ! [X1 : $i,X0 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.04/2.32 inference(negated_conjecture,[status(cth)],[f204])).
% 13.04/2.32 thf(f208,plain,(
% 13.04/2.32 (emptyI = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 13.04/2.32 inference(rectify,[],[f24])).
% 13.04/2.32 thf(f209,plain,(
% 13.04/2.32 (emptyI = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.04/2.32 inference(fool_elimination,[],[f208])).
% 13.04/2.32 thf(f210,plain,(
% 13.04/2.32 (! [X0 : $i] : (in @ emptyset @ (powerset @ X0)) = emptyinPowerset)),
% 13.04/2.32 inference(rectify,[],[f38])).
% 13.04/2.32 thf(f211,plain,(
% 13.04/2.32 (emptyinPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.04/2.32 inference(fool_elimination,[],[f210])).
% 13.04/2.32 thf(f212,plain,(
% 13.04/2.32 (powersetsubset = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (subset @ (powerset @ X1) @ (powerset @ X0))))),
% 13.04/2.32 inference(rectify,[],[f98])).
% 13.04/2.32 thf(f213,plain,(
% 13.04/2.32 (powersetsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f212])).
% 13.04/2.32 thf(f216,plain,(
% 13.04/2.32 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3)))) = exuE3u)),
% 13.04/2.32 inference(rectify,[],[f68])).
% 13.04/2.32 thf(f217,plain,(
% 13.04/2.32 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f216])).
% 13.04/2.32 thf(f218,plain,(
% 13.04/2.32 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 13.04/2.32 inference(rectify,[],[f165])).
% 13.04/2.32 thf(f219,plain,(
% 13.04/2.32 (theprop = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0))))))),
% 13.04/2.32 inference(fool_elimination,[],[f218])).
% 13.04/2.32 thf(f222,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : ($i > $i > $o),X2 : $i] : (breln @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[X3 : $i, X4 : $i] : ((X1 @ X3 @ X4))))) = setOfPairsIsBReln)),
% 13.04/2.32 inference(rectify,[],[f189])).
% 13.04/2.32 thf(f223,plain,(
% 13.04/2.32 (setOfPairsIsBReln = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4))))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f222])).
% 13.04/2.32 thf(f224,plain,(
% 13.04/2.32 (exuE1 = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : (! [X3 : $i] : ((X0 @ X3) => (X2 = X3)) & (X0 @ X2))))),
% 13.04/2.32 inference(rectify,[],[f17])).
% 13.04/2.32 thf(f225,plain,(
% 13.04/2.32 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f224])).
% 13.04/2.32 thf(f226,plain,(
% 13.04/2.32 (singletonsuniq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f162])).
% 13.04/2.32 thf(f229,plain,(
% 13.04/2.32 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 13.04/2.32 inference(rectify,[],[f21])).
% 13.04/2.32 thf(f230,plain,(
% 13.04/2.32 (notinemptyset = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.04/2.32 inference(fool_elimination,[],[f229])).
% 13.04/2.32 thf(f233,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X0) = binintersectRsub)),
% 13.04/2.32 inference(rectify,[],[f116])).
% 13.04/2.32 thf(f234,plain,(
% 13.04/2.32 (binintersectRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1)))))))),
% 13.04/2.32 inference(fool_elimination,[],[f233])).
% 13.04/2.32 thf(f237,plain,(
% 13.04/2.32 (setukpairinjR11 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f170])).
% 13.04/2.32 thf(f244,plain,(
% 13.04/2.32 (subsetRefl = ! [X0 : $i] : (subset @ X0 @ X0))),
% 13.04/2.32 inference(rectify,[],[f88])).
% 13.04/2.32 thf(f245,plain,(
% 13.04/2.32 (subsetRefl = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))))),
% 13.04/2.32 inference(fool_elimination,[],[f244])).
% 13.04/2.32 thf(f246,plain,(
% 13.04/2.32 (exuI2 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X2 = X1)) => (exu @ (^[X3 : $i] : ((X0 @ X3))))))),
% 13.04/2.32 inference(rectify,[],[f65])).
% 13.04/2.32 thf(f247,plain,(
% 13.04/2.32 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f246])).
% 13.04/2.32 thf(f252,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X1 @ X2)) => ((in @ X0 @ X2) | (X0 = X1))) = setadjoinOr)),
% 13.04/2.32 inference(rectify,[],[f35])).
% 13.04/2.32 thf(f253,plain,(
% 13.04/2.32 (setadjoinOr = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0)))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f252])).
% 13.04/2.32 thf(f254,plain,(
% 13.04/2.32 (exuI1 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X3 : $i] : ((X0 @ X3))))))),
% 13.04/2.32 inference(rectify,[],[f63])).
% 13.04/2.32 thf(f255,plain,(
% 13.04/2.32 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f254])).
% 13.04/2.32 thf(f256,plain,(
% 13.04/2.32 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) & (breln @ X0 @ X1 @ X2))))),
% 13.04/2.32 inference(rectify,[],[f194])).
% 13.04/2.32 thf(f257,plain,(
% 13.04/2.32 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f256])).
% 13.04/2.32 thf(f260,plain,(
% 13.04/2.32 (setukpairIR = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 13.04/2.32 inference(rectify,[],[f137])).
% 13.04/2.32 thf(f261,plain,(
% 13.04/2.32 (setukpairIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f260])).
% 13.04/2.32 thf(f262,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))) = setextsub)),
% 13.04/2.32 inference(rectify,[],[f93])).
% 13.04/2.32 thf(f263,plain,(
% 13.04/2.32 (setextsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f262])).
% 13.04/2.32 thf(f264,plain,(
% 13.04/2.32 (emptyset__Cong = ((emptyset = emptyset)))),
% 13.04/2.32 inference(fool_elimination,[],[f70])).
% 13.04/2.32 thf(f267,plain,(
% 13.04/2.32 (! [X0 : $i] : (in @ X0 @ (powerset @ X0)) = inPowerset)),
% 13.04/2.32 inference(rectify,[],[f97])).
% 13.04/2.32 thf(f268,plain,(
% 13.04/2.32 (inPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0))))))),
% 13.04/2.32 inference(fool_elimination,[],[f267])).
% 13.04/2.32 thf(f269,plain,(
% 13.04/2.32 (binintersectSubset1 = ! [X0 : $i,X1 : $i] : ((((binintersect @ X1 @ X0)) = X1) => (subset @ X1 @ X0)))),
% 13.04/2.32 inference(rectify,[],[f118])).
% 13.04/2.32 thf(f270,plain,(
% 13.04/2.32 (binintersectSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f269])).
% 13.04/2.32 thf(f271,plain,(
% 13.04/2.32 (omega0Ax = ((in @ emptyset @ omega)))),
% 13.04/2.32 inference(fool_elimination,[],[f7])).
% 13.04/2.32 thf(f274,plain,(
% 13.04/2.32 (subsetemptysetimpeq = ! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)))),
% 13.04/2.32 inference(rectify,[],[f94])).
% 13.04/2.32 thf(f275,plain,(
% 13.04/2.32 (subsetemptysetimpeq = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0))))))),
% 13.04/2.32 inference(fool_elimination,[],[f274])).
% 13.04/2.32 thf(f276,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0))) = setunionE2)),
% 13.04/2.32 inference(rectify,[],[f152])).
% 13.04/2.32 thf(f277,plain,(
% 13.04/2.32 (setunionE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y0 @ Y2)))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f276])).
% 13.04/2.32 thf(f278,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X2 = X0) | (X2 = X1))) = upairset2E)),
% 13.04/2.32 inference(rectify,[],[f143])).
% 13.04/2.32 thf(f279,plain,(
% 13.04/2.32 (upairset2E = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y0)))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f278])).
% 13.04/2.32 thf(f280,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ X2) => ~(in @ X0 @ (setminus @ X2 @ X1))) = setminusILneg)),
% 13.04/2.32 inference(rectify,[],[f126])).
% 13.04/2.32 thf(f281,plain,(
% 13.04/2.32 (setminusILneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f280])).
% 13.04/2.32 thf(f282,plain,(
% 13.04/2.32 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 13.04/2.32 inference(rectify,[],[f82])).
% 13.04/2.32 thf(f283,plain,(
% 13.04/2.32 (emptysetsubset = ((!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0)))))),
% 13.04/2.32 inference(fool_elimination,[],[f282])).
% 13.04/2.32 thf(f284,plain,(
% 13.04/2.32 (binunionIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (binunion @ X0 @ X2))))),
% 13.04/2.32 inference(rectify,[],[f103])).
% 13.04/2.32 thf(f285,plain,(
% 13.04/2.32 (binunionIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y2 @ Y0)))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f284])).
% 13.04/2.32 thf(f286,plain,(
% 13.04/2.32 (binintersectSubset2 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X1 @ X0)) = X1)))),
% 13.04/2.32 inference(rectify,[],[f112])).
% 13.04/2.32 thf(f287,plain,(
% 13.04/2.32 (binintersectSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f286])).
% 13.04/2.32 thf(f288,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setunion @ X0)) = ((setunion @ X1)))) = setunion__Cong)),
% 13.04/2.32 inference(rectify,[],[f73])).
% 13.04/2.32 thf(f289,plain,(
% 13.04/2.32 (setunion__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f288])).
% 13.04/2.32 thf(f296,plain,(
% 13.04/2.32 (descrp = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => (X0 @ (descr @ (^[X2 : $i] : ((X0 @ X2)))))))),
% 13.04/2.32 inference(rectify,[],[f13])).
% 13.04/2.32 thf(f297,plain,(
% 13.04/2.32 (descrp = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f296])).
% 13.04/2.32 thf(f298,plain,(
% 13.04/2.32 (setunionsingleton2 = ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))),
% 13.04/2.32 inference(rectify,[],[f154])).
% 13.04/2.32 thf(f299,plain,(
% 13.04/2.32 (setunionsingleton2 = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset)))))))),
% 13.04/2.32 inference(fool_elimination,[],[f298])).
% 13.04/2.32 thf(f302,plain,(
% 13.04/2.32 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & $true)))),
% 13.04/2.32 inference(rectify,[],[f45])).
% 13.04/2.32 thf(f303,plain,(
% 13.04/2.32 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f302])).
% 13.04/2.32 thf(f304,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = upairset2IR)),
% 13.04/2.32 inference(rectify,[],[f102])).
% 13.04/2.32 thf(f305,plain,(
% 13.04/2.32 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f304])).
% 13.04/2.32 thf(f308,plain,(
% 13.04/2.32 ((^[X0 : $i, X1 : ($i > $o)] : ((singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))) = ex1)),
% 13.04/2.32 inference(rectify,[],[f158])).
% 13.04/2.32 thf(f309,plain,(
% 13.04/2.32 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f308])).
% 13.04/2.32 thf(f310,plain,(
% 13.04/2.32 (upairsetIR = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 13.04/2.32 inference(rectify,[],[f52])).
% 13.04/2.32 thf(f311,plain,(
% 13.04/2.32 (upairsetIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f310])).
% 13.04/2.32 thf(f316,plain,(
% 13.04/2.32 (! [X0 : ($i > $o),X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X1) => ~(X0 @ X3))) = quantDeMorgan3)),
% 13.04/2.32 inference(rectify,[],[f57])).
% 13.04/2.32 thf(f317,plain,(
% 13.04/2.32 (quantDeMorgan3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f316])).
% 13.04/2.32 thf(f318,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (emptyset = ((binintersect @ X1 @ X0)))) = disjointsetsI1)),
% 13.04/2.32 inference(rectify,[],[f115])).
% 13.04/2.32 thf(f319,plain,(
% 13.04/2.32 (disjointsetsI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f318])).
% 13.04/2.32 thf(f322,plain,(
% 13.04/2.32 (setukpairinjL = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X0 @ X2)) = ((kpair @ X3 @ X1))) => (X0 = X3)))),
% 13.04/2.32 inference(rectify,[],[f169])).
% 13.04/2.32 thf(f323,plain,(
% 13.04/2.32 (setukpairinjL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f322])).
% 13.04/2.32 thf(f324,plain,(
% 13.04/2.32 (setminusIRneg = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X1 @ X0))))),
% 13.04/2.32 inference(rectify,[],[f127])).
% 13.04/2.32 thf(f325,plain,(
% 13.04/2.32 (setminusIRneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f324])).
% 13.04/2.32 thf(f330,plain,(
% 13.04/2.32 (setukpairinjR = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X1 @ X2)) = ((kpair @ X0 @ X3))) => (X2 = X3)))),
% 13.04/2.32 inference(rectify,[],[f175])).
% 13.04/2.32 thf(f331,plain,(
% 13.04/2.32 (setukpairinjR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f330])).
% 13.04/2.32 thf(f338,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : (((kfst @ (kpair @ X1 @ X0))) = X1) = kfstpairEq)),
% 13.04/2.32 inference(rectify,[],[f166])).
% 13.04/2.32 thf(f339,plain,(
% 13.04/2.32 (kfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0)))))))),
% 13.04/2.32 inference(fool_elimination,[],[f338])).
% 13.04/2.32 thf(f340,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X2 @ X0)) => (in @ X1 @ X0)) = binintersectER)),
% 13.04/2.32 inference(rectify,[],[f114])).
% 13.04/2.32 thf(f341,plain,(
% 13.04/2.32 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f340])).
% 13.04/2.32 thf(f342,plain,(
% 13.04/2.32 (setadjoinSub2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => (subset @ X2 @ (setadjoin @ X1 @ X0))))),
% 13.04/2.32 inference(rectify,[],[f91])).
% 13.04/2.32 thf(f343,plain,(
% 13.04/2.32 (setadjoinSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2)))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f342])).
% 13.04/2.32 thf(f352,plain,(
% 13.04/2.32 (cartprodfstpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kfst @ (kpair @ X2 @ X3))) = X2))))),
% 13.04/2.32 inference(rectify,[],[f183])).
% 13.04/2.32 thf(f353,plain,(
% 13.04/2.32 (cartprodfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0)))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f352])).
% 13.04/2.32 thf(f356,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (in @ X1 @ (setminus @ X0 @ X2)))) = setminusI)),
% 13.04/2.32 inference(rectify,[],[f120])).
% 13.04/2.32 thf(f357,plain,(
% 13.04/2.32 (setminusI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f356])).
% 13.04/2.32 thf(f358,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 13.04/2.32 inference(rectify,[],[f95])).
% 13.04/2.32 thf(f359,plain,(
% 13.04/2.32 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f358])).
% 13.04/2.32 thf(f360,plain,(
% 13.04/2.32 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 13.04/2.32 inference(rectify,[],[f23])).
% 13.04/2.32 thf(f361,plain,(
% 13.04/2.32 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f360])).
% 13.04/2.32 thf(f362,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((in @ X3 @ (binunion @ X0 @ X2)) => (((in @ X3 @ X0) => X1) => (((in @ X3 @ X2) => X1) => X1))) = binunionEcases)),
% 13.04/2.32 inference(rectify,[],[f104])).
% 13.04/2.32 thf(f363,plain,(
% 13.04/2.32 (binunionEcases = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y1)) => (((in @ Y0 @ Y3) => Y2) => (((in @ Y0 @ Y1) => Y2) => Y2)))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f362])).
% 13.04/2.32 thf(f364,plain,(
% 13.04/2.32 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 13.04/2.32 inference(fool_elimination,[],[f27])).
% 13.04/2.32 thf(f367,plain,(
% 13.04/2.32 (upairsetIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 13.04/2.32 inference(rectify,[],[f51])).
% 13.04/2.32 thf(f368,plain,(
% 13.04/2.32 (upairsetIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f367])).
% 13.04/2.32 thf(f371,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : ($i > $o)] : ((in @ X0 @ emptyset) => (X1 @ X0)) = vacuousDall)),
% 13.04/2.32 inference(rectify,[],[f54])).
% 13.04/2.32 thf(f372,plain,(
% 13.04/2.32 (vacuousDall = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f371])).
% 13.04/2.32 thf(f375,plain,(
% 13.04/2.32 (! [X0 : $i] : (in @ emptyset @ (powerset @ X0)) = emptyInPowerset)),
% 13.04/2.32 inference(rectify,[],[f39])).
% 13.04/2.32 thf(f376,plain,(
% 13.04/2.32 (emptyInPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.04/2.32 inference(fool_elimination,[],[f375])).
% 13.04/2.32 thf(f377,plain,(
% 13.04/2.32 (singletoninpowunion = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X0 @ X2)))))),
% 13.04/2.32 inference(rectify,[],[f142])).
% 13.04/2.32 thf(f378,plain,(
% 13.04/2.32 (singletoninpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f377])).
% 13.04/2.32 thf(f383,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X0 @ X2)) => ~(in @ X1 @ X2)) = setminusER)),
% 13.04/2.32 inference(rectify,[],[f122])).
% 13.04/2.32 thf(f384,plain,(
% 13.04/2.32 (setminusER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (~ (in @ Y1 @ Y0)))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f383])).
% 13.04/2.32 thf(f385,plain,(
% 13.04/2.32 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 13.04/2.32 inference(rectify,[],[f20])).
% 13.04/2.32 thf(f386,plain,(
% 13.04/2.32 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false)))))),
% 13.04/2.32 inference(fool_elimination,[],[f385])).
% 13.04/2.32 thf(f387,plain,(
% 13.04/2.32 (omega__Cong = ((omega = omega)))),
% 13.04/2.32 inference(fool_elimination,[],[f74])).
% 13.04/2.32 thf(f388,plain,(
% 13.04/2.32 (! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : ((X0 @ X3))))) => (in @ X2 @ X1)) = dsetconstrEL)),
% 13.04/2.32 inference(rectify,[],[f15])).
% 13.04/2.32 thf(f389,plain,(
% 13.04/2.32 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y0 @ Y1))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f388])).
% 13.04/2.32 thf(f390,plain,(
% 13.04/2.32 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 13.04/2.32 inference(rectify,[],[f59])).
% 13.04/2.32 thf(f391,plain,(
% 13.04/2.32 (prop2setI = ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))))))),
% 13.04/2.32 inference(fool_elimination,[],[f390])).
% 13.04/2.32 thf(f392,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) = ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) => (X0 = X1)) = setukpairinjL2)),
% 13.04/2.32 inference(rectify,[],[f168])).
% 13.04/2.32 thf(f393,plain,(
% 13.04/2.32 (setukpairinjL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f392])).
% 13.04/2.32 thf(f394,plain,(
% 13.04/2.32 (dpsetconstrEL2 = ! [X0 : $i,X1 : ($i > $i > $o),X2 : $i,X3 : $i,X4 : $i] : ((in @ (kpair @ X0 @ X3) @ (dpsetconstr @ X2 @ X4 @ (^[X5 : $i, X6 : $i] : ((X1 @ X5 @ X6))))) => (in @ X3 @ X4)))),
% 13.04/2.32 inference(rectify,[],[f192])).
% 13.04/2.32 thf(f395,plain,(
% 13.04/2.32 (dpsetconstrEL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y1) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (in @ Y1 @ Y0))))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f394])).
% 13.04/2.32 thf(f396,plain,(
% 13.04/2.32 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 13.04/2.32 inference(fool_elimination,[],[f32])).
% 13.04/2.32 thf(f397,plain,(
% 13.04/2.32 (prop2setE = ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 13.04/2.32 inference(rectify,[],[f18])).
% 13.04/2.32 thf(f398,plain,(
% 13.04/2.32 (prop2setE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1)))))))),
% 13.04/2.32 inference(fool_elimination,[],[f397])).
% 13.04/2.32 thf(f399,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : (((binintersect @ X1 @ (binunion @ X0 @ X2))) = ((binunion @ (binintersect @ X1 @ X0) @ (binintersect @ X1 @ X2)))) = bs114d)),
% 13.04/2.32 inference(rectify,[],[f119])).
% 13.04/2.32 thf(f400,plain,(
% 13.04/2.32 (bs114d = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y1 @ (binunion @ Y2 @ Y0)) = (binunion @ (binintersect @ Y1 @ Y2) @ (binintersect @ Y1 @ Y0)))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f399])).
% 13.04/2.32 thf(f405,plain,(
% 13.04/2.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kpair @ X2 @ X3)) = ((kpair @ X2 @ X3))))) = cartprodmempaircEq)),
% 13.04/2.32 inference(rectify,[],[f182])).
% 13.04/2.32 thf(f406,plain,(
% 13.04/2.32 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3))))))))))))))),
% 13.04/2.32 inference(fool_elimination,[],[f405])).
% 13.04/2.32 thf(f407,plain,(
% 13.04/2.32 (notsubsetI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => ~(subset @ X1 @ X2))))),
% 13.04/2.32 inference(rectify,[],[f85])).
% 13.04/2.33 thf(f408,plain,(
% 13.04/2.33 (notsubsetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (subset @ Y1 @ Y0))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f407])).
% 13.04/2.33 thf(f409,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetAx)),
% 13.04/2.33 inference(rectify,[],[f5])).
% 13.04/2.33 thf(f410,plain,(
% 13.04/2.33 (powersetAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f409])).
% 13.04/2.33 thf(f411,plain,(
% 13.04/2.33 (! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : ((X0 @ X3))))) => (X0 @ X1)) = dsetconstrER)),
% 13.04/2.33 inference(rectify,[],[f16])).
% 13.04/2.33 thf(f412,plain,(
% 13.04/2.33 (dsetconstrER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f411])).
% 13.04/2.33 thf(f419,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X0)) <=> ((X1 = X2) | (in @ X2 @ X0))) = setadjoinAx)),
% 13.04/2.33 inference(rectify,[],[f4])).
% 13.04/2.33 thf(f420,plain,(
% 13.04/2.33 (setadjoinAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) = ((in @ Y0 @ Y2) | (Y1 = Y0)))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f419])).
% 13.04/2.33 thf(f425,plain,(
% 13.04/2.33 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3)))) = exuEu)),
% 13.04/2.33 inference(rectify,[],[f75])).
% 13.04/2.33 thf(f426,plain,(
% 13.04/2.33 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f425])).
% 13.04/2.33 thf(f429,plain,(
% 13.04/2.33 (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)) = nonemptyI1)),
% 13.04/2.33 inference(rectify,[],[f30])).
% 13.04/2.33 thf(f430,plain,(
% 13.04/2.33 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0))))))),
% 13.04/2.33 inference(fool_elimination,[],[f429])).
% 13.04/2.33 thf(f431,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))) = notinsingleton)),
% 13.04/2.33 inference(rectify,[],[f47])).
% 13.04/2.33 thf(f432,plain,(
% 13.04/2.33 (notinsingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f431])).
% 13.04/2.33 thf(f433,plain,(
% 13.04/2.33 ~(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 => ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X2 @ X3) @ X0)) => (func @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[X4 : $i] : ((X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.04/2.33 inference(rectify,[],[f205])).
% 13.04/2.33 thf(f434,plain,(
% 13.04/2.33 ($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 => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (lam @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f433])).
% 13.04/2.33 thf(f435,plain,(
% 13.04/2.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f186])).
% 13.04/2.33 thf(f436,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : (~(subset @ X1 @ X0) => (X0 != X1)) = notequalI1)),
% 13.04/2.33 inference(rectify,[],[f86])).
% 13.04/2.33 thf(f437,plain,(
% 13.04/2.33 (notequalI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f436])).
% 13.04/2.33 thf(f442,plain,(
% 13.04/2.33 (eqinunit = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 13.04/2.33 inference(rectify,[],[f48])).
% 13.04/2.33 thf(f443,plain,(
% 13.04/2.33 (eqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f442])).
% 13.04/2.33 thf(f444,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (symdiff @ X1 @ X2)))) = symdiffI2)),
% 13.04/2.33 inference(rectify,[],[f132])).
% 13.04/2.33 thf(f445,plain,(
% 13.04/2.33 (symdiffI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f444])).
% 13.04/2.33 thf(f446,plain,(
% 13.04/2.33 (exuI3 = ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X3 : $i] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))) => (exu @ (^[X4 : $i] : ((X0 @ X4)))))))),
% 13.04/2.33 inference(rectify,[],[f64])).
% 13.04/2.33 thf(f447,plain,(
% 13.04/2.33 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f446])).
% 13.04/2.33 thf(f448,plain,(
% 13.04/2.33 (dpsetconstrEL1 = ! [X0 : ($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 @ X4 @ X3)))),
% 13.04/2.33 inference(rectify,[],[f191])).
% 13.04/2.33 thf(f449,plain,(
% 13.04/2.33 (dpsetconstrEL1 = ((!! @ $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 @ Y0 @ Y1))))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f448])).
% 13.04/2.33 thf(f450,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
% 13.04/2.33 inference(rectify,[],[f81])).
% 13.04/2.33 thf(f451,plain,(
% 13.04/2.33 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f450])).
% 13.04/2.33 thf(f452,plain,(
% 13.04/2.33 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 13.04/2.33 inference(rectify,[],[f3])).
% 13.04/2.33 thf(f453,plain,(
% 13.04/2.33 (emptysetAx = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.04/2.33 inference(fool_elimination,[],[f452])).
% 13.04/2.33 thf(f458,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => (((setadjoin @ X0 @ X2)) = ((setadjoin @ X1 @ X3))))) = setadjoin__Cong)),
% 13.04/2.33 inference(rectify,[],[f71])).
% 13.04/2.33 thf(f459,plain,(
% 13.04/2.33 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f458])).
% 13.04/2.33 thf(f460,plain,(
% 13.04/2.33 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = noeltsimpempty)),
% 13.04/2.33 inference(rectify,[],[f25])).
% 13.04/2.33 thf(f461,plain,(
% 13.04/2.33 (noeltsimpempty = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.04/2.33 inference(fool_elimination,[],[f460])).
% 13.04/2.33 thf(f462,plain,(
% 13.04/2.33 (! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((X0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : ((X0 @ X3))))))) = dsetconstrI)),
% 13.04/2.33 inference(rectify,[],[f14])).
% 13.04/2.33 thf(f463,plain,(
% 13.04/2.33 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3))))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f462])).
% 13.04/2.33 thf(f464,plain,(
% 13.04/2.33 (setminusLsub = ! [X0 : $i,X1 : $i] : (subset @ (setminus @ X1 @ X0) @ X1))),
% 13.04/2.33 inference(rectify,[],[f128])).
% 13.04/2.33 thf(f465,plain,(
% 13.04/2.33 (setminusLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0)))))))),
% 13.04/2.33 inference(fool_elimination,[],[f464])).
% 13.04/2.33 thf(f466,plain,(
% 13.04/2.33 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)))),
% 13.04/2.33 inference(rectify,[],[f46])).
% 13.04/2.33 thf(f467,plain,(
% 13.04/2.33 (uniqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f466])).
% 13.04/2.33 thf(f468,plain,(
% 13.04/2.33 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 13.04/2.33 inference(rectify,[],[f80])).
% 13.04/2.33 thf(f469,plain,(
% 13.04/2.33 (eqimpsubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f468])).
% 13.04/2.33 thf(f470,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))) = powersetI)),
% 13.04/2.33 inference(rectify,[],[f37])).
% 13.04/2.33 thf(f471,plain,(
% 13.04/2.33 (powersetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f470])).
% 13.04/2.33 thf(f474,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X2 @ X3) @ X0)) => (func @ X1 @ X0 @ (dpsetconstr @ X1 @ X0 @ (^[X4 : $i, X5 : $i] : ((((X2 @ X4)) = X5)))))) = lamProp)),
% 13.04/2.33 inference(rectify,[],[f202])).
% 13.04/2.33 thf(f475,plain,(
% 13.04/2.33 (lamProp = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y0 @ Y3) = Y4)))))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f474])).
% 13.04/2.33 thf(f478,plain,(
% 13.04/2.33 (sepInPowerset = ! [X0 : ($i > $o),X1 : $i] : (in @ (dsetconstr @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) @ (powerset @ X1)))),
% 13.04/2.33 inference(rectify,[],[f99])).
% 13.04/2.33 thf(f479,plain,(
% 13.04/2.33 (sepInPowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f478])).
% 13.04/2.33 thf(f482,plain,(
% 13.04/2.33 ((^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 13.04/2.33 inference(rectify,[],[f1])).
% 13.04/2.33 thf(f483,plain,(
% 13.04/2.33 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f482])).
% 13.04/2.33 thf(f486,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))) = binunionIL)),
% 13.04/2.33 inference(rectify,[],[f101])).
% 13.04/2.33 thf(f487,plain,(
% 13.04/2.33 (binunionIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1)))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f486])).
% 13.04/2.33 thf(f489,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (in @ X0 @ (setadjoin @ X1 @ emptyset))) = singletonsswitch)),
% 13.04/2.33 inference(rectify,[],[f49])).
% 13.04/2.33 thf(f490,plain,(
% 13.04/2.33 (singletonsswitch = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f489])).
% 13.04/2.33 thf(f493,plain,(
% 13.04/2.33 (setminusSubset1 = ! [X0 : $i,X1 : $i] : ((emptyset = ((setminus @ X1 @ X0))) => (subset @ X1 @ X0)))),
% 13.04/2.33 inference(rectify,[],[f129])).
% 13.04/2.33 thf(f494,plain,(
% 13.04/2.33 (setminusSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f493])).
% 13.04/2.33 thf(f495,plain,(
% 13.04/2.33 (ksndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0)))))))),
% 13.04/2.33 inference(fool_elimination,[],[f177])).
% 13.04/2.33 thf(f498,plain,(
% 13.04/2.33 (setoftrueEq = ! [X0 : $i] : (((dsetconstr @ X0 @ (^[X1 : $i] : ($true)))) = X0))),
% 13.04/2.33 inference(rectify,[],[f36])).
% 13.04/2.33 thf(f499,plain,(
% 13.04/2.33 (setoftrueEq = ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0)))))),
% 13.04/2.33 inference(fool_elimination,[],[f498])).
% 13.04/2.33 thf(f500,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ (binintersect @ X1 @ X0)))) = binintersectI)),
% 13.04/2.33 inference(rectify,[],[f108])).
% 13.04/2.33 thf(f501,plain,(
% 13.04/2.33 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f500])).
% 13.04/2.33 thf(f506,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (((kpair @ (kfst @ X1) @ (ksnd @ X1))) = X1)) = cartprodpairsurjEq)),
% 13.04/2.33 inference(rectify,[],[f185])).
% 13.04/2.33 thf(f507,plain,(
% 13.04/2.33 (cartprodpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f506])).
% 13.04/2.33 thf(f508,plain,(
% 13.04/2.33 (! [X0 : ($i > $o),X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X1) => ~(X0 @ X3))) = notdexE)),
% 13.04/2.33 inference(rectify,[],[f61])).
% 13.04/2.33 thf(f509,plain,(
% 13.04/2.33 (notdexE = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f508])).
% 13.04/2.33 thf(f510,plain,(
% 13.04/2.33 (setunionAx = ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X1) & (in @ X0 @ X2)) <=> (in @ X0 @ (setunion @ X1))))),
% 13.04/2.33 inference(rectify,[],[f6])).
% 13.04/2.33 thf(f511,plain,(
% 13.04/2.33 (setunionAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0)))) = (in @ Y1 @ (setunion @ Y0)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f510])).
% 13.04/2.33 thf(f514,plain,(
% 13.04/2.33 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 13.04/2.33 inference(rectify,[],[f28])).
% 13.04/2.33 thf(f515,plain,(
% 13.04/2.33 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f514])).
% 13.04/2.33 thf(f516,plain,(
% 13.04/2.33 (! [X0 : ($i > $o),X1 : $i] : (subset @ (dsetconstr @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) @ X1) = sepSubset)),
% 13.04/2.33 inference(rectify,[],[f100])).
% 13.04/2.33 thf(f517,plain,(
% 13.04/2.33 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ Y0)))))))),
% 13.04/2.33 inference(fool_elimination,[],[f516])).
% 13.04/2.33 thf(f518,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X0 @ X2)) => (in @ (kfst @ X1) @ X0)) = cartprodfstin)),
% 13.04/2.33 inference(rectify,[],[f167])).
% 13.04/2.33 thf(f519,plain,(
% 13.04/2.33 (cartprodfstin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (kfst @ Y1) @ Y2))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f518])).
% 13.04/2.33 thf(f520,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 13.04/2.33 inference(rectify,[],[f138])).
% 13.04/2.33 thf(f521,plain,(
% 13.04/2.33 (kpairiskpair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f520])).
% 13.04/2.33 thf(f522,plain,(
% 13.04/2.33 (subsetE2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => (~(in @ X1 @ X0) => ~(in @ X1 @ X2))))),
% 13.04/2.33 inference(rectify,[],[f84])).
% 13.04/2.33 thf(f523,plain,(
% 13.04/2.33 (subsetE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f522])).
% 13.04/2.33 thf(f528,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 13.04/2.33 inference(rectify,[],[f78])).
% 13.04/2.33 thf(f529,plain,(
% 13.04/2.33 (subsetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f528])).
% 13.04/2.33 thf(f530,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = secondinupair)),
% 13.04/2.33 inference(rectify,[],[f135])).
% 13.04/2.33 thf(f531,plain,(
% 13.04/2.33 (secondinupair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f530])).
% 13.04/2.33 thf(f532,plain,(
% 13.04/2.33 (kpairp = ! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)))),
% 13.04/2.33 inference(rectify,[],[f139])).
% 13.04/2.33 thf(f533,plain,(
% 13.04/2.33 (kpairp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f532])).
% 13.04/2.33 thf(f534,plain,(
% 13.04/2.33 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 13.04/2.33 inference(rectify,[],[f19])).
% 13.04/2.33 thf(f535,plain,(
% 13.04/2.33 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f534])).
% 13.04/2.33 thf(f536,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X3 @ X0) => (in @ X2 @ X1)))) = inCongP)),
% 13.04/2.33 inference(rectify,[],[f66])).
% 13.04/2.33 thf(f537,plain,(
% 13.04/2.33 (inCongP = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) => (in @ Y3 @ Y0))))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f536])).
% 13.04/2.33 thf(f540,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)) = powersetE1)),
% 13.04/2.33 inference(rectify,[],[f96])).
% 13.04/2.33 thf(f541,plain,(
% 13.04/2.33 (powersetE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f540])).
% 13.04/2.33 thf(f542,plain,(
% 13.04/2.33 (setukpairIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))),
% 13.04/2.33 inference(rectify,[],[f136])).
% 13.04/2.33 thf(f543,plain,(
% 13.04/2.33 (setukpairIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f542])).
% 13.04/2.33 thf(f550,plain,(
% 13.04/2.33 (cartprodpairin = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (kpair @ X1 @ X3) @ (cartprod @ X0 @ X2)))))),
% 13.04/2.33 inference(rectify,[],[f149])).
% 13.04/2.33 thf(f551,plain,(
% 13.04/2.33 (cartprodpairin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0))))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f550])).
% 13.04/2.33 thf(f552,plain,(
% 13.04/2.33 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 13.04/2.33 inference(rectify,[],[f31])).
% 13.04/2.33 thf(f553,plain,(
% 13.04/2.33 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f552])).
% 13.04/2.33 thf(f556,plain,(
% 13.04/2.33 (eqimpsubset2 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 13.04/2.33 inference(rectify,[],[f79])).
% 13.04/2.33 thf(f557,plain,(
% 13.04/2.33 (eqimpsubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f556])).
% 13.04/2.33 thf(f560,plain,(
% 13.04/2.33 (quantDeMorgan2 = ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2)) => ~ ? [X3 : $i] : ((in @ X3 @ X0) & (X1 @ X3))))),
% 13.04/2.33 inference(rectify,[],[f56])).
% 13.04/2.33 thf(f561,plain,(
% 13.04/2.33 (quantDeMorgan2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f560])).
% 13.04/2.33 thf(f562,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X1 @ X2)) => (iskpair @ X0)) = cartprodmempair)),
% 13.04/2.33 inference(rectify,[],[f151])).
% 13.04/2.33 thf(f563,plain,(
% 13.04/2.33 (cartprodmempair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (iskpair @ Y2))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f562])).
% 13.04/2.33 thf(f564,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X1) = binintersectLsub)),
% 13.04/2.33 inference(rectify,[],[f111])).
% 13.04/2.33 thf(f565,plain,(
% 13.04/2.33 (binintersectLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0)))))))),
% 13.04/2.33 inference(fool_elimination,[],[f564])).
% 13.04/2.33 thf(f566,plain,(
% 13.04/2.33 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((X0 = ((setadjoin @ X1 @ emptyset))) & (in @ X1 @ X0)))))),
% 13.04/2.33 inference(rectify,[],[f156])).
% 13.04/2.33 thf(f567,plain,(
% 13.04/2.33 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 13.04/2.33 inference(fool_elimination,[],[f566])).
% 13.04/2.33 thf(f568,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (powerset @ (setunion @ X1)))) = subPowSU)),
% 13.04/2.33 inference(rectify,[],[f43])).
% 13.04/2.33 thf(f569,plain,(
% 13.04/2.33 (subPowSU = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f568])).
% 13.04/2.33 thf(f572,plain,(
% 13.04/2.33 (! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((X0 @ X2) <=> (in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : ((X0 @ X3))))))) = setbeta)),
% 13.04/2.33 inference(rectify,[],[f26])).
% 13.04/2.33 thf(f573,plain,(
% 13.04/2.33 (setbeta = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) = (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3))))))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f572])).
% 13.04/2.33 thf(f574,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (emptyset = ((setminus @ X1 @ X0)))) = setminusSubset2)),
% 13.04/2.33 inference(rectify,[],[f123])).
% 13.04/2.33 thf(f575,plain,(
% 13.04/2.33 (setminusSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f574])).
% 13.04/2.33 thf(f578,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X1 @ X0)) = binunionLsub)),
% 13.04/2.33 inference(rectify,[],[f106])).
% 13.04/2.33 thf(f579,plain,(
% 13.04/2.33 (binunionLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f578])).
% 13.04/2.33 thf(f580,plain,(
% 13.04/2.33 (setadjoinSub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)))),
% 13.04/2.33 inference(rectify,[],[f90])).
% 13.04/2.33 thf(f581,plain,(
% 13.04/2.33 (setadjoinSub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f580])).
% 13.04/2.33 thf(f584,plain,(
% 13.04/2.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (setadjoin @ X2 @ X0))) = setadjoinIR)),
% 13.04/2.33 inference(rectify,[],[f33])).
% 13.04/2.33 thf(f585,plain,(
% 13.04/2.33 (setadjoinIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2)))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f584])).
% 13.04/2.33 thf(f586,plain,(
% 13.04/2.33 (exuE3e = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : (X0 @ X2)))),
% 13.04/2.33 inference(rectify,[],[f22])).
% 13.04/2.33 thf(f587,plain,(
% 13.04/2.33 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f586])).
% 13.04/2.33 thf(f594,plain,(
% 13.04/2.33 (setukpairinjR12 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset)))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f171])).
% 13.04/2.33 thf(f595,plain,(
% 13.04/2.33 (setunionsingleton = ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0)))))),
% 13.04/2.33 inference(fool_elimination,[],[f155])).
% 13.04/2.33 thf(f600,plain,(
% 13.04/2.33 ((^[X0 : $i, X1 : $i, X2 : ($i > $i)] : ((dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((((X2 @ X3)) = X4)))))) = lam)),
% 13.04/2.33 inference(rectify,[],[f203])).
% 13.04/2.33 thf(f601,plain,(
% 13.04/2.33 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 13.04/2.33 inference(fool_elimination,[],[f600])).
% 13.04/2.33 thf(f602,plain,(
% 13.04/2.33 (binunionLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f579])).
% 13.04/2.33 thf(f604,plain,(
% 13.04/2.33 (emptyinPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f211])).
% 13.04/2.33 thf(f605,plain,(
% 13.04/2.33 (setukpairIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f543])).
% 13.04/2.33 thf(f607,plain,(
% 13.04/2.33 (setunionE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y0 @ Y2)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f277])).
% 13.04/2.33 thf(f608,plain,(
% 13.04/2.33 (binintersectSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f270])).
% 13.04/2.33 thf(f610,plain,(
% 13.04/2.33 (binintersectRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f234])).
% 13.04/2.33 thf(f611,plain,(
% 13.04/2.33 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f501])).
% 13.04/2.33 thf(f613,plain,(
% 13.04/2.33 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f483])).
% 13.04/2.33 thf(f614,plain,(
% 13.04/2.33 (vacuousDall = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f372])).
% 13.04/2.33 thf(f616,plain,(
% 13.04/2.33 (prop2setI = ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f391])).
% 13.04/2.33 thf(f617,plain,(
% 13.04/2.33 ($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 => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (lam @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f434])).
% 13.04/2.33 thf(f619,plain,(
% 13.04/2.33 (lamProp = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y0 @ Y3) = Y4)))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f475])).
% 13.04/2.33 thf(f621,plain,(
% 13.04/2.33 (subsetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f529])).
% 13.04/2.33 thf(f622,plain,(
% 13.04/2.33 (cartprodpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f507])).
% 13.04/2.33 thf(f624,plain,(
% 13.04/2.33 (notinemptyset = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f230])).
% 13.04/2.33 thf(f625,plain,(
% 13.04/2.33 (sepInPowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f479])).
% 13.04/2.33 thf(f626,plain,(
% 13.04/2.33 (upairsetIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f311])).
% 13.04/2.33 thf(f628,plain,(
% 13.04/2.33 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f255])).
% 13.04/2.33 thf(f630,plain,(
% 13.04/2.33 (quantDeMorgan3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f317])).
% 13.04/2.33 thf(f633,plain,(
% 13.04/2.33 (setukpairinjL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f393])).
% 13.04/2.33 thf(f634,plain,(
% 13.04/2.33 (singletoninpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f378])).
% 13.04/2.33 thf(f636,plain,(
% 13.04/2.33 (eqimpsubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f557])).
% 13.04/2.33 thf(f640,plain,(
% 13.04/2.33 (powersetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f471])).
% 13.04/2.33 thf(f641,plain,(
% 13.04/2.33 (omega0Ax = ((in @ emptyset @ omega)))),
% 13.04/2.33 inference(cnf_transformation,[],[f271])).
% 13.04/2.33 thf(f643,plain,(
% 13.04/2.33 (setukpairinjL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f323])).
% 13.04/2.33 thf(f644,plain,(
% 13.04/2.33 (eqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f443])).
% 13.04/2.33 thf(f645,plain,(
% 13.04/2.33 (omega__Cong = ((omega = omega)))),
% 13.04/2.33 inference(cnf_transformation,[],[f387])).
% 13.04/2.33 thf(f647,plain,(
% 13.04/2.33 (setbeta = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) = (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f573])).
% 13.04/2.33 thf(f648,plain,(
% 13.04/2.33 (cartprodmempair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (iskpair @ Y2))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f563])).
% 13.04/2.33 thf(f649,plain,(
% 13.04/2.33 (quantDeMorgan2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f561])).
% 13.04/2.33 thf(f651,plain,(
% 13.04/2.33 (subsetRefl = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))))),
% 13.04/2.33 inference(cnf_transformation,[],[f245])).
% 13.04/2.33 thf(f652,plain,(
% 13.04/2.33 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f451])).
% 13.04/2.33 thf(f653,plain,(
% 13.04/2.33 (singletonsuniq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f226])).
% 13.04/2.33 thf(f656,plain,(
% 13.04/2.33 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f426])).
% 13.04/2.33 thf(f657,plain,(
% 13.04/2.33 (binintersectSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f287])).
% 13.04/2.33 thf(f658,plain,(
% 13.04/2.33 (singletonsswitch = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f490])).
% 13.04/2.33 thf(f659,plain,(
% 13.04/2.33 (emptysetAx = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f453])).
% 13.04/2.33 thf(f662,plain,(
% 13.04/2.33 (setextsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f263])).
% 13.04/2.33 thf(f665,plain,(
% 13.04/2.33 (inPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f268])).
% 13.04/2.33 thf(f666,plain,(
% 13.04/2.33 (kpairiskpair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f521])).
% 13.04/2.33 thf(f667,plain,(
% 13.04/2.33 (notequalI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f437])).
% 13.04/2.33 thf(f668,plain,(
% 13.04/2.33 (emptyI = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f209])).
% 13.04/2.33 thf(f670,plain,(
% 13.04/2.33 (binunionIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y2 @ Y0)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f285])).
% 13.04/2.33 thf(f671,plain,(
% 13.04/2.33 (setadjoinAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) = ((in @ Y0 @ Y2) | (Y1 = Y0)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f420])).
% 13.04/2.33 thf(f673,plain,(
% 13.04/2.33 (setunionAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0)))) = (in @ Y1 @ (setunion @ Y0)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f511])).
% 13.04/2.33 thf(f674,plain,(
% 13.04/2.33 (setminusSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f494])).
% 13.04/2.33 thf(f675,plain,(
% 13.04/2.33 (prop2setE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f398])).
% 13.04/2.33 thf(f677,plain,(
% 13.04/2.33 (setukpairIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f261])).
% 13.04/2.33 thf(f678,plain,(
% 13.04/2.33 (dpsetconstrEL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y1) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (in @ Y1 @ Y0))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f395])).
% 13.04/2.33 thf(f679,plain,(
% 13.04/2.33 (setunion__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f289])).
% 13.04/2.33 thf(f680,plain,(
% 13.04/2.33 (subsetemptysetimpeq = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f275])).
% 13.04/2.33 thf(f681,plain,(
% 13.04/2.33 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f225])).
% 13.04/2.33 thf(f682,plain,(
% 13.04/2.33 (subsetE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f523])).
% 13.04/2.33 thf(f685,plain,(
% 13.04/2.33 (notdexE = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f509])).
% 13.04/2.33 thf(f686,plain,(
% 13.04/2.33 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f309])).
% 13.04/2.33 thf(f687,plain,(
% 13.04/2.33 (powersetE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f541])).
% 13.04/2.33 thf(f688,plain,(
% 13.04/2.33 (upairsetIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f368])).
% 13.04/2.33 thf(f691,plain,(
% 13.04/2.33 (dpsetconstrEL1 = ((!! @ $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 @ Y0 @ Y1))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f449])).
% 13.04/2.33 thf(f692,plain,(
% 13.04/2.33 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f257])).
% 13.04/2.33 thf(f696,plain,(
% 13.04/2.33 (binunionEcases = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y1)) => (((in @ Y0 @ Y3) => Y2) => (((in @ Y0 @ Y1) => Y2) => Y2)))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f363])).
% 13.04/2.33 thf(f698,plain,(
% 13.04/2.33 (disjointsetsI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f319])).
% 13.04/2.33 thf(f700,plain,(
% 13.04/2.33 (emptysetsubset = ((!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0)))))),
% 13.04/2.33 inference(cnf_transformation,[],[f283])).
% 13.04/2.33 thf(f701,plain,(
% 13.04/2.33 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false)))))),
% 13.04/2.33 inference(cnf_transformation,[],[f386])).
% 13.04/2.33 thf(f704,plain,(
% 13.04/2.33 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f567])).
% 13.04/2.33 thf(f706,plain,(
% 13.04/2.33 (emptyInPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f376])).
% 13.04/2.33 thf(f707,plain,(
% 13.04/2.33 (powersetsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f213])).
% 13.04/2.33 thf(f708,plain,(
% 13.04/2.33 (emptyset__Cong = ((emptyset = emptyset)))),
% 13.04/2.33 inference(cnf_transformation,[],[f264])).
% 13.04/2.33 thf(f709,plain,(
% 13.04/2.33 (subPowSU = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f569])).
% 13.04/2.33 thf(f710,plain,(
% 13.04/2.33 (setukpairinjR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f331])).
% 13.04/2.33 thf(f712,plain,(
% 13.04/2.33 (setminusI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f357])).
% 13.04/2.33 thf(f716,plain,(
% 13.04/2.33 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 13.04/2.33 inference(cnf_transformation,[],[f364])).
% 13.04/2.33 thf(f719,plain,(
% 13.04/2.33 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f515])).
% 13.04/2.33 thf(f721,plain,(
% 13.04/2.33 (setadjoinSub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f581])).
% 13.04/2.33 thf(f722,plain,(
% 13.04/2.33 (theprop = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f219])).
% 13.04/2.33 thf(f725,plain,(
% 13.04/2.33 (noeltsimpempty = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f461])).
% 13.04/2.33 thf(f731,plain,(
% 13.04/2.33 (ksndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f495])).
% 13.04/2.33 thf(f733,plain,(
% 13.04/2.33 (uniqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f467])).
% 13.04/2.33 thf(f734,plain,(
% 13.04/2.33 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f406])).
% 13.04/2.33 thf(f736,plain,(
% 13.04/2.33 (setadjoinOr = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f253])).
% 13.04/2.33 thf(f737,plain,(
% 13.04/2.33 (setminusSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f575])).
% 13.04/2.33 thf(f738,plain,(
% 13.04/2.33 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f359])).
% 13.04/2.33 thf(f739,plain,(
% 13.04/2.33 (descrp = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f297])).
% 13.04/2.33 thf(f740,plain,(
% 13.04/2.33 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f247])).
% 13.04/2.33 thf(f741,plain,(
% 13.04/2.33 (powersetAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f410])).
% 13.04/2.33 thf(f743,plain,(
% 13.04/2.33 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ Y0)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f517])).
% 13.04/2.33 thf(f744,plain,(
% 13.04/2.33 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f463])).
% 13.04/2.33 thf(f745,plain,(
% 13.04/2.33 (binintersectLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f565])).
% 13.04/2.33 thf(f746,plain,(
% 13.04/2.33 (cartprodpairin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f551])).
% 13.04/2.33 thf(f747,plain,(
% 13.04/2.33 (kfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f339])).
% 13.04/2.33 thf(f748,plain,(
% 13.04/2.33 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f601])).
% 13.04/2.33 thf(f749,plain,(
% 13.04/2.33 (setOfPairsIsBReln = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f223])).
% 13.04/2.33 thf(f750,plain,(
% 13.04/2.33 (secondinupair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f531])).
% 13.04/2.33 thf(f751,plain,(
% 13.04/2.33 (dsetconstrER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f412])).
% 13.04/2.33 thf(f752,plain,(
% 13.04/2.33 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f341])).
% 13.04/2.33 thf(f754,plain,(
% 13.04/2.33 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f430])).
% 13.04/2.33 thf(f755,plain,(
% 13.04/2.33 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f361])).
% 13.04/2.33 thf(f756,plain,(
% 13.04/2.33 (symdiffI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f445])).
% 13.04/2.33 thf(f757,plain,(
% 13.04/2.33 (setukpairinjR12 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f594])).
% 13.04/2.33 thf(f758,plain,(
% 13.04/2.33 (setunionsingleton = ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0)))))),
% 13.04/2.33 inference(cnf_transformation,[],[f595])).
% 13.04/2.33 thf(f759,plain,(
% 13.04/2.33 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f305])).
% 13.04/2.33 thf(f760,plain,(
% 13.04/2.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f435])).
% 13.04/2.33 thf(f762,plain,(
% 13.04/2.33 (exuI3 = ((!! @ ($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)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f447])).
% 13.04/2.33 thf(f763,plain,(
% 13.04/2.33 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y0 @ Y1))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f389])).
% 13.04/2.33 thf(f764,plain,(
% 13.04/2.33 (setminusLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f465])).
% 13.04/2.33 thf(f765,plain,(
% 13.04/2.33 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f553])).
% 13.04/2.33 thf(f766,plain,(
% 13.04/2.33 (cartprodfstin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (kfst @ Y1) @ Y2))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f519])).
% 13.04/2.33 thf(f770,plain,(
% 13.04/2.33 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f535])).
% 13.04/2.33 thf(f771,plain,(
% 13.04/2.33 (inCongP = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) => (in @ Y3 @ Y0))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f537])).
% 13.04/2.33 thf(f772,plain,(
% 13.04/2.33 (setadjoinSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f343])).
% 13.04/2.33 thf(f773,plain,(
% 13.04/2.33 (eqimpsubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f469])).
% 13.04/2.33 thf(f775,plain,(
% 13.04/2.33 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f217])).
% 13.04/2.33 thf(f777,plain,(
% 13.04/2.33 (setminusILneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f281])).
% 13.04/2.33 thf(f778,plain,(
% 13.04/2.33 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f459])).
% 13.04/2.33 thf(f779,plain,(
% 13.04/2.33 (notsubsetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (subset @ Y1 @ Y0))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f408])).
% 13.04/2.33 thf(f780,plain,(
% 13.04/2.33 (setunionsingleton2 = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset)))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f299])).
% 13.04/2.33 thf(f781,plain,(
% 13.04/2.33 (setukpairinjR11 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f237])).
% 13.04/2.33 thf(f782,plain,(
% 13.04/2.33 (setminusER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (~ (in @ Y1 @ Y0)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f384])).
% 13.04/2.33 thf(f786,plain,(
% 13.04/2.33 (setminusIRneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f325])).
% 13.04/2.33 thf(f787,plain,(
% 13.04/2.33 (setadjoinIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f585])).
% 13.04/2.33 thf(f790,plain,(
% 13.04/2.33 (upairset2E = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y0)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f279])).
% 13.04/2.33 thf(f791,plain,(
% 13.04/2.33 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0)))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f303])).
% 13.04/2.33 thf(f796,plain,(
% 13.04/2.33 (binunionIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f487])).
% 13.04/2.33 thf(f798,plain,(
% 13.04/2.33 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 13.04/2.33 inference(cnf_transformation,[],[f396])).
% 13.04/2.33 thf(f799,plain,(
% 13.04/2.33 (notinsingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f432])).
% 13.04/2.33 thf(f800,plain,(
% 13.04/2.33 (cartprodfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0)))))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f353])).
% 13.04/2.33 thf(f802,plain,(
% 13.04/2.33 (setoftrueEq = ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0)))))),
% 13.04/2.33 inference(cnf_transformation,[],[f499])).
% 13.04/2.33 thf(f803,plain,(
% 13.04/2.33 (kpairp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f533])).
% 13.04/2.33 thf(f804,plain,(
% 13.04/2.33 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f587])).
% 13.04/2.33 thf(f805,plain,(
% 13.04/2.33 (bs114d = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y1 @ (binunion @ Y2 @ Y0)) = (binunion @ (binintersect @ Y1 @ Y2) @ (binintersect @ Y1 @ Y0)))))))))))),
% 13.04/2.33 inference(cnf_transformation,[],[f400])).
% 13.04/2.33 thf(f807,definition,(
% 13.04/2.33 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 13.04/2.33 introduced(theory,[fool_exhaustiveness_axiom])).
% 13.04/2.33 thf(f808,plain,(
% 13.04/2.33 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f686,f704])).
% 13.04/2.33 thf(f809,plain,(
% 13.04/2.33 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y6) & ((setadjoin @ Y7 @ emptyset) = Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f692,f760,f808])).
% 13.04/2.33 thf(f810,plain,(
% 13.04/2.33 (((~ (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 => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 13.04/2.33 inference(definition_unfolding,[],[f617,f809,f748])).
% 13.04/2.33 thf(f812,plain,(
% 13.04/2.33 (lamProp = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y0 @ Y3) = Y4)))))))))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f619,f809])).
% 13.04/2.33 thf(f813,plain,(
% 13.04/2.33 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f628,f613])).
% 13.04/2.33 thf(f817,plain,(
% 13.04/2.33 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f656,f613])).
% 13.04/2.33 thf(f821,plain,(
% 13.04/2.33 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f681,f613])).
% 13.04/2.33 thf(f828,plain,(
% 13.04/2.33 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f719,f716])).
% 13.04/2.33 thf(f829,plain,(
% 13.04/2.33 (theprop = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & ((setadjoin @ Y2 @ emptyset) = Y1))))) @ Y0) => (in @ (setunion @ Y0) @ Y0))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f722,f704])).
% 13.04/2.33 thf(f830,plain,(
% 13.04/2.33 (descrp = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f739,f613])).
% 13.04/2.33 thf(f831,plain,(
% 13.04/2.33 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f740,f613])).
% 13.04/2.33 thf(f832,plain,(
% 13.04/2.33 (setOfPairsIsBReln = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4))))))))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f749,f760])).
% 13.04/2.33 thf(f833,plain,(
% 13.04/2.33 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => ((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f754,f716])).
% 13.04/2.33 thf(f835,plain,(
% 13.04/2.33 (exuI3 = ((!! @ ($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]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f762,f613])).
% 13.04/2.33 thf(f837,plain,(
% 13.04/2.33 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f775,f613])).
% 13.04/2.33 thf(f839,plain,(
% 13.04/2.33 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0)))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f791,f716])).
% 13.04/2.33 thf(f841,plain,(
% 13.04/2.33 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 13.04/2.33 inference(definition_unfolding,[],[f804,f613])).
% 13.04/2.33 thf(f842,definition,(
% 13.04/2.33 (sF0 = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 13.04/2.33 thf(f843,plain,(
% 13.04/2.33 (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) = sF0)),
% 13.04/2.33 inference(reorient_equations,[],[f842])).
% 13.04/2.33 thf(f844,definition,(
% 13.04/2.33 (sF1 = ((lamProp => sF0)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 13.04/2.33 thf(f845,plain,(
% 13.04/2.33 (((lamProp => sF0)) = sF1)),
% 13.04/2.33 inference(reorient_equations,[],[f844])).
% 13.04/2.33 thf(f846,definition,(
% 13.04/2.33 (sF2 = ((funcinfuncset => sF1)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 13.04/2.33 thf(f847,definition,(
% 13.04/2.33 (sF3 = ((ap2p => sF2)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 13.04/2.33 thf(f848,plain,(
% 13.04/2.33 (((ap2p => sF2)) = sF3)),
% 13.04/2.33 inference(reorient_equations,[],[f847])).
% 13.04/2.33 thf(f849,definition,(
% 13.04/2.33 (sF4 = ((infuncsetfunc => sF3)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 13.04/2.33 thf(f850,plain,(
% 13.04/2.33 (((infuncsetfunc => sF3)) = sF4)),
% 13.04/2.33 inference(reorient_equations,[],[f849])).
% 13.04/2.33 thf(f851,definition,(
% 13.04/2.33 (sF5 = ((app => sF4)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 13.04/2.33 thf(f852,definition,(
% 13.04/2.33 (sF6 = ((apProp => sF5)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 13.04/2.33 thf(f853,plain,(
% 13.04/2.33 (((apProp => sF5)) = sF6)),
% 13.04/2.33 inference(reorient_equations,[],[f852])).
% 13.04/2.33 thf(f854,definition,(
% 13.04/2.33 (sF7 = ((funcImageSingleton => sF6)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 13.04/2.33 thf(f855,definition,(
% 13.04/2.33 (sF8 = ((dpsetconstrER => sF7)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
% 13.04/2.33 thf(f856,definition,(
% 13.04/2.33 (sF9 = ((dpsetconstrEL2 => sF8)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
% 13.04/2.33 thf(f857,definition,(
% 13.04/2.33 (sF10 = ((dpsetconstrEL1 => sF9)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
% 13.04/2.33 thf(f858,definition,(
% 13.04/2.33 (sF11 = ((dpsetconstrERa => sF10)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
% 13.04/2.33 thf(f859,plain,(
% 13.04/2.33 (((dpsetconstrERa => sF10)) = sF11)),
% 13.04/2.33 inference(reorient_equations,[],[f858])).
% 13.04/2.33 thf(f860,definition,(
% 13.04/2.33 (sF12 = ((setOfPairsIsBReln => sF11)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 13.04/2.33 thf(f861,definition,(
% 13.04/2.33 (sF13 = ((dpsetconstrSub => sF12)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
% 13.04/2.33 thf(f862,plain,(
% 13.04/2.33 (((dpsetconstrSub => sF12)) = sF13)),
% 13.04/2.33 inference(reorient_equations,[],[f861])).
% 13.04/2.33 thf(f863,definition,(
% 13.04/2.33 (sF14 = ((dpsetconstrI => sF13)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
% 13.04/2.33 thf(f864,definition,(
% 13.04/2.33 (sF15 = ((cartprodpairsurjEq => sF14)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
% 13.04/2.33 thf(f865,definition,(
% 13.04/2.33 (sF16 = ((cartprodsndpairEq => sF15)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF16])],[function_definition])).
% 13.04/2.33 thf(f866,definition,(
% 13.04/2.33 (sF17 = ((cartprodfstpairEq => sF16)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF17])],[function_definition])).
% 13.04/2.33 thf(f867,definition,(
% 13.04/2.33 (sF18 = ((cartprodmempaircEq => sF17)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF18])],[function_definition])).
% 13.04/2.33 thf(f868,definition,(
% 13.04/2.33 (sF19 = ((cartprodpairmemER => sF18)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF19])],[function_definition])).
% 13.04/2.33 thf(f869,definition,(
% 13.04/2.33 (sF20 = ((cartprodpairmemEL => sF19)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF20])],[function_definition])).
% 13.04/2.33 thf(f870,plain,(
% 13.04/2.33 (((cartprodpairmemEL => sF19)) = sF20)),
% 13.04/2.33 inference(reorient_equations,[],[f869])).
% 13.04/2.33 thf(f871,definition,(
% 13.04/2.33 (sF21 = ((cartprodsndin => sF20)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF21])],[function_definition])).
% 13.04/2.33 thf(f872,plain,(
% 13.04/2.33 (((cartprodsndin => sF20)) = sF21)),
% 13.04/2.33 inference(reorient_equations,[],[f871])).
% 13.04/2.33 thf(f873,definition,(
% 13.04/2.33 (sF22 = ((kpairsurjEq => sF21)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF22])],[function_definition])).
% 13.04/2.33 thf(f874,definition,(
% 13.04/2.33 (sF23 = ((ksndpairEq => sF22)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF23])],[function_definition])).
% 13.04/2.33 thf(f875,definition,(
% 13.04/2.33 (sF24 = ((ksndsingleton => sF23)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF24])],[function_definition])).
% 13.04/2.33 thf(f876,plain,(
% 13.04/2.33 (((ksndsingleton => sF23)) = sF24)),
% 13.04/2.33 inference(reorient_equations,[],[f875])).
% 13.04/2.33 thf(f877,definition,(
% 13.04/2.33 (sF25 = ((setukpairinjR => sF24)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF25])],[function_definition])).
% 13.04/2.33 thf(f878,definition,(
% 13.04/2.33 (sF26 = ((setukpairinjR2 => sF25)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF26])],[function_definition])).
% 13.04/2.33 thf(f879,definition,(
% 13.04/2.33 (sF27 = ((upairequniteq => sF26)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF27])],[function_definition])).
% 13.04/2.33 thf(f880,definition,(
% 13.04/2.33 (sF28 = ((setukpairinjR1 => sF27)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF28])],[function_definition])).
% 13.04/2.33 thf(f881,plain,(
% 13.04/2.33 (((setukpairinjR1 => sF27)) = sF28)),
% 13.04/2.33 inference(reorient_equations,[],[f880])).
% 13.04/2.33 thf(f882,definition,(
% 13.04/2.33 (sF29 = ((setukpairinjR12 => sF28)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF29])],[function_definition])).
% 13.04/2.33 thf(f883,plain,(
% 13.04/2.33 (((setukpairinjR12 => sF28)) = sF29)),
% 13.04/2.33 inference(reorient_equations,[],[f882])).
% 13.04/2.33 thf(f884,definition,(
% 13.04/2.33 (sF30 = ((setukpairinjR11 => sF29)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF30])],[function_definition])).
% 13.04/2.33 thf(f885,plain,(
% 13.04/2.33 (((setukpairinjR11 => sF29)) = sF30)),
% 13.04/2.33 inference(reorient_equations,[],[f884])).
% 13.04/2.33 thf(f886,definition,(
% 13.04/2.33 (sF31 = ((setukpairinjL => sF30)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF31])],[function_definition])).
% 13.04/2.33 thf(f887,plain,(
% 13.04/2.33 (((setukpairinjL => sF30)) = sF31)),
% 13.04/2.33 inference(reorient_equations,[],[f886])).
% 13.04/2.33 thf(f888,definition,(
% 13.04/2.33 (sF32 = ((setukpairinjL2 => sF31)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF32])],[function_definition])).
% 13.04/2.33 thf(f889,definition,(
% 13.04/2.33 (sF33 = ((cartprodfstin => sF32)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF33])],[function_definition])).
% 13.04/2.33 thf(f890,plain,(
% 13.04/2.33 (((cartprodfstin => sF32)) = sF33)),
% 13.04/2.33 inference(reorient_equations,[],[f889])).
% 13.04/2.33 thf(f891,definition,(
% 13.04/2.33 (sF34 = ((kfstpairEq => sF33)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF34])],[function_definition])).
% 13.04/2.33 thf(f892,definition,(
% 13.04/2.33 (sF35 = ((theprop => sF34)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF35])],[function_definition])).
% 13.04/2.33 thf(f893,plain,(
% 13.04/2.33 (((theprop => sF34)) = sF35)),
% 13.04/2.33 inference(reorient_equations,[],[f892])).
% 13.04/2.33 thf(f894,definition,(
% 13.04/2.33 (sF36 = ((kfstsingleton => sF35)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF36])],[function_definition])).
% 13.04/2.33 thf(f895,plain,(
% 13.04/2.33 (((kfstsingleton => sF35)) = sF36)),
% 13.04/2.33 inference(reorient_equations,[],[f894])).
% 13.04/2.33 thf(f896,definition,(
% 13.04/2.33 (sF37 = ((setukpairinjL1 => sF36)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF37])],[function_definition])).
% 13.04/2.33 thf(f897,definition,(
% 13.04/2.33 (sF38 = ((singletonsuniq => sF37)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF38])],[function_definition])).
% 13.04/2.33 thf(f898,plain,(
% 13.04/2.33 (((singletonsuniq => sF37)) = sF38)),
% 13.04/2.33 inference(reorient_equations,[],[f897])).
% 13.04/2.33 thf(f899,definition,(
% 13.04/2.33 (sF39 = ((ex1I2 => sF38)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF39])],[function_definition])).
% 13.04/2.33 thf(f900,definition,(
% 13.04/2.33 (sF40 = ((ex1I => sF39)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF40])],[function_definition])).
% 13.04/2.33 thf(f901,plain,(
% 13.04/2.33 (((ex1I => sF39)) = sF40)),
% 13.04/2.33 inference(reorient_equations,[],[f900])).
% 13.04/2.33 thf(f902,definition,(
% 13.04/2.33 (sF41 = ((ex1E1 => sF40)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF41])],[function_definition])).
% 13.04/2.33 thf(f903,plain,(
% 13.04/2.33 (((ex1E1 => sF40)) = sF41)),
% 13.04/2.33 inference(reorient_equations,[],[f902])).
% 13.04/2.33 thf(f904,definition,(
% 13.04/2.33 (sF42 = ((singletonprop => sF41)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF42])],[function_definition])).
% 13.04/2.33 thf(f905,plain,(
% 13.04/2.33 (((singletonprop => sF41)) = sF42)),
% 13.04/2.33 inference(reorient_equations,[],[f904])).
% 13.04/2.33 thf(f906,definition,(
% 13.04/2.33 (sF43 = ((setunionsingleton => sF42)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF43])],[function_definition])).
% 13.04/2.33 thf(f907,plain,(
% 13.04/2.33 (((setunionsingleton => sF42)) = sF43)),
% 13.04/2.33 inference(reorient_equations,[],[f906])).
% 13.04/2.33 thf(f908,definition,(
% 13.04/2.33 (sF44 = ((setunionsingleton2 => sF43)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF44])],[function_definition])).
% 13.04/2.33 thf(f909,plain,(
% 13.04/2.33 (((setunionsingleton2 => sF43)) = sF44)),
% 13.04/2.33 inference(reorient_equations,[],[f908])).
% 13.04/2.33 thf(f910,definition,(
% 13.04/2.33 (sF45 = ((setunionsingleton1 => sF44)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF45])],[function_definition])).
% 13.04/2.33 thf(f911,definition,(
% 13.04/2.33 (sF46 = ((setunionE2 => sF45)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF46])],[function_definition])).
% 13.04/2.33 thf(f912,plain,(
% 13.04/2.33 (((setunionE2 => sF45)) = sF46)),
% 13.04/2.33 inference(reorient_equations,[],[f911])).
% 13.04/2.33 thf(f913,definition,(
% 13.04/2.33 (sF47 = ((cartprodmempair => sF46)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF47])],[function_definition])).
% 13.04/2.33 thf(f914,definition,(
% 13.04/2.33 (sF48 = ((cartprodmempair1 => sF47)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF48])],[function_definition])).
% 13.04/2.33 thf(f915,plain,(
% 13.04/2.33 (((cartprodmempair1 => sF47)) = sF48)),
% 13.04/2.33 inference(reorient_equations,[],[f914])).
% 13.04/2.33 thf(f916,definition,(
% 13.04/2.33 (sF49 = ((cartprodpairin => sF48)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF49])],[function_definition])).
% 13.04/2.33 thf(f917,plain,(
% 13.04/2.33 (((cartprodpairin => sF48)) = sF49)),
% 13.04/2.33 inference(reorient_equations,[],[f916])).
% 13.04/2.33 thf(f918,definition,(
% 13.04/2.33 (sF50 = ((ubforcartprodlem3 => sF49)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF50])],[function_definition])).
% 13.04/2.33 thf(f919,plain,(
% 13.04/2.33 (((ubforcartprodlem3 => sF49)) = sF50)),
% 13.04/2.33 inference(reorient_equations,[],[f918])).
% 13.04/2.33 thf(f920,definition,(
% 13.04/2.33 (sF51 = ((ubforcartprodlem2 => sF50)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF51])],[function_definition])).
% 13.04/2.33 thf(f921,plain,(
% 13.04/2.33 (((ubforcartprodlem2 => sF50)) = sF51)),
% 13.04/2.33 inference(reorient_equations,[],[f920])).
% 13.04/2.33 thf(f922,definition,(
% 13.04/2.33 (sF52 = ((ubforcartprodlem1 => sF51)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF52])],[function_definition])).
% 13.04/2.33 thf(f923,definition,(
% 13.04/2.33 (sF53 = ((upairinpowunion => sF52)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF53])],[function_definition])).
% 13.04/2.33 thf(f924,plain,(
% 13.04/2.33 (((upairinpowunion => sF52)) = sF53)),
% 13.04/2.33 inference(reorient_equations,[],[f923])).
% 13.04/2.33 thf(f925,definition,(
% 13.04/2.33 (sF54 = ((upairsubunion => sF53)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF54])],[function_definition])).
% 13.04/2.33 thf(f926,definition,(
% 13.04/2.33 (sF55 = ((upairset2E => sF54)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF55])],[function_definition])).
% 13.04/2.33 thf(f927,definition,(
% 13.04/2.33 (sF56 = ((singletoninpowunion => sF55)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF56])],[function_definition])).
% 13.04/2.33 thf(f928,plain,(
% 13.04/2.33 (((singletoninpowunion => sF55)) = sF56)),
% 13.04/2.33 inference(reorient_equations,[],[f927])).
% 13.04/2.33 thf(f929,definition,(
% 13.04/2.33 (sF57 = ((singletoninpowerset => sF56)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF57])],[function_definition])).
% 13.04/2.33 thf(f930,plain,(
% 13.04/2.33 (((singletoninpowerset => sF56)) = sF57)),
% 13.04/2.33 inference(reorient_equations,[],[f929])).
% 13.04/2.33 thf(f931,definition,(
% 13.04/2.33 (sF58 = ((singletonsubset => sF57)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF58])],[function_definition])).
% 13.04/2.33 thf(f932,plain,(
% 13.04/2.33 (((singletonsubset => sF57)) = sF58)),
% 13.04/2.33 inference(reorient_equations,[],[f931])).
% 13.04/2.33 thf(f933,definition,(
% 13.04/2.33 (sF59 = ((kpairp => sF58)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF59])],[function_definition])).
% 13.04/2.33 thf(f934,plain,(
% 13.04/2.33 (((kpairp => sF58)) = sF59)),
% 13.04/2.33 inference(reorient_equations,[],[f933])).
% 13.04/2.33 thf(f935,definition,(
% 13.04/2.33 (sF60 = ((kpairiskpair => sF59)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF60])],[function_definition])).
% 13.04/2.33 thf(f936,definition,(
% 13.04/2.33 (sF61 = ((setukpairIR => sF60)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF61])],[function_definition])).
% 13.04/2.33 thf(f937,plain,(
% 13.04/2.33 (((setukpairIR => sF60)) = sF61)),
% 13.04/2.33 inference(reorient_equations,[],[f936])).
% 13.04/2.33 thf(f938,definition,(
% 13.04/2.33 (sF62 = ((setukpairIL => sF61)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF62])],[function_definition])).
% 13.04/2.33 thf(f939,plain,(
% 13.04/2.33 (((setukpairIL => sF61)) = sF62)),
% 13.04/2.33 inference(reorient_equations,[],[f938])).
% 13.04/2.33 thf(f940,definition,(
% 13.04/2.33 (sF63 = ((secondinupair => sF62)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF63])],[function_definition])).
% 13.04/2.33 thf(f941,definition,(
% 13.04/2.33 (sF64 = ((symdiffIneg2 => sF63)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF64])],[function_definition])).
% 13.04/2.33 thf(f942,plain,(
% 13.04/2.33 (((symdiffIneg2 => sF63)) = sF64)),
% 13.04/2.33 inference(reorient_equations,[],[f941])).
% 13.04/2.33 thf(f943,definition,(
% 13.04/2.33 (sF65 = ((symdiffIneg1 => sF64)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF65])],[function_definition])).
% 13.04/2.33 thf(f944,plain,(
% 13.04/2.33 (((symdiffIneg1 => sF64)) = sF65)),
% 13.04/2.33 inference(reorient_equations,[],[f943])).
% 13.04/2.33 thf(f945,definition,(
% 13.04/2.33 (sF66 = ((symdiffI2 => sF65)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF66])],[function_definition])).
% 13.04/2.33 thf(f946,definition,(
% 13.04/2.33 (sF67 = ((symdiffI1 => sF66)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF67])],[function_definition])).
% 13.04/2.33 thf(f947,plain,(
% 13.04/2.33 (((symdiffI1 => sF66)) = sF67)),
% 13.04/2.33 inference(reorient_equations,[],[f946])).
% 13.04/2.33 thf(f948,definition,(
% 13.04/2.33 (sF68 = ((symdiffE => sF67)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF68])],[function_definition])).
% 13.04/2.33 thf(f949,definition,(
% 13.04/2.33 (sF69 = ((setminusSubset1 => sF68)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF69])],[function_definition])).
% 13.04/2.33 thf(f950,plain,(
% 13.04/2.33 (((setminusSubset1 => sF68)) = sF69)),
% 13.04/2.33 inference(reorient_equations,[],[f949])).
% 13.04/2.33 thf(f951,definition,(
% 13.04/2.33 (sF70 = ((setminusLsub => sF69)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF70])],[function_definition])).
% 13.04/2.33 thf(f952,definition,(
% 13.04/2.33 (sF71 = ((setminusIRneg => sF70)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF71])],[function_definition])).
% 13.04/2.33 thf(f953,plain,(
% 13.04/2.33 (((setminusIRneg => sF70)) = sF71)),
% 13.04/2.33 inference(reorient_equations,[],[f952])).
% 13.04/2.33 thf(f954,definition,(
% 13.04/2.33 (sF72 = ((setminusILneg => sF71)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF72])],[function_definition])).
% 13.04/2.33 thf(f955,plain,(
% 13.04/2.33 (((setminusILneg => sF71)) = sF72)),
% 13.04/2.33 inference(reorient_equations,[],[f954])).
% 13.04/2.33 thf(f956,definition,(
% 13.04/2.33 (sF73 = ((setminusELneg => sF72)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF73])],[function_definition])).
% 13.04/2.33 thf(f957,definition,(
% 13.04/2.33 (sF74 = ((setminusERneg => sF73)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF74])],[function_definition])).
% 13.04/2.33 thf(f958,plain,(
% 13.04/2.33 (((setminusERneg => sF73)) = sF74)),
% 13.04/2.33 inference(reorient_equations,[],[f957])).
% 13.04/2.33 thf(f959,definition,(
% 13.04/2.33 (sF75 = ((setminusSubset2 => sF74)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF75])],[function_definition])).
% 13.04/2.33 thf(f960,plain,(
% 13.04/2.33 (((setminusSubset2 => sF74)) = sF75)),
% 13.04/2.33 inference(reorient_equations,[],[f959])).
% 13.04/2.33 thf(f961,definition,(
% 13.04/2.33 (sF76 = ((setminusER => sF75)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF76])],[function_definition])).
% 13.04/2.33 thf(f962,plain,(
% 13.04/2.33 (((setminusER => sF75)) = sF76)),
% 13.04/2.33 inference(reorient_equations,[],[f961])).
% 13.04/2.33 thf(f963,definition,(
% 13.04/2.33 (sF77 = ((setminusEL => sF76)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF77])],[function_definition])).
% 13.04/2.33 thf(f964,definition,(
% 13.04/2.33 (sF78 = ((setminusI => sF77)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF78])],[function_definition])).
% 13.04/2.33 thf(f965,definition,(
% 13.04/2.33 (sF79 = ((bs114d => sF78)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF79])],[function_definition])).
% 13.04/2.33 thf(f966,definition,(
% 13.04/2.33 (sF80 = ((binintersectSubset1 => sF79)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF80])],[function_definition])).
% 13.04/2.33 thf(f967,plain,(
% 13.04/2.33 (((binintersectSubset1 => sF79)) = sF80)),
% 13.04/2.33 inference(reorient_equations,[],[f966])).
% 13.04/2.33 thf(f968,definition,(
% 13.04/2.33 (sF81 = ((binintersectSubset4 => sF80)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF81])],[function_definition])).
% 13.04/2.33 thf(f969,definition,(
% 13.04/2.33 (sF82 = ((binintersectRsub => sF81)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF82])],[function_definition])).
% 13.04/2.33 thf(f970,definition,(
% 13.04/2.33 (sF83 = ((disjointsetsI1 => sF82)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF83])],[function_definition])).
% 13.04/2.33 thf(f971,plain,(
% 13.04/2.33 (((disjointsetsI1 => sF82)) = sF83)),
% 13.04/2.33 inference(reorient_equations,[],[f970])).
% 13.04/2.33 thf(f972,definition,(
% 13.04/2.33 (sF84 = ((binintersectER => sF83)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF84])],[function_definition])).
% 13.04/2.33 thf(f973,definition,(
% 13.04/2.33 (sF85 = ((binintersectSubset3 => sF84)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF85])],[function_definition])).
% 13.04/2.33 thf(f974,definition,(
% 13.04/2.33 (sF86 = ((binintersectSubset2 => sF85)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF86])],[function_definition])).
% 13.04/2.33 thf(f975,plain,(
% 13.04/2.33 (((binintersectSubset2 => sF85)) = sF86)),
% 13.04/2.33 inference(reorient_equations,[],[f974])).
% 13.04/2.33 thf(f976,definition,(
% 13.04/2.33 (sF87 = ((binintersectLsub => sF86)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF87])],[function_definition])).
% 13.04/2.33 thf(f977,plain,(
% 13.04/2.33 (((binintersectLsub => sF86)) = sF87)),
% 13.04/2.33 inference(reorient_equations,[],[f976])).
% 13.04/2.33 thf(f978,definition,(
% 13.04/2.33 (sF88 = ((binintersectEL => sF87)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF88])],[function_definition])).
% 13.04/2.33 thf(f979,plain,(
% 13.04/2.33 (((binintersectEL => sF87)) = sF88)),
% 13.04/2.33 inference(reorient_equations,[],[f978])).
% 13.04/2.33 thf(f980,definition,(
% 13.04/2.33 (sF89 = ((binintersectSubset5 => sF88)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF89])],[function_definition])).
% 13.04/2.33 thf(f981,plain,(
% 13.04/2.33 (((binintersectSubset5 => sF88)) = sF89)),
% 13.04/2.33 inference(reorient_equations,[],[f980])).
% 13.04/2.33 thf(f982,definition,(
% 13.04/2.33 (sF90 = ((binintersectI => sF89)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF90])],[function_definition])).
% 13.04/2.33 thf(f983,definition,(
% 13.04/2.33 (sF91 = ((binunionRsub => sF90)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF91])],[function_definition])).
% 13.04/2.33 thf(f984,plain,(
% 13.04/2.33 (((binunionRsub => sF90)) = sF91)),
% 13.04/2.33 inference(reorient_equations,[],[f983])).
% 13.04/2.33 thf(f985,definition,(
% 13.04/2.33 (sF92 = ((binunionLsub => sF91)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF92])],[function_definition])).
% 13.04/2.33 thf(f986,definition,(
% 13.04/2.33 (sF93 = ((binunionE => sF92)))),
% 13.04/2.33 introduced(definition,[new_symbols(definition,[sF93])],[function_definition])).
% 13.04/2.33 thf(f987,plain,(
% 13.04/2.33 (((binunionE => sF92)) = sF93)),
% 13.04/2.34 inference(reorient_equations,[],[f986])).
% 13.04/2.34 thf(f988,definition,(
% 13.04/2.34 (sF94 = ((binunionEcases => sF93)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF94])],[function_definition])).
% 13.04/2.34 thf(f989,definition,(
% 13.04/2.34 (sF95 = ((binunionIR => sF94)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF95])],[function_definition])).
% 13.04/2.34 thf(f990,definition,(
% 13.04/2.34 (sF96 = ((upairset2IR => sF95)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF96])],[function_definition])).
% 13.04/2.34 thf(f991,definition,(
% 13.04/2.34 (sF97 = ((binunionIL => sF96)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF97])],[function_definition])).
% 13.04/2.34 thf(f992,plain,(
% 13.04/2.34 (((binunionIL => sF96)) = sF97)),
% 13.04/2.34 inference(reorient_equations,[],[f991])).
% 13.04/2.34 thf(f993,definition,(
% 13.04/2.34 (sF98 = ((sepSubset => sF97)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF98])],[function_definition])).
% 13.04/2.34 thf(f994,definition,(
% 13.04/2.34 (sF99 = ((sepInPowerset => sF98)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF99])],[function_definition])).
% 13.04/2.34 thf(f995,plain,(
% 13.04/2.34 (((sepInPowerset => sF98)) = sF99)),
% 13.04/2.34 inference(reorient_equations,[],[f994])).
% 13.04/2.34 thf(f996,definition,(
% 13.04/2.34 (sF100 = ((powersetsubset => sF99)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF100])],[function_definition])).
% 13.04/2.34 thf(f997,plain,(
% 13.04/2.34 (((powersetsubset => sF99)) = sF100)),
% 13.04/2.34 inference(reorient_equations,[],[f996])).
% 13.04/2.34 thf(f998,definition,(
% 13.04/2.34 (sF101 = ((inPowerset => sF100)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF101])],[function_definition])).
% 13.04/2.34 thf(f999,plain,(
% 13.04/2.34 (((inPowerset => sF100)) = sF101)),
% 13.04/2.34 inference(reorient_equations,[],[f998])).
% 13.04/2.34 thf(f1000,definition,(
% 13.04/2.34 (sF102 = ((powersetE1 => sF101)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF102])],[function_definition])).
% 13.04/2.34 thf(f1001,plain,(
% 13.04/2.34 (((powersetE1 => sF101)) = sF102)),
% 13.04/2.34 inference(reorient_equations,[],[f1000])).
% 13.04/2.34 thf(f1002,definition,(
% 13.04/2.34 (sF103 = ((powersetI1 => sF102)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF103])],[function_definition])).
% 13.04/2.34 thf(f1003,definition,(
% 13.04/2.34 (sF104 = ((subsetemptysetimpeq => sF103)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF104])],[function_definition])).
% 13.04/2.34 thf(f1004,definition,(
% 13.04/2.34 (sF105 = ((setextsub => sF104)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF105])],[function_definition])).
% 13.04/2.34 thf(f1005,definition,(
% 13.04/2.34 (sF106 = ((subset2powerset => sF105)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF106])],[function_definition])).
% 13.04/2.34 thf(f1006,definition,(
% 13.04/2.34 (sF107 = ((setadjoinSub2 => sF106)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF107])],[function_definition])).
% 13.04/2.34 thf(f1007,definition,(
% 13.04/2.34 (sF108 = ((setadjoinSub => sF107)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF108])],[function_definition])).
% 13.04/2.34 thf(f1008,definition,(
% 13.04/2.34 (sF109 = ((subsetTrans => sF108)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF109])],[function_definition])).
% 13.04/2.34 thf(f1009,definition,(
% 13.04/2.34 (sF110 = ((subsetRefl => sF109)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF110])],[function_definition])).
% 13.04/2.34 thf(f1010,plain,(
% 13.04/2.34 (((subsetRefl => sF109)) = sF110)),
% 13.04/2.34 inference(reorient_equations,[],[f1009])).
% 13.04/2.34 thf(f1011,definition,(
% 13.04/2.34 (sF111 = ((notequalI2 => sF110)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF111])],[function_definition])).
% 13.04/2.34 thf(f1012,definition,(
% 13.04/2.34 (sF112 = ((notequalI1 => sF111)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF112])],[function_definition])).
% 13.04/2.34 thf(f1013,plain,(
% 13.04/2.34 (((notequalI1 => sF111)) = sF112)),
% 13.04/2.34 inference(reorient_equations,[],[f1012])).
% 13.04/2.34 thf(f1014,definition,(
% 13.04/2.34 (sF113 = ((notsubsetI => sF112)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF113])],[function_definition])).
% 13.04/2.34 thf(f1015,plain,(
% 13.04/2.34 (((notsubsetI => sF112)) = sF113)),
% 13.04/2.34 inference(reorient_equations,[],[f1014])).
% 13.04/2.34 thf(f1016,definition,(
% 13.04/2.34 (sF114 = ((subsetE2 => sF113)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF114])],[function_definition])).
% 13.04/2.34 thf(f1017,definition,(
% 13.04/2.34 (sF115 = ((subsetE => sF114)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF115])],[function_definition])).
% 13.04/2.34 thf(f1018,plain,(
% 13.04/2.34 (((subsetE => sF114)) = sF115)),
% 13.04/2.34 inference(reorient_equations,[],[f1017])).
% 13.04/2.34 thf(f1019,definition,(
% 13.04/2.34 (sF116 = ((emptysetsubset => sF115)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF116])],[function_definition])).
% 13.04/2.34 thf(f1020,definition,(
% 13.04/2.34 (sF117 = ((subsetI2 => sF116)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF117])],[function_definition])).
% 13.04/2.34 thf(f1021,definition,(
% 13.04/2.34 (sF118 = ((eqimpsubset1 => sF117)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF118])],[function_definition])).
% 13.04/2.34 thf(f1022,plain,(
% 13.04/2.34 (((eqimpsubset1 => sF117)) = sF118)),
% 13.04/2.34 inference(reorient_equations,[],[f1021])).
% 13.04/2.34 thf(f1023,definition,(
% 13.04/2.34 (sF119 = ((eqimpsubset2 => sF118)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF119])],[function_definition])).
% 13.04/2.34 thf(f1024,plain,(
% 13.04/2.34 (((eqimpsubset2 => sF118)) = sF119)),
% 13.04/2.34 inference(reorient_equations,[],[f1023])).
% 13.04/2.34 thf(f1025,definition,(
% 13.04/2.34 (sF120 = ((subsetI1 => sF119)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF120])],[function_definition])).
% 13.04/2.34 thf(f1026,definition,(
% 13.04/2.34 (sF121 = ((dsetconstr__Cong => sF120)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF121])],[function_definition])).
% 13.04/2.34 thf(f1027,plain,(
% 13.04/2.34 (((dsetconstr__Cong => sF120)) = sF121)),
% 13.04/2.34 inference(reorient_equations,[],[f1026])).
% 13.04/2.34 thf(f1028,definition,(
% 13.04/2.34 (sF122 = ((descr__Cong => sF121)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF122])],[function_definition])).
% 13.04/2.34 thf(f1029,plain,(
% 13.04/2.34 (((descr__Cong => sF121)) = sF122)),
% 13.04/2.34 inference(reorient_equations,[],[f1028])).
% 13.04/2.34 thf(f1030,definition,(
% 13.04/2.34 (sF123 = ((exuEu => sF122)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF123])],[function_definition])).
% 13.04/2.34 thf(f1031,plain,(
% 13.04/2.34 (((exuEu => sF122)) = sF123)),
% 13.04/2.34 inference(reorient_equations,[],[f1030])).
% 13.04/2.34 thf(f1032,definition,(
% 13.04/2.34 (sF124 = ((omega__Cong => sF123)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF124])],[function_definition])).
% 13.04/2.34 thf(f1033,definition,(
% 13.04/2.34 (sF125 = ((setunion__Cong => sF124)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF125])],[function_definition])).
% 13.04/2.34 thf(f1034,definition,(
% 13.04/2.34 (sF126 = ((powerset__Cong => sF125)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF126])],[function_definition])).
% 13.04/2.34 thf(f1035,definition,(
% 13.04/2.34 (sF127 = ((setadjoin__Cong => sF126)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF127])],[function_definition])).
% 13.04/2.34 thf(f1036,plain,(
% 13.04/2.34 (((setadjoin__Cong => sF126)) = sF127)),
% 13.04/2.34 inference(reorient_equations,[],[f1035])).
% 13.04/2.34 thf(f1037,definition,(
% 13.04/2.34 (sF128 = ((emptyset__Cong => sF127)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF128])],[function_definition])).
% 13.04/2.34 thf(f1038,definition,(
% 13.04/2.34 (sF129 = ((exu__Cong => sF128)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF129])],[function_definition])).
% 13.04/2.34 thf(f1039,definition,(
% 13.04/2.34 (sF130 = ((exuE3u => sF129)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF130])],[function_definition])).
% 13.04/2.34 thf(f1040,plain,(
% 13.04/2.34 (((exuE3u => sF129)) = sF130)),
% 13.04/2.34 inference(reorient_equations,[],[f1039])).
% 13.04/2.34 thf(f1041,definition,(
% 13.04/2.34 (sF131 = ((in__Cong => sF130)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF131])],[function_definition])).
% 13.04/2.34 thf(f1042,plain,(
% 13.04/2.34 (((in__Cong => sF130)) = sF131)),
% 13.04/2.34 inference(reorient_equations,[],[f1041])).
% 13.04/2.34 thf(f1043,definition,(
% 13.04/2.34 (sF132 = ((inCongP => sF131)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF132])],[function_definition])).
% 13.04/2.34 thf(f1044,plain,(
% 13.04/2.34 (((inCongP => sF131)) = sF132)),
% 13.04/2.34 inference(reorient_equations,[],[f1043])).
% 13.04/2.34 thf(f1045,definition,(
% 13.04/2.34 (sF133 = ((exuI2 => sF132)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF133])],[function_definition])).
% 13.04/2.34 thf(f1046,definition,(
% 13.04/2.34 (sF134 = ((exuI3 => sF133)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF134])],[function_definition])).
% 13.04/2.34 thf(f1047,plain,(
% 13.04/2.34 (((exuI3 => sF133)) = sF134)),
% 13.04/2.34 inference(reorient_equations,[],[f1046])).
% 13.04/2.34 thf(f1048,definition,(
% 13.04/2.34 (sF135 = ((exuI1 => sF134)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF135])],[function_definition])).
% 13.04/2.34 thf(f1049,definition,(
% 13.04/2.34 (sF136 = ((notdallE => sF135)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF136])],[function_definition])).
% 13.04/2.34 thf(f1050,plain,(
% 13.04/2.34 (((notdallE => sF135)) = sF136)),
% 13.04/2.34 inference(reorient_equations,[],[f1049])).
% 13.04/2.34 thf(f1051,definition,(
% 13.04/2.34 (sF137 = ((notdexE => sF136)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF137])],[function_definition])).
% 13.04/2.34 thf(f1052,plain,(
% 13.04/2.34 (((notdexE => sF136)) = sF137)),
% 13.04/2.34 inference(reorient_equations,[],[f1051])).
% 13.04/2.34 thf(f1053,definition,(
% 13.04/2.34 (sF138 = ((prop2set2propI => sF137)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF138])],[function_definition])).
% 13.04/2.34 thf(f1054,plain,(
% 13.04/2.34 (((prop2set2propI => sF137)) = sF138)),
% 13.04/2.34 inference(reorient_equations,[],[f1053])).
% 13.04/2.34 thf(f1055,definition,(
% 13.04/2.34 (sF139 = ((prop2setI => sF138)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF139])],[function_definition])).
% 13.04/2.34 thf(f1056,definition,(
% 13.04/2.34 (sF140 = ((quantDeMorgan4 => sF139)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF140])],[function_definition])).
% 13.04/2.34 thf(f1057,definition,(
% 13.04/2.34 (sF141 = ((quantDeMorgan3 => sF140)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF141])],[function_definition])).
% 13.04/2.34 thf(f1058,definition,(
% 13.04/2.34 (sF142 = ((quantDeMorgan2 => sF141)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF142])],[function_definition])).
% 13.04/2.34 thf(f1059,definition,(
% 13.04/2.34 (sF143 = ((quantDeMorgan1 => sF142)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF143])],[function_definition])).
% 13.04/2.34 thf(f1060,plain,(
% 13.04/2.34 (((quantDeMorgan1 => sF142)) = sF143)),
% 13.04/2.34 inference(reorient_equations,[],[f1059])).
% 13.04/2.34 thf(f1061,definition,(
% 13.04/2.34 (sF144 = ((vacuousDall => sF143)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF144])],[function_definition])).
% 13.04/2.34 thf(f1062,plain,(
% 13.04/2.34 (((vacuousDall => sF143)) = sF144)),
% 13.04/2.34 inference(reorient_equations,[],[f1061])).
% 13.04/2.34 thf(f1063,definition,(
% 13.04/2.34 (sF145 = ((emptyE1 => sF144)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF145])],[function_definition])).
% 13.04/2.34 thf(f1064,definition,(
% 13.04/2.34 (sF146 = ((upairsetIR => sF145)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF146])],[function_definition])).
% 13.04/2.34 thf(f1065,plain,(
% 13.04/2.34 (((upairsetIR => sF145)) = sF146)),
% 13.04/2.34 inference(reorient_equations,[],[f1064])).
% 13.04/2.34 thf(f1066,definition,(
% 13.04/2.34 (sF147 = ((upairsetIL => sF146)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF147])],[function_definition])).
% 13.04/2.34 thf(f1067,plain,(
% 13.04/2.34 (((upairsetIL => sF146)) = sF147)),
% 13.04/2.34 inference(reorient_equations,[],[f1066])).
% 13.04/2.34 thf(f1068,definition,(
% 13.04/2.34 (sF148 = ((upairsetE => sF147)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF148])],[function_definition])).
% 13.04/2.34 thf(f1069,definition,(
% 13.04/2.34 (sF149 = ((singletonsswitch => sF148)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF149])],[function_definition])).
% 13.04/2.34 thf(f1070,definition,(
% 13.04/2.34 (sF150 = ((eqinunit => sF149)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF150])],[function_definition])).
% 13.04/2.34 thf(f1071,definition,(
% 13.04/2.34 (sF151 = ((notinsingleton => sF150)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF151])],[function_definition])).
% 13.04/2.34 thf(f1072,definition,(
% 13.04/2.34 (sF152 = ((uniqinunit => sF151)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF152])],[function_definition])).
% 13.04/2.34 thf(f1073,definition,(
% 13.04/2.34 (sF153 = ((nonemptyImpWitness => sF152)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF153])],[function_definition])).
% 13.04/2.34 thf(f1074,definition,(
% 13.04/2.34 (sF154 = ((exuE2 => sF153)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF154])],[function_definition])).
% 13.04/2.34 thf(f1075,definition,(
% 13.04/2.34 (sF155 = ((subPowSU => sF154)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF155])],[function_definition])).
% 13.04/2.34 thf(f1076,definition,(
% 13.04/2.34 (sF156 = ((setunionE => sF155)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF156])],[function_definition])).
% 13.04/2.34 thf(f1077,plain,(
% 13.04/2.34 (((setunionE => sF155)) = sF156)),
% 13.04/2.34 inference(reorient_equations,[],[f1076])).
% 13.04/2.34 thf(f1078,definition,(
% 13.04/2.34 (sF157 = ((setunionI => sF156)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF157])],[function_definition])).
% 13.04/2.34 thf(f1079,plain,(
% 13.04/2.34 (((setunionI => sF156)) = sF157)),
% 13.04/2.34 inference(reorient_equations,[],[f1078])).
% 13.04/2.34 thf(f1080,definition,(
% 13.04/2.34 (sF158 = ((powersetE => sF157)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF158])],[function_definition])).
% 13.04/2.34 thf(f1081,definition,(
% 13.04/2.34 (sF159 = ((emptyInPowerset => sF158)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF159])],[function_definition])).
% 13.04/2.34 thf(f1082,plain,(
% 13.04/2.34 (((emptyInPowerset => sF158)) = sF159)),
% 13.04/2.34 inference(reorient_equations,[],[f1081])).
% 13.04/2.34 thf(f1083,definition,(
% 13.04/2.34 (sF160 = ((emptyinPowerset => sF159)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF160])],[function_definition])).
% 13.04/2.34 thf(f1084,plain,(
% 13.04/2.34 (((emptyinPowerset => sF159)) = sF160)),
% 13.04/2.34 inference(reorient_equations,[],[f1083])).
% 13.04/2.34 thf(f1085,definition,(
% 13.04/2.34 (sF161 = ((powersetI => sF160)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF161])],[function_definition])).
% 13.04/2.34 thf(f1086,definition,(
% 13.04/2.34 (sF162 = ((setoftrueEq => sF161)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF162])],[function_definition])).
% 13.04/2.34 thf(f1087,definition,(
% 13.04/2.34 (sF163 = ((setadjoinOr => sF162)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF163])],[function_definition])).
% 13.04/2.34 thf(f1088,plain,(
% 13.04/2.34 (((setadjoinOr => sF162)) = sF163)),
% 13.04/2.34 inference(reorient_equations,[],[f1087])).
% 13.04/2.34 thf(f1089,definition,(
% 13.04/2.34 (sF164 = ((setadjoinE => sF163)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF164])],[function_definition])).
% 13.04/2.34 thf(f1090,definition,(
% 13.04/2.34 (sF165 = ((setadjoinIR => sF164)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF165])],[function_definition])).
% 13.04/2.34 thf(f1091,plain,(
% 13.04/2.34 (((setadjoinIR => sF164)) = sF165)),
% 13.04/2.34 inference(reorient_equations,[],[f1090])).
% 13.04/2.34 thf(f1092,definition,(
% 13.04/2.34 (sF166 = ((emptyinunitempty => sF165)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF166])],[function_definition])).
% 13.04/2.34 thf(f1093,plain,(
% 13.04/2.34 (((emptyinunitempty => sF165)) = sF166)),
% 13.04/2.34 inference(reorient_equations,[],[f1092])).
% 13.04/2.34 thf(f1094,definition,(
% 13.04/2.34 (sF167 = ((setadjoinIL => sF166)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF167])],[function_definition])).
% 13.04/2.34 thf(f1095,plain,(
% 13.04/2.34 (((setadjoinIL => sF166)) = sF167)),
% 13.04/2.34 inference(reorient_equations,[],[f1094])).
% 13.04/2.34 thf(f1096,definition,(
% 13.04/2.34 (sF168 = ((nonemptyI1 => sF167)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF168])],[function_definition])).
% 13.04/2.34 thf(f1097,definition,(
% 13.04/2.34 (sF169 = ((nonemptyI => sF168)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF169])],[function_definition])).
% 13.04/2.34 thf(f1098,definition,(
% 13.04/2.34 (sF170 = ((nonemptyE1 => sF169)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF170])],[function_definition])).
% 13.04/2.34 thf(f1099,definition,(
% 13.04/2.34 (sF171 = ((setbeta => sF170)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF171])],[function_definition])).
% 13.04/2.34 thf(f1100,definition,(
% 13.04/2.34 (sF172 = ((noeltsimpempty => sF171)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF172])],[function_definition])).
% 13.04/2.34 thf(f1101,plain,(
% 13.04/2.34 (((noeltsimpempty => sF171)) = sF172)),
% 13.04/2.34 inference(reorient_equations,[],[f1100])).
% 13.04/2.34 thf(f1102,definition,(
% 13.04/2.34 (sF173 = ((emptyI => sF172)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF173])],[function_definition])).
% 13.04/2.34 thf(f1103,definition,(
% 13.04/2.34 (sF174 = ((setext => sF173)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF174])],[function_definition])).
% 13.04/2.34 thf(f1104,definition,(
% 13.04/2.34 (sF175 = ((exuE3e => sF174)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF175])],[function_definition])).
% 13.04/2.34 thf(f1105,definition,(
% 13.04/2.34 (sF176 = ((notinemptyset => sF175)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF176])],[function_definition])).
% 13.04/2.34 thf(f1106,definition,(
% 13.04/2.34 (sF177 = ((emptysetimpfalse => sF176)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF177])],[function_definition])).
% 13.04/2.34 thf(f1107,plain,(
% 13.04/2.34 (((emptysetimpfalse => sF176)) = sF177)),
% 13.04/2.34 inference(reorient_equations,[],[f1106])).
% 13.04/2.34 thf(f1108,definition,(
% 13.04/2.34 (sF178 = ((emptysetE => sF177)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF178])],[function_definition])).
% 13.04/2.34 thf(f1109,definition,(
% 13.04/2.34 (sF179 = ((prop2setE => sF178)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF179])],[function_definition])).
% 13.04/2.34 thf(f1110,definition,(
% 13.04/2.34 (sF180 = ((exuE1 => sF179)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF180])],[function_definition])).
% 13.04/2.34 thf(f1111,plain,(
% 13.04/2.34 (((exuE1 => sF179)) = sF180)),
% 13.04/2.34 inference(reorient_equations,[],[f1110])).
% 13.04/2.34 thf(f1112,definition,(
% 13.04/2.34 (sF181 = ((dsetconstrER => sF180)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF181])],[function_definition])).
% 13.04/2.34 thf(f1113,definition,(
% 13.04/2.34 (sF182 = ((dsetconstrEL => sF181)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF182])],[function_definition])).
% 13.04/2.34 thf(f1114,definition,(
% 13.04/2.34 (sF183 = ((dsetconstrI => sF182)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF183])],[function_definition])).
% 13.04/2.34 thf(f1115,definition,(
% 13.04/2.34 (sF184 = ((descrp => sF183)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF184])],[function_definition])).
% 13.04/2.34 thf(f1116,definition,(
% 13.04/2.34 (sF185 = ((wellorderingAx => sF184)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF185])],[function_definition])).
% 13.04/2.34 thf(f1117,plain,(
% 13.04/2.34 (((wellorderingAx => sF184)) = sF185)),
% 13.04/2.34 inference(reorient_equations,[],[f1116])).
% 13.04/2.34 thf(f1118,definition,(
% 13.04/2.34 (sF186 = ((foundationAx => sF185)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF186])],[function_definition])).
% 13.04/2.34 thf(f1119,definition,(
% 13.04/2.34 (sF187 = ((replAx => sF186)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF187])],[function_definition])).
% 13.04/2.34 thf(f1120,plain,(
% 13.04/2.34 (((replAx => sF186)) = sF187)),
% 13.04/2.34 inference(reorient_equations,[],[f1119])).
% 13.04/2.34 thf(f1121,definition,(
% 13.04/2.34 (sF188 = ((omegaIndAx => sF187)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF188])],[function_definition])).
% 13.04/2.34 thf(f1122,plain,(
% 13.04/2.34 (((omegaIndAx => sF187)) = sF188)),
% 13.04/2.34 inference(reorient_equations,[],[f1121])).
% 13.04/2.34 thf(f1123,definition,(
% 13.04/2.34 (sF189 = ((omegaSAx => sF188)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF189])],[function_definition])).
% 13.04/2.34 thf(f1124,plain,(
% 13.04/2.34 (((omegaSAx => sF188)) = sF189)),
% 13.04/2.34 inference(reorient_equations,[],[f1123])).
% 13.04/2.34 thf(f1125,definition,(
% 13.04/2.34 (sF190 = ((omega0Ax => sF189)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF190])],[function_definition])).
% 13.04/2.34 thf(f1126,definition,(
% 13.04/2.34 (sF191 = ((setunionAx => sF190)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF191])],[function_definition])).
% 13.04/2.34 thf(f1127,plain,(
% 13.04/2.34 (((setunionAx => sF190)) = sF191)),
% 13.04/2.34 inference(reorient_equations,[],[f1126])).
% 13.04/2.34 thf(f1128,definition,(
% 13.04/2.34 (sF192 = ((powersetAx => sF191)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF192])],[function_definition])).
% 13.04/2.34 thf(f1129,plain,(
% 13.04/2.34 (((powersetAx => sF191)) = sF192)),
% 13.04/2.34 inference(reorient_equations,[],[f1128])).
% 13.04/2.34 thf(f1130,definition,(
% 13.04/2.34 (sF193 = ((setadjoinAx => sF192)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF193])],[function_definition])).
% 13.04/2.34 thf(f1131,definition,(
% 13.04/2.34 (sF194 = ((emptysetAx => sF193)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF194])],[function_definition])).
% 13.04/2.34 thf(f1132,plain,(
% 13.04/2.34 (((emptysetAx => sF193)) = sF194)),
% 13.04/2.34 inference(reorient_equations,[],[f1131])).
% 13.04/2.34 thf(f1133,definition,(
% 13.04/2.34 (sF195 = ((setextAx => sF194)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF195])],[function_definition])).
% 13.04/2.34 thf(f1134,plain,(
% 13.04/2.34 (((setextAx => sF194)) = sF195)),
% 13.04/2.34 inference(reorient_equations,[],[f1133])).
% 13.04/2.34 thf(f1135,definition,(
% 13.04/2.34 (sF196 = ((~ sF195)))),
% 13.04/2.34 introduced(definition,[new_symbols(definition,[sF196])],[function_definition])).
% 13.04/2.34 thf(f1136,plain,(
% 13.04/2.34 (sF196 = $true)),
% 13.04/2.34 inference(definition_folding,[],[f810,f1135,f1134,f1132,f1130,f1129,f1127,f1125,f1124,f1122,f1120,f1118,f1117,f1115,f1114,f1113,f1112,f1111,f1109,f1108,f1107,f1105,f1104,f1103,f1102,f1101,f1099,f1098,f1097,f1096,f1095,f1093,f1091,f1089,f1088,f1086,f1085,f1084,f1082,f1080,f1079,f1077,f1075,f1074,f1073,f1072,f1071,f1070,f1069,f1068,f1067,f1065,f1063,f1062,f1060,f1058,f1057,f1056,f1055,f1054,f1052,f1050,f1048,f1047,f1045,f1044,f1042,f1040,f1038,f1037,f1036,f1034,f1033,f1032,f1031,f1029,f1027,f1025,f1024,f1022,f1020,f1019,f1018,f1016,f1015,f1013,f1011,f1010,f1008,f1007,f1006,f1005,f1004,f1003,f1002,f1001,f999,f997,f995,f993,f992,f990,f989,f988,f987,f985,f984,f982,f981,f979,f977,f975,f973,f972,f971,f969,f968,f967,f965,f964,f963,f962,f960,f958,f956,f955,f953,f951,f950,f948,f947,f945,f944,f942,f940,f939,f937,f935,f934,f932,f930,f928,f926,f925,f924,f922,f921,f919,f917,f915,f913,f912,f910,f909,f907,f905,f903,f901,f899,f898,f896,f895,f893,f891,f890,f888,f887,f885,f883,f881,f879,f878,f877,f876,f874,f873,f872,f870,f868,f867,f866,f865,f864,f863,f862,f860,f859,f857,f856,f855,f854,f853,f851,f850,f848,f846,f845,f843])).
% 13.04/2.34 thf(f1137,plain,(
% 13.04/2.34 (emptysetsubset = ((!! @ $i @ (subset @ emptyset))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f700])).
% 13.04/2.34 thf(f1139,plain,(
% 13.04/2.34 (lamProp = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => ((subset @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))) @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y6 : $i]: (= @ (Y0 @ Y6)))))))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y6 : $i]: (= @ (Y0 @ Y6))))))))))))))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f812])).
% 13.04/2.34 thf(f1142,plain,(
% 13.04/2.34 (setbeta = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) = (in @ Y0 @ (dsetconstr @ Y1 @ Y2))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f647])).
% 13.04/2.34 thf(f1146,plain,(
% 13.04/2.34 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f828])).
% 13.04/2.34 thf(f1147,plain,(
% 13.04/2.34 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => $true))))))))))))),
% 13.04/2.34 inference(boolean_simplification,[],[f734])).
% 13.04/2.34 thf(f1148,plain,(
% 13.04/2.34 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 13.04/2.34 inference(boolean_simplification,[],[f1147])).
% 13.04/2.34 thf(f1149,plain,(
% 13.04/2.34 (theprop = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f829])).
% 13.04/2.34 thf(f1150,plain,(
% 13.04/2.34 (sepInPowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f625])).
% 13.04/2.34 thf(f1152,plain,(
% 13.04/2.34 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0)))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f743])).
% 13.04/2.34 thf(f1153,plain,(
% 13.04/2.34 (emptyset__Cong = $true)),
% 13.04/2.34 inference(boolean_simplification,[],[f708])).
% 13.04/2.34 thf(f1155,plain,(
% 13.04/2.34 (omega__Cong = $true)),
% 13.04/2.34 inference(boolean_simplification,[],[f645])).
% 13.04/2.34 thf(f1157,plain,(
% 13.04/2.34 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f817])).
% 13.04/2.34 thf(f1158,plain,(
% 13.04/2.34 (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => ((subset @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))) @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y6 : $i]: (= @ (Y0 @ Y6)))))))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y6 : $i]: (= @ (Y0 @ Y6))))))))))))))))))))))) = sF0)),
% 13.04/2.34 inference(beta-eta_normalization,[],[f843])).
% 13.04/2.34 thf(f1160,plain,(
% 13.04/2.34 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f831])).
% 13.04/2.34 thf(f1162,plain,(
% 13.04/2.34 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f744])).
% 13.04/2.34 thf(f1165,plain,(
% 13.04/2.34 (dsetconstrER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f751])).
% 13.04/2.34 thf(f1166,plain,(
% 13.04/2.34 (dpsetconstrEL1 = ((!! @ $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 @ Y0 @ Y1))))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f691])).
% 13.04/2.34 thf(f1169,plain,(
% 13.04/2.34 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.04/2.34 inference(boolean_simplification,[],[f701])).
% 13.04/2.34 thf(f1170,plain,(
% 13.04/2.34 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f835])).
% 13.04/2.34 thf(f1171,plain,(
% 13.04/2.34 (descrp = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0)))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f830])).
% 13.04/2.34 thf(f1173,plain,(
% 13.04/2.34 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f841])).
% 13.04/2.34 thf(f1176,plain,(
% 13.04/2.34 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f763])).
% 13.04/2.34 thf(f1177,plain,(
% 13.04/2.34 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f837])).
% 13.04/2.34 thf(f1179,plain,(
% 13.04/2.34 (setOfPairsIsBReln = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f832])).
% 13.04/2.34 thf(f1181,plain,(
% 13.04/2.34 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0)))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f839])).
% 13.04/2.34 thf(f1182,plain,(
% 13.04/2.34 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 13.04/2.34 inference(boolean_simplification,[],[f1181])).
% 13.04/2.34 thf(f1184,plain,(
% 13.04/2.34 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f821])).
% 13.04/2.34 thf(f1185,plain,(
% 13.04/2.34 (exuE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))))),
% 13.04/2.34 inference(boolean_simplification,[],[f1184])).
% 13.04/2.34 thf(f1187,plain,(
% 13.04/2.34 (dpsetconstrEL2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y1) @ (dpsetconstr @ Y2 @ Y0 @ Y3)) => (in @ Y1 @ Y0))))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f678])).
% 13.04/2.34 thf(f1188,plain,(
% 13.04/2.34 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f813])).
% 13.04/2.34 thf(f1189,plain,(
% 13.04/2.34 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0)))))))),
% 13.04/2.34 inference(beta-eta_normalization,[],[f833])).
% 13.04/2.34 thf(f1192,plain,(
% 13.04/2.34 (((~ sF195)) = $true)),
% 13.04/2.34 inference(backward_demodulation,[],[f1135,f1136])).
% 13.04/2.34 thf(f1193,plain,(
% 13.04/2.34 ($false = sF195)),
% 13.04/2.34 inference(not_proxy_clausification,[],[f1192])).
% 13.04/2.34 thf(f1198,plain,(
% 13.04/2.34 (((setextAx => sF194)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1134,f1193])).
% 13.04/2.34 thf(f1202,plain,(
% 13.04/2.34 ($false = sF194)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1198])).
% 13.04/2.34 thf(f1216,plain,(
% 13.04/2.34 (((emptysetAx => sF193)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1132,f1202])).
% 13.04/2.34 thf(f1219,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => sF193)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1216,f659])).
% 13.04/2.34 thf(f1220,plain,(
% 13.04/2.34 (((notinemptyset => sF193)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1219,f624])).
% 13.04/2.34 thf(f1222,plain,(
% 13.04/2.34 (notinemptyset = $true)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1220])).
% 13.04/2.34 thf(f1223,plain,(
% 13.04/2.34 (((notinemptyset => $true)) = $false) | (sF193 = $false)),
% 13.04/2.34 inference(superposition,[],[f1220,f807])).
% 13.04/2.34 thf(f1226,plain,(
% 13.04/2.34 (sF193 = $false) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1223])).
% 13.04/2.34 thf(f1227,plain,(
% 13.04/2.34 (sF193 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1226])).
% 13.04/2.34 thf(f1231,plain,(
% 13.04/2.34 ($false = ((setadjoinAx => sF192)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1130,f1227])).
% 13.04/2.34 thf(f1235,plain,(
% 13.04/2.34 ((($true => sF175)) = sF176)),
% 13.04/2.34 inference(backward_demodulation,[],[f1105,f1222])).
% 13.04/2.34 thf(f1236,plain,(
% 13.04/2.34 ($true = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 13.04/2.34 inference(backward_demodulation,[],[f624,f1222])).
% 13.04/2.34 thf(f1237,plain,(
% 13.04/2.34 (sF176 = sF175)),
% 13.04/2.34 inference(boolean_simplification,[],[f1235])).
% 13.04/2.34 thf(f1238,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) = ((in @ Y0 @ Y2) | (Y1 = Y0))))))))) => sF192)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1231,f671])).
% 13.04/2.34 thf(f1243,plain,(
% 13.04/2.34 (emptysetimpfalse = $true)),
% 13.04/2.34 inference(backward_demodulation,[],[f1169,f1236])).
% 13.04/2.34 thf(f1245,plain,(
% 13.04/2.34 (sF177 = ((emptysetimpfalse => sF175)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1107,f1237])).
% 13.04/2.34 thf(f1246,plain,(
% 13.04/2.34 ((($true => sF175)) = sF177)),
% 13.04/2.34 inference(forward_demodulation,[],[f1245,f1243])).
% 13.04/2.34 thf(f1247,plain,(
% 13.04/2.34 (sF177 = sF175)),
% 13.04/2.34 inference(boolean_simplification,[],[f1246])).
% 13.04/2.34 thf(f1248,plain,(
% 13.04/2.34 (sF178 = ((emptysetE => sF175)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1108,f1247])).
% 13.04/2.34 thf(f1249,plain,(
% 13.04/2.34 (sF178 = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => sF175)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1248,f770])).
% 13.04/2.34 thf(f1276,plain,(
% 13.04/2.34 (sF175 = $false) | (sF178 = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => $true)))),
% 13.04/2.34 inference(superposition,[],[f1249,f807])).
% 13.04/2.34 thf(f1279,plain,(
% 13.04/2.34 (sF178 = $true) | (sF175 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1276])).
% 13.04/2.34 thf(f1293,plain,(
% 13.04/2.34 ($false = sF192)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1238])).
% 13.04/2.34 thf(f1303,plain,(
% 13.04/2.34 (((powersetAx => sF191)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1129,f1293])).
% 13.04/2.34 thf(f1308,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => sF191)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1303,f741])).
% 13.04/2.34 thf(f1309,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => (setunionAx => sF190))) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1308,f1127])).
% 13.04/2.34 thf(f1310,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0)))) = (in @ Y1 @ (setunion @ Y0))))))) => sF190))))),
% 13.04/2.34 inference(forward_demodulation,[],[f1309,f673])).
% 13.04/2.34 thf(f1313,plain,(
% 13.04/2.34 (sF190 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0)))) = (in @ Y1 @ (setunion @ Y0))))))) => $true))) = $false)),
% 13.04/2.34 inference(superposition,[],[f1310,f807])).
% 13.04/2.34 thf(f1318,plain,(
% 13.04/2.34 (sF190 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => $true)))),
% 13.04/2.34 inference(boolean_simplification,[],[f1313])).
% 13.04/2.34 thf(f1319,plain,(
% 13.04/2.34 (sF190 = $false) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1318])).
% 13.04/2.34 thf(f1320,plain,(
% 13.04/2.34 (sF190 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1319])).
% 13.04/2.34 thf(f1327,plain,(
% 13.04/2.34 ($false = ((omega0Ax => sF189)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1125,f1320])).
% 13.04/2.34 thf(f1343,plain,(
% 13.04/2.34 ($false = (((in @ emptyset @ omega) => sF189)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1327,f641])).
% 13.04/2.34 thf(f1353,plain,(
% 13.04/2.34 (sF189 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1343])).
% 13.04/2.34 thf(f1367,plain,(
% 13.04/2.34 (((omegaSAx => sF188)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1124,f1353])).
% 13.04/2.34 thf(f1370,plain,(
% 13.04/2.34 ($false = sF188)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1367])).
% 13.04/2.34 thf(f1382,plain,(
% 13.04/2.34 ($false = ((omegaIndAx => sF187)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1122,f1370])).
% 13.04/2.34 thf(f1387,plain,(
% 13.04/2.34 ($false = ((omegaIndAx => $true))) | (sF187 = $false)),
% 13.04/2.34 inference(superposition,[],[f1382,f807])).
% 13.04/2.34 thf(f1391,plain,(
% 13.04/2.34 ($true = $false) | (sF187 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1387])).
% 13.04/2.34 thf(f1392,plain,(
% 13.04/2.34 (sF187 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1391])).
% 13.04/2.34 thf(f1395,plain,(
% 13.04/2.34 (((replAx => sF186)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1120,f1392])).
% 13.04/2.34 thf(f1404,plain,(
% 13.04/2.34 (sF186 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1395])).
% 13.04/2.34 thf(f1418,plain,(
% 13.04/2.34 (((foundationAx => sF185)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1118,f1404])).
% 13.04/2.34 thf(f1419,plain,(
% 13.04/2.34 ($false = sF185)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1418])).
% 13.04/2.34 thf(f1429,plain,(
% 13.04/2.34 (((wellorderingAx => sF184)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1117,f1419])).
% 13.04/2.34 thf(f1438,plain,(
% 13.04/2.34 (sF184 = $false) | (((wellorderingAx => $true)) = $false)),
% 13.04/2.34 inference(superposition,[],[f1429,f807])).
% 13.04/2.34 thf(f1442,plain,(
% 13.04/2.34 (sF184 = $false) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1438])).
% 13.04/2.34 thf(f1443,plain,(
% 13.04/2.34 (sF184 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1442])).
% 13.04/2.34 thf(f1446,plain,(
% 13.04/2.34 (((descrp => sF183)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1115,f1443])).
% 13.04/2.34 thf(f1451,plain,(
% 13.04/2.34 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => sF183)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1446,f1171])).
% 13.04/2.34 thf(f1459,plain,(
% 13.04/2.34 (sF183 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1451])).
% 13.04/2.34 thf(f1469,plain,(
% 13.04/2.34 (((dsetconstrI => sF182)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1114,f1459])).
% 13.04/2.34 thf(f1476,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => sF182)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1469,f1162])).
% 13.04/2.34 thf(f1479,plain,(
% 13.04/2.34 (sF182 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => $true)) = $false)),
% 13.04/2.34 inference(superposition,[],[f1476,f807])).
% 13.04/2.34 thf(f1483,plain,(
% 13.04/2.34 ($true = $false) | (sF182 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1479])).
% 13.04/2.34 thf(f1484,plain,(
% 13.04/2.34 (sF182 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1483])).
% 13.04/2.34 thf(f1491,plain,(
% 13.04/2.34 ($false = ((dsetconstrEL => sF181)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1113,f1484])).
% 13.04/2.34 thf(f1494,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => sF181)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1491,f1176])).
% 13.04/2.34 thf(f1497,plain,(
% 13.04/2.34 (sF181 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1494])).
% 13.04/2.34 thf(f1507,plain,(
% 13.04/2.34 ($false = ((dsetconstrER => sF180)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1112,f1497])).
% 13.04/2.34 thf(f1512,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) => sF180)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1507,f1165])).
% 13.04/2.34 thf(f1517,plain,(
% 13.04/2.34 ($false = sF180)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1512])).
% 13.04/2.34 thf(f1527,plain,(
% 13.04/2.34 (((exuE1 => sF179)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1111,f1517])).
% 13.04/2.34 thf(f1532,plain,(
% 13.04/2.34 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))) => sF179)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1527,f1185])).
% 13.04/2.34 thf(f1539,plain,(
% 13.04/2.34 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))) => $true))) | ($false = sF179)),
% 13.04/2.34 inference(superposition,[],[f1532,f807])).
% 13.04/2.34 thf(f1543,plain,(
% 13.04/2.34 ($true = $false) | ($false = sF179)),
% 13.04/2.34 inference(boolean_simplification,[],[f1539])).
% 13.04/2.34 thf(f1544,plain,(
% 13.04/2.34 ($false = sF179)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1543])).
% 13.04/2.34 thf(f1551,plain,(
% 13.04/2.34 ($false = ((prop2setE => sF178)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1109,f1544])).
% 13.04/2.34 thf(f1552,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => sF178)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1551,f675])).
% 13.04/2.34 thf(f1553,plain,(
% 13.04/2.34 (sF178 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1552])).
% 13.04/2.34 thf(f1564,plain,(
% 13.04/2.34 (sF175 = $false) | ($true = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1279,f1553])).
% 13.04/2.34 thf(f1567,plain,(
% 13.04/2.34 (sF175 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1564])).
% 13.04/2.34 thf(f1576,plain,(
% 13.04/2.34 (((exuE3e => sF174)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1104,f1567])).
% 13.04/2.34 thf(f1578,plain,(
% 13.04/2.34 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => sF174)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1576,f1173])).
% 13.04/2.34 thf(f1597,plain,(
% 13.04/2.34 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => $true)) = $false) | (sF174 = $false)),
% 13.04/2.34 inference(superposition,[],[f1578,f807])).
% 13.04/2.34 thf(f1602,plain,(
% 13.04/2.34 ($true = $false) | (sF174 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1597])).
% 13.04/2.34 thf(f1603,plain,(
% 13.04/2.34 (sF174 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1602])).
% 13.04/2.34 thf(f1611,plain,(
% 13.04/2.34 (((setext => sF173)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1103,f1603])).
% 13.04/2.34 thf(f1612,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => sF173)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1611,f755])).
% 13.04/2.34 thf(f1613,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => (emptyI => sF172))) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1612,f1102])).
% 13.04/2.34 thf(f1614,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => sF172))))),
% 13.04/2.34 inference(forward_demodulation,[],[f1613,f668])).
% 13.04/2.34 thf(f1640,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true)))) | ($false = sF172)),
% 13.04/2.34 inference(superposition,[],[f1614,f807])).
% 13.04/2.34 thf(f1648,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => $true)) = $false) | ($false = sF172)),
% 13.04/2.34 inference(boolean_simplification,[],[f1640])).
% 13.04/2.34 thf(f1649,plain,(
% 13.04/2.34 ($false = sF172) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1648])).
% 13.04/2.34 thf(f1650,plain,(
% 13.04/2.34 ($false = sF172)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1649])).
% 13.04/2.34 thf(f1657,plain,(
% 13.04/2.34 ($false = ((noeltsimpempty => sF171)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1101,f1650])).
% 13.04/2.34 thf(f1667,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => sF171)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1657,f725])).
% 13.04/2.34 thf(f1676,plain,(
% 13.04/2.34 ($false = sF171) | ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true)) = $false)),
% 13.04/2.34 inference(superposition,[],[f1667,f807])).
% 13.04/2.34 thf(f1679,plain,(
% 13.04/2.34 ($false = sF171) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1676])).
% 13.04/2.34 thf(f1680,plain,(
% 13.04/2.34 ($false = sF171)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1679])).
% 13.04/2.34 thf(f1689,plain,(
% 13.04/2.34 ($false = ((setbeta => sF170)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1099,f1680])).
% 13.04/2.34 thf(f1692,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) = (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => sF170)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1689,f1142])).
% 13.04/2.34 thf(f1693,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) = (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => (nonemptyE1 => sF169))))),
% 13.04/2.34 inference(forward_demodulation,[],[f1692,f1098])).
% 13.04/2.34 thf(f1698,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) = (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => (nonemptyE1 => $true))) = $false) | (sF169 = $false)),
% 13.04/2.34 inference(superposition,[],[f1693,f807])).
% 13.04/2.34 thf(f1707,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) = (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => $true))) | (sF169 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1698])).
% 13.04/2.34 thf(f1708,plain,(
% 13.04/2.34 (sF169 = $false) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1707])).
% 13.04/2.34 thf(f1709,plain,(
% 13.04/2.34 (sF169 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1708])).
% 13.04/2.34 thf(f1720,plain,(
% 13.04/2.34 ($false = ((nonemptyI => sF168)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1097,f1709])).
% 13.04/2.34 thf(f1734,plain,(
% 13.04/2.34 ($false = sF168)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1720])).
% 13.04/2.34 thf(f1748,plain,(
% 13.04/2.34 ($false = ((nonemptyI1 => sF167)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1096,f1734])).
% 13.04/2.34 thf(f1751,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => sF167)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1748,f1189])).
% 13.04/2.34 thf(f1752,plain,(
% 13.04/2.34 (sF167 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1751])).
% 13.04/2.34 thf(f1762,plain,(
% 13.04/2.34 (((setadjoinIL => sF166)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1095,f1752])).
% 13.04/2.34 thf(f1767,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => sF166)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1762,f765])).
% 13.04/2.34 thf(f1772,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => $true))) | (sF166 = $false)),
% 13.04/2.34 inference(superposition,[],[f1767,f807])).
% 13.04/2.34 thf(f1775,plain,(
% 13.04/2.34 ($true = $false) | (sF166 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1772])).
% 13.04/2.34 thf(f1776,plain,(
% 13.04/2.34 (sF166 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1775])).
% 13.04/2.34 thf(f1780,plain,(
% 13.04/2.34 (((emptyinunitempty => sF165)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1093,f1776])).
% 13.04/2.34 thf(f1787,plain,(
% 13.04/2.34 ($false = (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => sF165)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1780,f798])).
% 13.04/2.34 thf(f1790,plain,(
% 13.04/2.34 (sF165 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1787])).
% 13.04/2.34 thf(f1800,plain,(
% 13.04/2.34 (((setadjoinIR => sF164)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1091,f1790])).
% 13.04/2.34 thf(f1805,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => sF164)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1800,f787])).
% 13.04/2.34 thf(f1808,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => $true)) = $false) | (sF164 = $false)),
% 13.04/2.34 inference(superposition,[],[f1805,f807])).
% 13.04/2.34 thf(f1811,plain,(
% 13.04/2.34 ($true = $false) | (sF164 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1808])).
% 13.04/2.34 thf(f1812,plain,(
% 13.04/2.34 (sF164 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1811])).
% 13.04/2.34 thf(f1816,plain,(
% 13.04/2.34 (((setadjoinE => sF163)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1089,f1812])).
% 13.04/2.34 thf(f1827,plain,(
% 13.04/2.34 ($false = sF163) | (((setadjoinE => $true)) = $false)),
% 13.04/2.34 inference(superposition,[],[f1816,f807])).
% 13.04/2.34 thf(f1830,plain,(
% 13.04/2.34 ($true = $false) | ($false = sF163)),
% 13.04/2.34 inference(boolean_simplification,[],[f1827])).
% 13.04/2.34 thf(f1831,plain,(
% 13.04/2.34 ($false = sF163)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1830])).
% 13.04/2.34 thf(f1835,plain,(
% 13.04/2.34 ($false = ((setadjoinOr => sF162)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1088,f1831])).
% 13.04/2.34 thf(f1842,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0))))))))) => sF162)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1835,f736])).
% 13.04/2.34 thf(f1845,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0))))))))) => (setoftrueEq => sF161))) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1842,f1086])).
% 13.04/2.34 thf(f1846,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => sF161))) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1845,f802])).
% 13.04/2.34 thf(f1886,plain,(
% 13.04/2.34 (sF161 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => $true))))),
% 13.04/2.34 inference(superposition,[],[f1846,f807])).
% 13.04/2.34 thf(f1891,plain,(
% 13.04/2.34 (sF161 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0))))))))) => $true)) = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1886])).
% 13.04/2.34 thf(f1892,plain,(
% 13.04/2.34 ($true = $false) | (sF161 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1891])).
% 13.04/2.34 thf(f1893,plain,(
% 13.04/2.34 (sF161 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1892])).
% 13.04/2.34 thf(f1900,plain,(
% 13.04/2.34 ($false = ((powersetI => sF160)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1085,f1893])).
% 13.04/2.34 thf(f1915,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => sF160)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f1900,f640])).
% 13.04/2.34 thf(f1928,plain,(
% 13.04/2.34 ($false = sF160) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => $true)) = $false)),
% 13.04/2.34 inference(superposition,[],[f1915,f807])).
% 13.04/2.34 thf(f1932,plain,(
% 13.04/2.34 ($false = sF160) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1928])).
% 13.04/2.34 thf(f1933,plain,(
% 13.04/2.34 ($false = sF160)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1932])).
% 13.04/2.34 thf(f1940,plain,(
% 13.04/2.34 (((emptyinPowerset => sF159)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1084,f1933])).
% 13.04/2.34 thf(f1943,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => sF159)))),
% 13.04/2.34 inference(forward_demodulation,[],[f1940,f604])).
% 13.04/2.34 thf(f1944,plain,(
% 13.04/2.34 ($false = sF159)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1943])).
% 13.04/2.34 thf(f1945,plain,(
% 13.04/2.34 ($true = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1943])).
% 13.04/2.34 thf(f1954,plain,(
% 13.04/2.34 (((emptyInPowerset => sF158)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1082,f1944])).
% 13.04/2.34 thf(f1958,plain,(
% 13.04/2.34 (emptyInPowerset = $true)),
% 13.04/2.34 inference(backward_demodulation,[],[f706,f1945])).
% 13.04/2.34 thf(f1964,plain,(
% 13.04/2.34 ((($true => sF158)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1954,f1958])).
% 13.04/2.34 thf(f1965,plain,(
% 13.04/2.34 (sF158 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f1964])).
% 13.04/2.34 thf(f1966,plain,(
% 13.04/2.34 ($false = ((powersetE => sF157)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1080,f1965])).
% 13.04/2.34 thf(f1971,plain,(
% 13.04/2.34 (((powersetE => $true)) = $false) | ($false = sF157)),
% 13.04/2.34 inference(superposition,[],[f1966,f807])).
% 13.04/2.34 thf(f1975,plain,(
% 13.04/2.34 ($true = $false) | ($false = sF157)),
% 13.04/2.34 inference(boolean_simplification,[],[f1971])).
% 13.04/2.34 thf(f1976,plain,(
% 13.04/2.34 ($false = sF157)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f1975])).
% 13.04/2.34 thf(f1983,plain,(
% 13.04/2.34 ($false = ((setunionI => sF156)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1079,f1976])).
% 13.04/2.34 thf(f1984,plain,(
% 13.04/2.34 ($false = sF156)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1983])).
% 13.04/2.34 thf(f1994,plain,(
% 13.04/2.34 (((setunionE => sF155)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1077,f1984])).
% 13.04/2.34 thf(f2003,plain,(
% 13.04/2.34 (sF155 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f1994])).
% 13.04/2.34 thf(f2013,plain,(
% 13.04/2.34 ($false = ((subPowSU => sF154)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1075,f2003])).
% 13.04/2.34 thf(f2020,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => sF154)))),
% 13.04/2.34 inference(forward_demodulation,[],[f2013,f709])).
% 13.04/2.34 thf(f2023,plain,(
% 13.04/2.34 (sF154 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2020])).
% 13.04/2.34 thf(f2037,plain,(
% 13.04/2.34 ($false = ((exuE2 => sF153)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1074,f2023])).
% 13.04/2.34 thf(f2038,plain,(
% 13.04/2.34 (sF153 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2037])).
% 13.04/2.34 thf(f2048,plain,(
% 13.04/2.34 (((nonemptyImpWitness => sF152)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1073,f2038])).
% 13.04/2.34 thf(f2051,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => sF152)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2048,f1182])).
% 13.04/2.34 thf(f2054,plain,(
% 13.04/2.34 (((nonemptyE1 => sF152)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2051,f1146])).
% 13.04/2.34 thf(f2055,plain,(
% 13.04/2.34 (sF152 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2054])).
% 13.04/2.34 thf(f2065,plain,(
% 13.04/2.34 (((uniqinunit => sF151)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1072,f2055])).
% 13.04/2.34 thf(f2070,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => sF151)))),
% 13.04/2.34 inference(forward_demodulation,[],[f2065,f733])).
% 13.04/2.34 thf(f2088,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => $true)) = $false) | (sF151 = $false)),
% 13.04/2.34 inference(superposition,[],[f2070,f807])).
% 13.04/2.34 thf(f2093,plain,(
% 13.04/2.34 ($true = $false) | (sF151 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f2088])).
% 13.04/2.34 thf(f2094,plain,(
% 13.04/2.34 (sF151 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f2093])).
% 13.04/2.34 thf(f2102,plain,(
% 13.04/2.34 ($false = ((notinsingleton => sF150)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1071,f2094])).
% 13.04/2.34 thf(f2103,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => sF150)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2102,f799])).
% 13.04/2.34 thf(f2104,plain,(
% 13.04/2.34 ($false = sF150)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2103])).
% 13.04/2.34 thf(f2114,plain,(
% 13.04/2.34 ($false = ((eqinunit => sF149)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1070,f2104])).
% 13.04/2.34 thf(f2121,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => sF149)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2114,f644])).
% 13.04/2.34 thf(f2122,plain,(
% 13.04/2.34 (sF149 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2121])).
% 13.04/2.34 thf(f2132,plain,(
% 13.04/2.34 ($false = ((singletonsswitch => sF148)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1069,f2122])).
% 13.04/2.34 thf(f2139,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => sF148)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2132,f658])).
% 13.04/2.34 thf(f2142,plain,(
% 13.04/2.34 ($false = sF148) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)) = $false)),
% 13.04/2.34 inference(superposition,[],[f2139,f807])).
% 13.04/2.34 thf(f2145,plain,(
% 13.04/2.34 ($true = $false) | ($false = sF148)),
% 13.04/2.34 inference(boolean_simplification,[],[f2142])).
% 13.04/2.34 thf(f2146,plain,(
% 13.04/2.34 ($false = sF148)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f2145])).
% 13.04/2.34 thf(f2150,plain,(
% 13.04/2.34 ($false = ((upairsetE => sF147)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1068,f2146])).
% 13.04/2.34 thf(f2161,plain,(
% 13.04/2.34 ($false = sF147)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2150])).
% 13.04/2.34 thf(f2171,plain,(
% 13.04/2.34 (((upairsetIL => sF146)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1067,f2161])).
% 13.04/2.34 thf(f2176,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => sF146)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2171,f688])).
% 13.04/2.34 thf(f2181,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true))) | ($false = sF146)),
% 13.04/2.34 inference(superposition,[],[f2176,f807])).
% 13.04/2.34 thf(f2184,plain,(
% 13.04/2.34 ($false = sF146) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f2181])).
% 13.04/2.34 thf(f2185,plain,(
% 13.04/2.34 ($false = sF146)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f2184])).
% 13.04/2.34 thf(f2189,plain,(
% 13.04/2.34 (((upairsetIR => sF145)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1065,f2185])).
% 13.04/2.34 thf(f2196,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => sF145)))),
% 13.04/2.34 inference(forward_demodulation,[],[f2189,f626])).
% 13.04/2.34 thf(f2197,plain,(
% 13.04/2.34 (sF145 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2196])).
% 13.04/2.34 thf(f2198,plain,(
% 13.04/2.34 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2196])).
% 13.04/2.34 thf(f2207,plain,(
% 13.04/2.34 (((emptyE1 => sF144)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1063,f2197])).
% 13.04/2.34 thf(f2210,plain,(
% 13.04/2.34 (secondinupair = $true)),
% 13.04/2.34 inference(backward_demodulation,[],[f750,f2198])).
% 13.04/2.34 thf(f2211,plain,(
% 13.04/2.34 (upairset2IR = $true)),
% 13.04/2.34 inference(backward_demodulation,[],[f759,f2198])).
% 13.04/2.34 thf(f2216,plain,(
% 13.04/2.34 (sF96 = (($true => sF95)))),
% 13.04/2.34 inference(backward_demodulation,[],[f990,f2211])).
% 13.04/2.34 thf(f2217,plain,(
% 13.04/2.34 (sF96 = sF95)),
% 13.04/2.34 inference(boolean_simplification,[],[f2216])).
% 13.04/2.34 thf(f2218,plain,(
% 13.04/2.34 ((($true => sF62)) = sF63)),
% 13.04/2.34 inference(backward_demodulation,[],[f940,f2210])).
% 13.04/2.34 thf(f2219,plain,(
% 13.04/2.34 (sF62 = sF63)),
% 13.04/2.34 inference(boolean_simplification,[],[f2218])).
% 13.04/2.34 thf(f2220,plain,(
% 13.04/2.34 (((binunionIL => sF95)) = sF97)),
% 13.04/2.34 inference(backward_demodulation,[],[f992,f2217])).
% 13.04/2.34 thf(f2221,plain,(
% 13.04/2.34 (((symdiffIneg2 => sF62)) = sF64)),
% 13.04/2.34 inference(backward_demodulation,[],[f942,f2219])).
% 13.04/2.34 thf(f2222,plain,(
% 13.04/2.34 (sF97 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => sF95)))),
% 13.04/2.34 inference(forward_demodulation,[],[f2220,f796])).
% 13.04/2.34 thf(f2235,plain,(
% 13.04/2.34 ($false = sF144)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2207])).
% 13.04/2.34 thf(f2245,plain,(
% 13.04/2.34 (((vacuousDall => sF143)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1062,f2235])).
% 13.04/2.34 thf(f2250,plain,(
% 13.04/2.34 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => sF143)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2245,f614])).
% 13.04/2.34 thf(f2257,plain,(
% 13.04/2.34 (((symdiffIneg2 => $true)) = sF64) | (sF62 = $false)),
% 13.04/2.34 inference(superposition,[],[f2221,f807])).
% 13.04/2.34 thf(f2261,plain,(
% 13.04/2.34 (sF62 = $false) | ($true = sF64)),
% 13.04/2.34 inference(boolean_simplification,[],[f2257])).
% 13.04/2.34 thf(f2265,plain,(
% 13.04/2.34 (sF143 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2250])).
% 13.04/2.34 thf(f2279,plain,(
% 13.04/2.34 (((quantDeMorgan1 => sF142)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1060,f2265])).
% 13.04/2.34 thf(f2282,plain,(
% 13.04/2.34 (((quantDeMorgan1 => $true)) = $false) | ($false = sF142)),
% 13.04/2.34 inference(superposition,[],[f2279,f807])).
% 13.04/2.34 thf(f2285,plain,(
% 13.04/2.34 ($true = $false) | ($false = sF142)),
% 13.04/2.34 inference(boolean_simplification,[],[f2282])).
% 13.04/2.34 thf(f2286,plain,(
% 13.04/2.34 ($false = sF142)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f2285])).
% 13.04/2.34 thf(f2290,plain,(
% 13.04/2.34 ($false = ((quantDeMorgan2 => sF141)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1058,f2286])).
% 13.04/2.34 thf(f2297,plain,(
% 13.04/2.34 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => sF141)))),
% 13.04/2.34 inference(forward_demodulation,[],[f2290,f649])).
% 13.04/2.34 thf(f2302,plain,(
% 13.04/2.34 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => $true)) = sF97) | ($false = sF95)),
% 13.04/2.34 inference(superposition,[],[f2222,f807])).
% 13.04/2.34 thf(f2306,plain,(
% 13.04/2.34 (sF97 = $true) | ($false = sF95)),
% 13.04/2.34 inference(boolean_simplification,[],[f2302])).
% 13.04/2.34 thf(f2404,plain,(
% 13.04/2.34 (sF141 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2297])).
% 13.04/2.34 thf(f2416,plain,(
% 13.04/2.34 (((quantDeMorgan3 => sF140)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1057,f2404])).
% 13.04/2.34 thf(f2417,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => sF140)))),
% 13.04/2.34 inference(forward_demodulation,[],[f2416,f630])).
% 13.04/2.34 thf(f2419,plain,(
% 13.04/2.34 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))))))))))),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2417])).
% 13.04/2.34 thf(f2420,plain,(
% 13.04/2.34 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => $true))) | (sF140 = $false)),
% 13.04/2.34 inference(superposition,[],[f2417,f807])).
% 13.04/2.34 thf(f2423,plain,(
% 13.04/2.34 (sF140 = $false) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f2420])).
% 13.04/2.34 thf(f2424,plain,(
% 13.04/2.34 (sF140 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f2423])).
% 13.04/2.34 thf(f2428,plain,(
% 13.04/2.34 ($false = ((quantDeMorgan4 => sF139)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1056,f2424])).
% 13.04/2.34 thf(f2432,plain,(
% 13.04/2.34 (notdexE = $true)),
% 13.04/2.34 inference(backward_demodulation,[],[f685,f2419])).
% 13.04/2.34 thf(f2438,plain,(
% 13.04/2.34 (sF137 = (($true => sF136)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1052,f2432])).
% 13.04/2.34 thf(f2439,plain,(
% 13.04/2.34 (sF137 = sF136)),
% 13.04/2.34 inference(boolean_simplification,[],[f2438])).
% 13.04/2.34 thf(f2440,plain,(
% 13.04/2.34 (sF137 = ((notdallE => sF135)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1050,f2439])).
% 13.04/2.34 thf(f2447,plain,(
% 13.04/2.34 (sF139 = $false)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2428])).
% 13.04/2.34 thf(f2457,plain,(
% 13.04/2.34 ($false = ((prop2setI => sF138)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1055,f2447])).
% 13.04/2.34 thf(f2464,plain,(
% 13.04/2.34 ($false = (((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => sF138)))),
% 13.04/2.34 inference(forward_demodulation,[],[f2457,f616])).
% 13.04/2.34 thf(f2465,plain,(
% 13.04/2.34 ((((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => (prop2set2propI => sF137))) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2464,f1054])).
% 13.04/2.34 thf(f2468,plain,(
% 13.04/2.34 (sF135 = $false) | (sF137 = ((notdallE => $true)))),
% 13.04/2.34 inference(superposition,[],[f2440,f807])).
% 13.04/2.34 thf(f2472,plain,(
% 13.04/2.34 (sF137 = $true) | (sF135 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f2468])).
% 13.04/2.34 thf(f2478,plain,(
% 13.04/2.34 ((((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => (prop2set2propI => $true))) = $false) | (sF137 = $false)),
% 13.04/2.34 inference(superposition,[],[f2465,f807])).
% 13.04/2.34 thf(f2484,plain,(
% 13.04/2.34 ((((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => $true)) = $false) | (sF137 = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f2478])).
% 13.04/2.34 thf(f2485,plain,(
% 13.04/2.34 (sF137 = $false) | ($true = $false)),
% 13.04/2.34 inference(boolean_simplification,[],[f2484])).
% 13.04/2.34 thf(f2486,plain,(
% 13.04/2.34 (sF137 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f2485])).
% 13.04/2.34 thf(f2500,plain,(
% 13.04/2.34 ($true = $false) | (sF135 = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f2472,f2486])).
% 13.04/2.34 thf(f2502,plain,(
% 13.04/2.34 (sF135 = $false)),
% 13.04/2.34 inference(trivial_inequality_removal,[],[f2500])).
% 13.04/2.34 thf(f2516,plain,(
% 13.04/2.34 (((exuI1 => sF134)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1048,f2502])).
% 13.04/2.34 thf(f2521,plain,(
% 13.04/2.34 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => sF134)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2516,f1188])).
% 13.04/2.34 thf(f2567,plain,(
% 13.04/2.34 ($false = sF134)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2521])).
% 13.04/2.34 thf(f2577,plain,(
% 13.04/2.34 (((exuI3 => sF133)) = $false)),
% 13.04/2.34 inference(backward_demodulation,[],[f1047,f2567])).
% 13.04/2.34 thf(f2580,plain,(
% 13.04/2.34 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => sF133)))),
% 13.04/2.34 inference(forward_demodulation,[],[f2577,f1170])).
% 13.04/2.34 thf(f2583,plain,(
% 13.04/2.34 ($false = sF133)),
% 13.04/2.34 inference(imp_proxy_clausification,[],[f2580])).
% 13.04/2.34 thf(f2599,plain,(
% 13.04/2.34 ($false = ((exuI2 => sF132)))),
% 13.04/2.34 inference(backward_demodulation,[],[f1045,f2583])).
% 13.04/2.34 thf(f2600,plain,(
% 13.04/2.34 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => sF132)) = $false)),
% 13.04/2.34 inference(forward_demodulation,[],[f2599,f1160])).
% 13.04/2.34 thf(f2603,plain,(
% 13.04/2.34 (sF132 = $false) | ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f2600,f807])).
% 13.04/2.35 thf(f2606,plain,(
% 13.04/2.35 ($true = $false) | (sF132 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2603])).
% 13.04/2.35 thf(f2607,plain,(
% 13.04/2.35 (sF132 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2606])).
% 13.04/2.35 thf(f2613,plain,(
% 13.04/2.35 (((inCongP => sF131)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1044,f2607])).
% 13.04/2.35 thf(f2616,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) => (in @ Y3 @ Y0)))))))))))) => sF131)))),
% 13.04/2.35 inference(forward_demodulation,[],[f2613,f771])).
% 13.04/2.35 thf(f2619,plain,(
% 13.04/2.35 ($false = sF131) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) => (in @ Y3 @ Y0)))))))))))) => $true)))),
% 13.04/2.35 inference(superposition,[],[f2616,f807])).
% 13.04/2.35 thf(f2622,plain,(
% 13.04/2.35 ($false = sF131) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2619])).
% 13.04/2.35 thf(f2623,plain,(
% 13.04/2.35 ($false = sF131)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2622])).
% 13.04/2.35 thf(f2627,plain,(
% 13.04/2.35 (((in__Cong => sF130)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1042,f2623])).
% 13.04/2.35 thf(f2638,plain,(
% 13.04/2.35 ($false = sF130)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f2627])).
% 13.04/2.35 thf(f2648,plain,(
% 13.04/2.35 (((exuE3u => sF129)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1040,f2638])).
% 13.04/2.35 thf(f2651,plain,(
% 13.04/2.35 ($false = ((exuE3u => (exu__Cong => sF128))))),
% 13.04/2.35 inference(forward_demodulation,[],[f2648,f1038])).
% 13.04/2.35 thf(f2655,plain,(
% 13.04/2.35 (exuE3u = $true)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f2651])).
% 13.04/2.35 thf(f2656,plain,(
% 13.04/2.35 ($false = ((exuE3u => (exu__Cong => $true)))) | (sF128 = $false)),
% 13.04/2.35 inference(superposition,[],[f2651,f807])).
% 13.04/2.35 thf(f2664,plain,(
% 13.04/2.35 (sF128 = $false) | (((exuE3u => $true)) = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2656])).
% 13.04/2.35 thf(f2665,plain,(
% 13.04/2.35 ($true = $false) | (sF128 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2664])).
% 13.04/2.35 thf(f2666,plain,(
% 13.04/2.35 (sF128 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2665])).
% 13.04/2.35 thf(f2670,plain,(
% 13.04/2.35 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 13.04/2.35 inference(backward_demodulation,[],[f1177,f2655])).
% 13.04/2.35 thf(f2676,plain,(
% 13.04/2.35 ($false = ((emptyset__Cong => sF127)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1037,f2666])).
% 13.04/2.35 thf(f2684,plain,(
% 13.04/2.35 (exuEu = $true)),
% 13.04/2.35 inference(backward_demodulation,[],[f1157,f2670])).
% 13.04/2.35 thf(f2689,plain,(
% 13.04/2.35 ($false = (($true => sF127)))),
% 13.04/2.35 inference(forward_demodulation,[],[f2676,f1153])).
% 13.04/2.35 thf(f2690,plain,(
% 13.04/2.35 (sF127 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2689])).
% 13.04/2.35 thf(f2693,plain,(
% 13.04/2.35 ((($true => sF122)) = sF123)),
% 13.04/2.35 inference(backward_demodulation,[],[f1031,f2684])).
% 13.04/2.35 thf(f2694,plain,(
% 13.04/2.35 (sF122 = sF123)),
% 13.04/2.35 inference(boolean_simplification,[],[f2693])).
% 13.04/2.35 thf(f2695,plain,(
% 13.04/2.35 (((setadjoin__Cong => sF126)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1036,f2690])).
% 13.04/2.35 thf(f2696,plain,(
% 13.04/2.35 (((descr__Cong => sF121)) = sF123)),
% 13.04/2.35 inference(backward_demodulation,[],[f1029,f2694])).
% 13.04/2.35 thf(f2697,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2)))))))))))) => sF126)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f2695,f778])).
% 13.04/2.35 thf(f2698,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2)))))))))))) => (powerset__Cong => sF125))))),
% 13.04/2.35 inference(forward_demodulation,[],[f2697,f1034])).
% 13.04/2.35 thf(f2711,plain,(
% 13.04/2.35 ($false = sF121) | (((descr__Cong => $true)) = sF123)),
% 13.04/2.35 inference(superposition,[],[f2696,f807])).
% 13.04/2.35 thf(f2715,plain,(
% 13.04/2.35 ($true = sF123) | ($false = sF121)),
% 13.04/2.35 inference(boolean_simplification,[],[f2711])).
% 13.04/2.35 thf(f2732,plain,(
% 13.04/2.35 (sF125 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2)))))))))))) => (powerset__Cong => $true))))),
% 13.04/2.35 inference(superposition,[],[f2698,f807])).
% 13.04/2.35 thf(f2742,plain,(
% 13.04/2.35 (sF125 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2)))))))))))) => $true)))),
% 13.04/2.35 inference(boolean_simplification,[],[f2732])).
% 13.04/2.35 thf(f2743,plain,(
% 13.04/2.35 ($true = $false) | (sF125 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2742])).
% 13.04/2.35 thf(f2744,plain,(
% 13.04/2.35 (sF125 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2743])).
% 13.04/2.35 thf(f2754,plain,(
% 13.04/2.35 ($false = ((setunion__Cong => sF124)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1033,f2744])).
% 13.04/2.35 thf(f2760,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => sF124)))),
% 13.04/2.35 inference(forward_demodulation,[],[f2754,f679])).
% 13.04/2.35 thf(f2763,plain,(
% 13.04/2.35 (sF124 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f2760])).
% 13.04/2.35 thf(f2773,plain,(
% 13.04/2.35 ($false = ((omega__Cong => sF123)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1032,f2763])).
% 13.04/2.35 thf(f2778,plain,(
% 13.04/2.35 ($false = (($true => sF123)))),
% 13.04/2.35 inference(forward_demodulation,[],[f2773,f1155])).
% 13.04/2.35 thf(f2779,plain,(
% 13.04/2.35 ($false = sF123)),
% 13.04/2.35 inference(boolean_simplification,[],[f2778])).
% 13.04/2.35 thf(f2784,plain,(
% 13.04/2.35 ($false = sF121) | ($true = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f2715,f2779])).
% 13.04/2.35 thf(f2788,plain,(
% 13.04/2.35 ($false = sF121)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2784])).
% 13.04/2.35 thf(f2790,plain,(
% 13.04/2.35 (((dsetconstr__Cong => sF120)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1027,f2788])).
% 13.04/2.35 thf(f2792,plain,(
% 13.04/2.35 (((dsetconstr__Cong => (subsetI1 => sF119))) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f2790,f1025])).
% 13.04/2.35 thf(f2807,plain,(
% 13.04/2.35 ($false = sF119) | (((dsetconstr__Cong => (subsetI1 => $true))) = $false)),
% 13.04/2.35 inference(superposition,[],[f2792,f807])).
% 13.04/2.35 thf(f2816,plain,(
% 13.04/2.35 ($false = sF119) | ($false = ((dsetconstr__Cong => $true)))),
% 13.04/2.35 inference(boolean_simplification,[],[f2807])).
% 13.04/2.35 thf(f2817,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF119)),
% 13.04/2.35 inference(boolean_simplification,[],[f2816])).
% 13.04/2.35 thf(f2818,plain,(
% 13.04/2.35 ($false = sF119)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2817])).
% 13.04/2.35 thf(f2827,plain,(
% 13.04/2.35 (((eqimpsubset2 => sF118)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1024,f2818])).
% 13.04/2.35 thf(f2833,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => sF118)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f2827,f636])).
% 13.04/2.35 thf(f2838,plain,(
% 13.04/2.35 (sF118 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f2833])).
% 13.04/2.35 thf(f2848,plain,(
% 13.04/2.35 (((eqimpsubset1 => sF117)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1022,f2838])).
% 13.04/2.35 thf(f2853,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => sF117)))),
% 13.04/2.35 inference(forward_demodulation,[],[f2848,f773])).
% 13.04/2.35 thf(f2856,plain,(
% 13.04/2.35 (sF117 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f2853])).
% 13.04/2.35 thf(f2866,plain,(
% 13.04/2.35 ($false = ((subsetI2 => sF116)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1020,f2856])).
% 13.04/2.35 thf(f2873,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => sF116)))),
% 13.04/2.35 inference(forward_demodulation,[],[f2866,f652])).
% 13.04/2.35 thf(f2874,plain,(
% 13.04/2.35 (((subsetI1 => sF116)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f2873,f621])).
% 13.04/2.35 thf(f2879,plain,(
% 13.04/2.35 ($false = ((subsetI1 => $true))) | (sF116 = $false)),
% 13.04/2.35 inference(superposition,[],[f2874,f807])).
% 13.04/2.35 thf(f2882,plain,(
% 13.04/2.35 (sF116 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2879])).
% 13.04/2.35 thf(f2883,plain,(
% 13.04/2.35 (sF116 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2882])).
% 13.04/2.35 thf(f2887,plain,(
% 13.04/2.35 ($false = ((emptysetsubset => sF115)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1019,f2883])).
% 13.04/2.35 thf(f2896,plain,(
% 13.04/2.35 ((((!! @ $i @ (subset @ emptyset)) => sF115)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f2887,f1137])).
% 13.04/2.35 thf(f2898,plain,(
% 13.04/2.35 ($false = sF115)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f2896])).
% 13.04/2.35 thf(f2908,plain,(
% 13.04/2.35 (((subsetE => sF114)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1018,f2898])).
% 13.04/2.35 thf(f2919,plain,(
% 13.04/2.35 (sF114 = $false) | (((subsetE => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f2908,f807])).
% 13.04/2.35 thf(f2923,plain,(
% 13.04/2.35 ($true = $false) | (sF114 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2919])).
% 13.04/2.35 thf(f2924,plain,(
% 13.04/2.35 (sF114 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2923])).
% 13.04/2.35 thf(f2927,plain,(
% 13.04/2.35 ($false = ((subsetE2 => sF113)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1016,f2924])).
% 13.04/2.35 thf(f2932,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => sF113)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f2927,f682])).
% 13.04/2.35 thf(f2969,plain,(
% 13.04/2.35 ($false = sF113) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f2932,f807])).
% 13.04/2.35 thf(f2972,plain,(
% 13.04/2.35 ($false = sF113) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f2969])).
% 13.04/2.35 thf(f2973,plain,(
% 13.04/2.35 ($false = sF113)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f2972])).
% 13.04/2.35 thf(f2977,plain,(
% 13.04/2.35 ($false = ((notsubsetI => sF112)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1015,f2973])).
% 13.04/2.35 thf(f2984,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (subset @ Y1 @ Y0)))))))))) => sF112)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f2977,f779])).
% 13.04/2.35 thf(f2985,plain,(
% 13.04/2.35 (sF112 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f2984])).
% 13.04/2.35 thf(f2995,plain,(
% 13.04/2.35 (((notequalI1 => sF111)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1013,f2985])).
% 13.04/2.35 thf(f3002,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => sF111)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f2995,f667])).
% 13.04/2.35 thf(f3003,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => (notequalI2 => sF110))))),
% 13.04/2.35 inference(forward_demodulation,[],[f3002,f1011])).
% 13.04/2.35 thf(f3008,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => (notequalI2 => $true))) = $false) | ($false = sF110)),
% 13.04/2.35 inference(superposition,[],[f3003,f807])).
% 13.04/2.35 thf(f3018,plain,(
% 13.04/2.35 ($false = sF110) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => $true)) = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3008])).
% 13.04/2.35 thf(f3019,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF110)),
% 13.04/2.35 inference(boolean_simplification,[],[f3018])).
% 13.04/2.35 thf(f3020,plain,(
% 13.04/2.35 ($false = sF110)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3019])).
% 13.04/2.35 thf(f3030,plain,(
% 13.04/2.35 (((subsetRefl => sF109)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1010,f3020])).
% 13.04/2.35 thf(f3036,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => sF109)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3030,f651])).
% 13.04/2.35 thf(f3039,plain,(
% 13.04/2.35 (sF109 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3036])).
% 13.04/2.35 thf(f3049,plain,(
% 13.04/2.35 (((subsetTrans => sF108)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1008,f3039])).
% 13.04/2.35 thf(f3056,plain,(
% 13.04/2.35 ($false = sF108)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3049])).
% 13.04/2.35 thf(f3066,plain,(
% 13.04/2.35 ($false = ((setadjoinSub => sF107)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1007,f3056])).
% 13.04/2.35 thf(f3071,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => sF107)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3066,f721])).
% 13.04/2.35 thf(f3072,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => (setadjoinSub2 => sF106))) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3071,f1006])).
% 13.04/2.35 thf(f3073,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => sF106))) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3072,f772])).
% 13.04/2.35 thf(f3094,plain,(
% 13.04/2.35 ($false = sF106) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => $true))) = $false)),
% 13.04/2.35 inference(superposition,[],[f3073,f807])).
% 13.04/2.35 thf(f3102,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => $true)) = $false) | ($false = sF106)),
% 13.04/2.35 inference(boolean_simplification,[],[f3094])).
% 13.04/2.35 thf(f3103,plain,(
% 13.04/2.35 ($false = sF106) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3102])).
% 13.04/2.35 thf(f3104,plain,(
% 13.04/2.35 ($false = sF106)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3103])).
% 13.04/2.35 thf(f3111,plain,(
% 13.04/2.35 ($false = ((subset2powerset => sF105)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1005,f3104])).
% 13.04/2.35 thf(f3131,plain,(
% 13.04/2.35 (sF105 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3111])).
% 13.04/2.35 thf(f3143,plain,(
% 13.04/2.35 ($false = ((setextsub => sF104)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1004,f3131])).
% 13.04/2.35 thf(f3146,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => sF104)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3143,f662])).
% 13.04/2.35 thf(f3158,plain,(
% 13.04/2.35 (sF104 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3146])).
% 13.04/2.35 thf(f3172,plain,(
% 13.04/2.35 (((subsetemptysetimpeq => sF103)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1003,f3158])).
% 13.04/2.35 thf(f3173,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => sF103)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3172,f680])).
% 13.04/2.35 thf(f3176,plain,(
% 13.04/2.35 ($false = sF103) | ((((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f3173,f807])).
% 13.04/2.35 thf(f3180,plain,(
% 13.04/2.35 ($false = sF103) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3176])).
% 13.04/2.35 thf(f3181,plain,(
% 13.04/2.35 ($false = sF103)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3180])).
% 13.04/2.35 thf(f3184,plain,(
% 13.04/2.35 ($false = ((powersetI1 => sF102)))),
% 13.04/2.35 inference(backward_demodulation,[],[f1002,f3181])).
% 13.04/2.35 thf(f3191,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => sF102)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3184,f738])).
% 13.04/2.35 thf(f3218,plain,(
% 13.04/2.35 ($false = sF102) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f3191,f807])).
% 13.04/2.35 thf(f3221,plain,(
% 13.04/2.35 ($false = sF102) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3218])).
% 13.04/2.35 thf(f3222,plain,(
% 13.04/2.35 ($false = sF102)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3221])).
% 13.04/2.35 thf(f3226,plain,(
% 13.04/2.35 (((powersetE1 => sF101)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f1001,f3222])).
% 13.04/2.35 thf(f3233,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => sF101)))),
% 13.04/2.35 inference(forward_demodulation,[],[f3226,f687])).
% 13.04/2.35 thf(f3238,plain,(
% 13.04/2.35 (sF101 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f3233,f807])).
% 13.04/2.35 thf(f3242,plain,(
% 13.04/2.35 (sF101 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3238])).
% 13.04/2.35 thf(f3243,plain,(
% 13.04/2.35 (sF101 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3242])).
% 13.04/2.35 thf(f3246,plain,(
% 13.04/2.35 (((inPowerset => sF100)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f999,f3243])).
% 13.04/2.35 thf(f3251,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => sF100)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3246,f665])).
% 13.04/2.35 thf(f3252,plain,(
% 13.04/2.35 ($false = sF100)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3251])).
% 13.04/2.35 thf(f3262,plain,(
% 13.04/2.35 (((powersetsubset => sF99)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f997,f3252])).
% 13.04/2.35 thf(f3265,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => sF99)))),
% 13.04/2.35 inference(forward_demodulation,[],[f3262,f707])).
% 13.04/2.35 thf(f3268,plain,(
% 13.04/2.35 ($false = sF99)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3265])).
% 13.04/2.35 thf(f3278,plain,(
% 13.04/2.35 (((sepInPowerset => sF98)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f995,f3268])).
% 13.04/2.35 thf(f3285,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => sF98)))),
% 13.04/2.35 inference(forward_demodulation,[],[f3278,f1150])).
% 13.04/2.35 thf(f3288,plain,(
% 13.04/2.35 (sF98 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f3285,f807])).
% 13.04/2.35 thf(f3292,plain,(
% 13.04/2.35 (sF98 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3288])).
% 13.04/2.35 thf(f3293,plain,(
% 13.04/2.35 (sF98 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3292])).
% 13.04/2.35 thf(f3300,plain,(
% 13.04/2.35 (((sepSubset => sF97)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f993,f3293])).
% 13.04/2.35 thf(f3301,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => sF97)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3300,f1152])).
% 13.04/2.35 thf(f3304,plain,(
% 13.04/2.35 (sF97 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => $true)))),
% 13.04/2.35 inference(superposition,[],[f3301,f807])).
% 13.04/2.35 thf(f3309,plain,(
% 13.04/2.35 ($true = $false) | (sF97 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3304])).
% 13.04/2.35 thf(f3310,plain,(
% 13.04/2.35 (sF97 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3309])).
% 13.04/2.35 thf(f3318,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF95)),
% 13.04/2.35 inference(backward_demodulation,[],[f2306,f3310])).
% 13.04/2.35 thf(f3321,plain,(
% 13.04/2.35 ($false = sF95)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3318])).
% 13.04/2.35 thf(f3323,plain,(
% 13.04/2.35 ($false = ((binunionIR => sF94)))),
% 13.04/2.35 inference(backward_demodulation,[],[f989,f3321])).
% 13.04/2.35 thf(f3326,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y2 @ Y0))))))))) => sF94)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3323,f670])).
% 13.04/2.35 thf(f3360,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y2 @ Y0))))))))) => $true)) = $false) | (sF94 = $false)),
% 13.04/2.35 inference(superposition,[],[f3326,f807])).
% 13.04/2.35 thf(f3363,plain,(
% 13.04/2.35 ($true = $false) | (sF94 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3360])).
% 13.04/2.35 thf(f3364,plain,(
% 13.04/2.35 (sF94 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3363])).
% 13.04/2.35 thf(f3370,plain,(
% 13.04/2.35 ($false = ((binunionEcases => sF93)))),
% 13.04/2.35 inference(backward_demodulation,[],[f988,f3364])).
% 13.04/2.35 thf(f3373,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y1)) => (((in @ Y0 @ Y3) => Y2) => (((in @ Y0 @ Y1) => Y2) => Y2))))))))))) => sF93)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3370,f696])).
% 13.04/2.35 thf(f3378,plain,(
% 13.04/2.35 ($false = sF93) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y1)) => (((in @ Y0 @ Y3) => Y2) => (((in @ Y0 @ Y1) => Y2) => Y2))))))))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f3373,f807])).
% 13.04/2.35 thf(f3381,plain,(
% 13.04/2.35 ($false = sF93) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3378])).
% 13.04/2.35 thf(f3382,plain,(
% 13.04/2.35 ($false = sF93)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3381])).
% 13.04/2.35 thf(f3386,plain,(
% 13.04/2.35 (((binunionE => sF92)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f987,f3382])).
% 13.04/2.35 thf(f3397,plain,(
% 13.04/2.35 ($false = ((binunionE => $true))) | (sF92 = $false)),
% 13.04/2.35 inference(superposition,[],[f3386,f807])).
% 13.04/2.35 thf(f3400,plain,(
% 13.04/2.35 ($true = $false) | (sF92 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3397])).
% 13.04/2.35 thf(f3401,plain,(
% 13.04/2.35 (sF92 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3400])).
% 13.04/2.35 thf(f3405,plain,(
% 13.04/2.35 (((binunionLsub => sF91)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f985,f3401])).
% 13.04/2.35 thf(f3412,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => sF91)))),
% 13.04/2.35 inference(forward_demodulation,[],[f3405,f602])).
% 13.04/2.35 thf(f3413,plain,(
% 13.04/2.35 (sF91 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3412])).
% 13.04/2.35 thf(f3423,plain,(
% 13.04/2.35 (((binunionRsub => sF90)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f984,f3413])).
% 13.04/2.35 thf(f3428,plain,(
% 13.04/2.35 (sF90 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3423])).
% 13.04/2.35 thf(f3438,plain,(
% 13.04/2.35 ($false = ((binintersectI => sF89)))),
% 13.04/2.35 inference(backward_demodulation,[],[f982,f3428])).
% 13.04/2.35 thf(f3441,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => sF89)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3438,f611])).
% 13.04/2.35 thf(f3492,plain,(
% 13.04/2.35 (sF89 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3441])).
% 13.04/2.35 thf(f3504,plain,(
% 13.04/2.35 (((binintersectSubset5 => sF88)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f981,f3492])).
% 13.04/2.35 thf(f3507,plain,(
% 13.04/2.35 (sF88 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3504])).
% 13.04/2.35 thf(f3519,plain,(
% 13.04/2.35 (((binintersectEL => sF87)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f979,f3507])).
% 13.04/2.35 thf(f3524,plain,(
% 13.04/2.35 ($false = sF87)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3519])).
% 13.04/2.35 thf(f3538,plain,(
% 13.04/2.35 (((binintersectLsub => sF86)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f977,f3524])).
% 13.04/2.35 thf(f3539,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => sF86)))),
% 13.04/2.35 inference(forward_demodulation,[],[f3538,f745])).
% 13.04/2.35 thf(f3540,plain,(
% 13.04/2.35 (sF86 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3539])).
% 13.04/2.35 thf(f3556,plain,(
% 13.04/2.35 (((binintersectSubset2 => sF85)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f975,f3540])).
% 13.04/2.35 thf(f3557,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => sF85)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3556,f657])).
% 13.04/2.35 thf(f3579,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => $true))) | (sF85 = $false)),
% 13.04/2.35 inference(superposition,[],[f3557,f807])).
% 13.04/2.35 thf(f3584,plain,(
% 13.04/2.35 ($true = $false) | (sF85 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3579])).
% 13.04/2.35 thf(f3585,plain,(
% 13.04/2.35 (sF85 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3584])).
% 13.04/2.35 thf(f3591,plain,(
% 13.04/2.35 ($false = ((binintersectSubset3 => sF84)))),
% 13.04/2.35 inference(backward_demodulation,[],[f973,f3585])).
% 13.04/2.35 thf(f3592,plain,(
% 13.04/2.35 ($false = sF84)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3591])).
% 13.04/2.35 thf(f3604,plain,(
% 13.04/2.35 ($false = ((binintersectER => sF83)))),
% 13.04/2.35 inference(backward_demodulation,[],[f972,f3592])).
% 13.04/2.35 thf(f3607,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))) => sF83)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3604,f752])).
% 13.04/2.35 thf(f3619,plain,(
% 13.04/2.35 (sF83 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3607])).
% 13.04/2.35 thf(f3633,plain,(
% 13.04/2.35 (((disjointsetsI1 => sF82)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f971,f3619])).
% 13.04/2.35 thf(f3634,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => sF82)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3633,f698])).
% 13.04/2.35 thf(f3657,plain,(
% 13.04/2.35 (sF82 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3634])).
% 13.04/2.35 thf(f3667,plain,(
% 13.04/2.35 (((binintersectRsub => sF81)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f969,f3657])).
% 13.04/2.35 thf(f3670,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => sF81)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3667,f610])).
% 13.04/2.35 thf(f3673,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => (binintersectSubset4 => sF80))) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3670,f968])).
% 13.04/2.35 thf(f3676,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => (binintersectSubset4 => $true)))) | ($false = sF80)),
% 13.04/2.35 inference(superposition,[],[f3673,f807])).
% 13.04/2.35 thf(f3682,plain,(
% 13.04/2.35 ($false = sF80) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => $true)) = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3676])).
% 13.04/2.35 thf(f3683,plain,(
% 13.04/2.35 ($false = sF80) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3682])).
% 13.04/2.35 thf(f3684,plain,(
% 13.04/2.35 ($false = sF80)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3683])).
% 13.04/2.35 thf(f3696,plain,(
% 13.04/2.35 (((binintersectSubset1 => sF79)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f967,f3684])).
% 13.04/2.35 thf(f3708,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => sF79)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3696,f608])).
% 13.04/2.35 thf(f3713,plain,(
% 13.04/2.35 ($false = sF79) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f3708,f807])).
% 13.04/2.35 thf(f3717,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF79)),
% 13.04/2.35 inference(boolean_simplification,[],[f3713])).
% 13.04/2.35 thf(f3718,plain,(
% 13.04/2.35 ($false = sF79)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3717])).
% 13.04/2.35 thf(f3721,plain,(
% 13.04/2.35 ($false = ((bs114d => sF78)))),
% 13.04/2.35 inference(backward_demodulation,[],[f965,f3718])).
% 13.04/2.35 thf(f3728,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y1 @ (binunion @ Y2 @ Y0)) = (binunion @ (binintersect @ Y1 @ Y2) @ (binintersect @ Y1 @ Y0))))))))) => sF78)))),
% 13.04/2.35 inference(forward_demodulation,[],[f3721,f805])).
% 13.04/2.35 thf(f3733,plain,(
% 13.04/2.35 ($false = sF78) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y1 @ (binunion @ Y2 @ Y0)) = (binunion @ (binintersect @ Y1 @ Y2) @ (binintersect @ Y1 @ Y0))))))))) => $true)))),
% 13.04/2.35 inference(superposition,[],[f3728,f807])).
% 13.04/2.35 thf(f3736,plain,(
% 13.04/2.35 ($false = sF78) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3733])).
% 13.04/2.35 thf(f3737,plain,(
% 13.04/2.35 ($false = sF78)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3736])).
% 13.04/2.35 thf(f3741,plain,(
% 13.04/2.35 ($false = ((setminusI => sF77)))),
% 13.04/2.35 inference(backward_demodulation,[],[f964,f3737])).
% 13.04/2.35 thf(f3746,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => sF77)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3741,f712])).
% 13.04/2.35 thf(f3753,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => $true)) = $false) | (sF77 = $false)),
% 13.04/2.35 inference(superposition,[],[f3746,f807])).
% 13.04/2.35 thf(f3756,plain,(
% 13.04/2.35 ($true = $false) | (sF77 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3753])).
% 13.04/2.35 thf(f3757,plain,(
% 13.04/2.35 (sF77 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3756])).
% 13.04/2.35 thf(f3763,plain,(
% 13.04/2.35 ($false = ((setminusEL => sF76)))),
% 13.04/2.35 inference(backward_demodulation,[],[f963,f3757])).
% 13.04/2.35 thf(f3768,plain,(
% 13.04/2.35 ($false = ((setminusEL => $true))) | ($false = sF76)),
% 13.04/2.35 inference(superposition,[],[f3763,f807])).
% 13.04/2.35 thf(f3771,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF76)),
% 13.04/2.35 inference(boolean_simplification,[],[f3768])).
% 13.04/2.35 thf(f3772,plain,(
% 13.04/2.35 ($false = sF76)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3771])).
% 13.04/2.35 thf(f3776,plain,(
% 13.04/2.35 ($false = ((setminusER => sF75)))),
% 13.04/2.35 inference(backward_demodulation,[],[f962,f3772])).
% 13.04/2.35 thf(f3781,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (~ (in @ Y1 @ Y0))))))))) => sF75)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3776,f782])).
% 13.04/2.35 thf(f3805,plain,(
% 13.04/2.35 (sF75 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3781])).
% 13.04/2.35 thf(f3819,plain,(
% 13.04/2.35 (((setminusSubset2 => sF74)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f960,f3805])).
% 13.04/2.35 thf(f3822,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => sF74)))),
% 13.04/2.35 inference(forward_demodulation,[],[f3819,f737])).
% 13.04/2.35 thf(f3823,plain,(
% 13.04/2.35 (sF74 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3822])).
% 13.04/2.35 thf(f3837,plain,(
% 13.04/2.35 (((setminusERneg => sF73)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f958,f3823])).
% 13.04/2.35 thf(f3838,plain,(
% 13.04/2.35 (sF73 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3837])).
% 13.04/2.35 thf(f3848,plain,(
% 13.04/2.35 ($false = ((setminusELneg => sF72)))),
% 13.04/2.35 inference(backward_demodulation,[],[f956,f3838])).
% 13.04/2.35 thf(f3853,plain,(
% 13.04/2.35 ($false = sF72)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3848])).
% 13.04/2.35 thf(f3863,plain,(
% 13.04/2.35 (((setminusILneg => sF71)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f955,f3853])).
% 13.04/2.35 thf(f3868,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => sF71)))),
% 13.04/2.35 inference(forward_demodulation,[],[f3863,f777])).
% 13.04/2.35 thf(f3875,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => $true)) = $false) | ($false = sF71)),
% 13.04/2.35 inference(superposition,[],[f3868,f807])).
% 13.04/2.35 thf(f3878,plain,(
% 13.04/2.35 ($false = sF71) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3875])).
% 13.04/2.35 thf(f3879,plain,(
% 13.04/2.35 ($false = sF71)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3878])).
% 13.04/2.35 thf(f3883,plain,(
% 13.04/2.35 (((setminusIRneg => sF70)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f953,f3879])).
% 13.04/2.35 thf(f3890,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => sF70)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3883,f786])).
% 13.04/2.35 thf(f3891,plain,(
% 13.04/2.35 ($false = sF70)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3890])).
% 13.04/2.35 thf(f3901,plain,(
% 13.04/2.35 ($false = ((setminusLsub => sF69)))),
% 13.04/2.35 inference(backward_demodulation,[],[f951,f3891])).
% 13.04/2.35 thf(f3908,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => sF69)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3901,f764])).
% 13.04/2.35 thf(f3911,plain,(
% 13.04/2.35 ($false = sF69) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => $true)))),
% 13.04/2.35 inference(superposition,[],[f3908,f807])).
% 13.04/2.35 thf(f3916,plain,(
% 13.04/2.35 ($false = sF69) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f3911])).
% 13.04/2.35 thf(f3917,plain,(
% 13.04/2.35 ($false = sF69)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f3916])).
% 13.04/2.35 thf(f3919,plain,(
% 13.04/2.35 (((setminusSubset1 => sF68)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f950,f3917])).
% 13.04/2.35 thf(f3922,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => sF68)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3919,f674])).
% 13.04/2.35 thf(f3925,plain,(
% 13.04/2.35 (sF68 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3922])).
% 13.04/2.35 thf(f3935,plain,(
% 13.04/2.35 (((symdiffE => sF67)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f948,f3925])).
% 13.04/2.35 thf(f3942,plain,(
% 13.04/2.35 ($false = sF67)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3935])).
% 13.04/2.35 thf(f3952,plain,(
% 13.04/2.35 (((symdiffI1 => sF66)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f947,f3942])).
% 13.04/2.35 thf(f3957,plain,(
% 13.04/2.35 ($false = sF66)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f3952])).
% 13.04/2.35 thf(f3967,plain,(
% 13.04/2.35 ($false = ((symdiffI2 => sF65)))),
% 13.04/2.35 inference(backward_demodulation,[],[f945,f3957])).
% 13.04/2.35 thf(f3972,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => sF65)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f3967,f756])).
% 13.04/2.35 thf(f4085,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => $true)) = $false) | ($false = sF65)),
% 13.04/2.35 inference(superposition,[],[f3972,f807])).
% 13.04/2.35 thf(f4088,plain,(
% 13.04/2.35 ($false = sF65) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4085])).
% 13.04/2.35 thf(f4089,plain,(
% 13.04/2.35 ($false = sF65)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4088])).
% 13.04/2.35 thf(f4093,plain,(
% 13.04/2.35 (((symdiffIneg1 => sF64)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f944,f4089])).
% 13.04/2.35 thf(f4104,plain,(
% 13.04/2.35 (sF64 = $false) | ($false = ((symdiffIneg1 => $true)))),
% 13.04/2.35 inference(superposition,[],[f4093,f807])).
% 13.04/2.35 thf(f4108,plain,(
% 13.04/2.35 ($true = $false) | (sF64 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4104])).
% 13.04/2.35 thf(f4109,plain,(
% 13.04/2.35 (sF64 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4108])).
% 13.04/2.35 thf(f4112,plain,(
% 13.04/2.35 (sF62 = $false) | ($true = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f2261,f4109])).
% 13.04/2.35 thf(f4116,plain,(
% 13.04/2.35 (sF62 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4112])).
% 13.04/2.35 thf(f4122,plain,(
% 13.04/2.35 (((setukpairIL => sF61)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f939,f4116])).
% 13.04/2.35 thf(f4124,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => sF61)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4122,f605])).
% 13.04/2.35 thf(f4139,plain,(
% 13.04/2.35 ($false = sF61)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4124])).
% 13.04/2.35 thf(f4153,plain,(
% 13.04/2.35 (((setukpairIR => sF60)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f937,f4139])).
% 13.04/2.35 thf(f4154,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => sF60)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4153,f677])).
% 13.04/2.35 thf(f4157,plain,(
% 13.04/2.35 (sF60 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => $true)))),
% 13.04/2.35 inference(superposition,[],[f4154,f807])).
% 13.04/2.35 thf(f4160,plain,(
% 13.04/2.35 (sF60 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4157])).
% 13.04/2.35 thf(f4161,plain,(
% 13.04/2.35 (sF60 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4160])).
% 13.04/2.35 thf(f4165,plain,(
% 13.04/2.35 ($false = ((kpairiskpair => sF59)))),
% 13.04/2.35 inference(backward_demodulation,[],[f935,f4161])).
% 13.04/2.35 thf(f4172,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => sF59)))),
% 13.04/2.35 inference(forward_demodulation,[],[f4165,f666])).
% 13.04/2.35 thf(f4175,plain,(
% 13.04/2.35 ($false = sF59)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4172])).
% 13.04/2.35 thf(f4187,plain,(
% 13.04/2.35 (((kpairp => sF58)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f934,f4175])).
% 13.04/2.35 thf(f4190,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => sF58)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4187,f803])).
% 13.04/2.35 thf(f4195,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => $true))) | (sF58 = $false)),
% 13.04/2.35 inference(superposition,[],[f4190,f807])).
% 13.04/2.35 thf(f4199,plain,(
% 13.04/2.35 ($true = $false) | (sF58 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4195])).
% 13.04/2.35 thf(f4200,plain,(
% 13.04/2.35 (sF58 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4199])).
% 13.04/2.35 thf(f4203,plain,(
% 13.04/2.35 (((singletonsubset => sF57)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f932,f4200])).
% 13.04/2.35 thf(f4210,plain,(
% 13.04/2.35 (((singletonsubset => (singletoninpowerset => sF56))) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4203,f930])).
% 13.04/2.35 thf(f4213,plain,(
% 13.04/2.35 (sF56 = $false) | (((singletonsubset => (singletoninpowerset => $true))) = $false)),
% 13.04/2.35 inference(superposition,[],[f4210,f807])).
% 13.04/2.35 thf(f4218,plain,(
% 13.04/2.35 (sF56 = $false) | ($false = ((singletonsubset => $true)))),
% 13.04/2.35 inference(boolean_simplification,[],[f4213])).
% 13.04/2.35 thf(f4219,plain,(
% 13.04/2.35 ($true = $false) | (sF56 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4218])).
% 13.04/2.35 thf(f4220,plain,(
% 13.04/2.35 (sF56 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4219])).
% 13.04/2.35 thf(f4228,plain,(
% 13.04/2.35 (((singletoninpowunion => sF55)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f928,f4220])).
% 13.04/2.35 thf(f4242,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0)))))))))) => sF55)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4228,f634])).
% 13.04/2.35 thf(f4269,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0)))))))))) => $true)) = $false) | ($false = sF55)),
% 13.04/2.35 inference(superposition,[],[f4242,f807])).
% 13.04/2.35 thf(f4274,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF55)),
% 13.04/2.35 inference(boolean_simplification,[],[f4269])).
% 13.04/2.35 thf(f4275,plain,(
% 13.04/2.35 ($false = sF55)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4274])).
% 13.04/2.35 thf(f4283,plain,(
% 13.04/2.35 ($false = ((upairset2E => sF54)))),
% 13.04/2.35 inference(backward_demodulation,[],[f926,f4275])).
% 13.04/2.35 thf(f4284,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y0))))))))) => sF54)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4283,f790])).
% 13.04/2.35 thf(f4355,plain,(
% 13.04/2.35 (sF54 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4284])).
% 13.04/2.35 thf(f4365,plain,(
% 13.04/2.35 ($false = ((upairsubunion => sF53)))),
% 13.04/2.35 inference(backward_demodulation,[],[f925,f4355])).
% 13.04/2.35 thf(f4370,plain,(
% 13.04/2.35 (((upairsubunion => (upairinpowunion => sF52))) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4365,f924])).
% 13.04/2.35 thf(f4377,plain,(
% 13.04/2.35 ($false = ((upairsubunion => (upairinpowunion => $true)))) | (sF52 = $false)),
% 13.04/2.35 inference(superposition,[],[f4370,f807])).
% 13.04/2.35 thf(f4382,plain,(
% 13.04/2.35 (sF52 = $false) | (((upairsubunion => $true)) = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4377])).
% 13.04/2.35 thf(f4383,plain,(
% 13.04/2.35 ($true = $false) | (sF52 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4382])).
% 13.04/2.35 thf(f4384,plain,(
% 13.04/2.35 (sF52 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4383])).
% 13.04/2.35 thf(f4395,plain,(
% 13.04/2.35 ($false = ((ubforcartprodlem1 => sF51)))),
% 13.04/2.35 inference(backward_demodulation,[],[f922,f4384])).
% 13.04/2.35 thf(f4413,plain,(
% 13.04/2.35 ($false = sF51)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4395])).
% 13.04/2.35 thf(f4423,plain,(
% 13.04/2.35 ($false = ((ubforcartprodlem2 => sF50)))),
% 13.04/2.35 inference(backward_demodulation,[],[f921,f4413])).
% 13.04/2.35 thf(f4432,plain,(
% 13.04/2.35 ($false = sF50)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4423])).
% 13.04/2.35 thf(f4442,plain,(
% 13.04/2.35 (((ubforcartprodlem3 => sF49)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f919,f4432])).
% 13.04/2.35 thf(f4453,plain,(
% 13.04/2.35 ($false = sF49) | ($false = ((ubforcartprodlem3 => $true)))),
% 13.04/2.35 inference(superposition,[],[f4442,f807])).
% 13.04/2.35 thf(f4456,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF49)),
% 13.04/2.35 inference(boolean_simplification,[],[f4453])).
% 13.04/2.35 thf(f4457,plain,(
% 13.04/2.35 ($false = sF49)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4456])).
% 13.04/2.35 thf(f4461,plain,(
% 13.04/2.35 (((cartprodpairin => sF48)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f917,f4457])).
% 13.04/2.35 thf(f4466,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => sF48)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4461,f746])).
% 13.04/2.35 thf(f4501,plain,(
% 13.04/2.35 ($false = sF48)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4466])).
% 13.04/2.35 thf(f4511,plain,(
% 13.04/2.35 (((cartprodmempair1 => sF47)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f915,f4501])).
% 13.04/2.35 thf(f4518,plain,(
% 13.04/2.35 (sF47 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4511])).
% 13.04/2.35 thf(f4528,plain,(
% 13.04/2.35 ($false = ((cartprodmempair => sF46)))),
% 13.04/2.35 inference(backward_demodulation,[],[f913,f4518])).
% 13.04/2.35 thf(f4535,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (iskpair @ Y2)))))))) => sF46)))),
% 13.04/2.35 inference(forward_demodulation,[],[f4528,f648])).
% 13.04/2.35 thf(f4538,plain,(
% 13.04/2.35 ($false = sF46) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (iskpair @ Y2)))))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f4535,f807])).
% 13.04/2.35 thf(f4541,plain,(
% 13.04/2.35 ($false = sF46) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4538])).
% 13.04/2.35 thf(f4542,plain,(
% 13.04/2.35 ($false = sF46)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4541])).
% 13.04/2.35 thf(f4546,plain,(
% 13.04/2.35 (((setunionE2 => sF45)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f912,f4542])).
% 13.04/2.35 thf(f4551,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y0 @ Y2))))))))) => sF45)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4546,f607])).
% 13.04/2.35 thf(f4556,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y0 @ Y2))))))))) => $true))) | (sF45 = $false)),
% 13.04/2.35 inference(superposition,[],[f4551,f807])).
% 13.04/2.35 thf(f4559,plain,(
% 13.04/2.35 ($true = $false) | (sF45 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4556])).
% 13.04/2.35 thf(f4560,plain,(
% 13.04/2.35 (sF45 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4559])).
% 13.04/2.35 thf(f4564,plain,(
% 13.04/2.35 (((setunionsingleton1 => sF44)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f910,f4560])).
% 13.04/2.35 thf(f4571,plain,(
% 13.04/2.35 ($false = sF44)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4564])).
% 13.04/2.35 thf(f4581,plain,(
% 13.04/2.35 (((setunionsingleton2 => sF43)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f909,f4571])).
% 13.04/2.35 thf(f4588,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => sF43)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4581,f780])).
% 13.04/2.35 thf(f4619,plain,(
% 13.04/2.35 (sF43 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4588])).
% 13.04/2.35 thf(f4635,plain,(
% 13.04/2.35 (((setunionsingleton => sF42)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f907,f4619])).
% 13.04/2.35 thf(f4636,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => sF42)))),
% 13.04/2.35 inference(forward_demodulation,[],[f4635,f758])).
% 13.04/2.35 thf(f4637,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => (singletonprop => sF41))))),
% 13.04/2.35 inference(forward_demodulation,[],[f4636,f905])).
% 13.04/2.35 thf(f4640,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => (singletonprop => $true)))) | (sF41 = $false)),
% 13.04/2.35 inference(superposition,[],[f4637,f807])).
% 13.04/2.35 thf(f4650,plain,(
% 13.04/2.35 (sF41 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => $true)))),
% 13.04/2.35 inference(boolean_simplification,[],[f4640])).
% 13.04/2.35 thf(f4651,plain,(
% 13.04/2.35 ($true = $false) | (sF41 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4650])).
% 13.04/2.35 thf(f4652,plain,(
% 13.04/2.35 (sF41 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4651])).
% 13.04/2.35 thf(f4662,plain,(
% 13.04/2.35 (((ex1E1 => sF40)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f903,f4652])).
% 13.04/2.35 thf(f4670,plain,(
% 13.04/2.35 ($false = sF40)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4662])).
% 13.04/2.35 thf(f4680,plain,(
% 13.04/2.35 (((ex1I => sF39)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f901,f4670])).
% 13.04/2.35 thf(f4691,plain,(
% 13.04/2.35 ($false = ((ex1I => $true))) | (sF39 = $false)),
% 13.04/2.35 inference(superposition,[],[f4680,f807])).
% 13.04/2.35 thf(f4695,plain,(
% 13.04/2.35 (sF39 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4691])).
% 13.04/2.35 thf(f4696,plain,(
% 13.04/2.35 (sF39 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4695])).
% 13.04/2.35 thf(f4703,plain,(
% 13.04/2.35 ($false = ((ex1I2 => sF38)))),
% 13.04/2.35 inference(backward_demodulation,[],[f899,f4696])).
% 13.04/2.35 thf(f4708,plain,(
% 13.04/2.35 ($false = ((ex1I2 => $true))) | ($false = sF38)),
% 13.04/2.35 inference(superposition,[],[f4703,f807])).
% 13.04/2.35 thf(f4711,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF38)),
% 13.04/2.35 inference(boolean_simplification,[],[f4708])).
% 13.04/2.35 thf(f4712,plain,(
% 13.04/2.35 ($false = sF38)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4711])).
% 13.04/2.35 thf(f4716,plain,(
% 13.04/2.35 ($false = ((singletonsuniq => sF37)))),
% 13.04/2.35 inference(backward_demodulation,[],[f898,f4712])).
% 13.04/2.35 thf(f4723,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => sF37)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4716,f653])).
% 13.04/2.35 thf(f4728,plain,(
% 13.04/2.35 (sF37 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4723])).
% 13.04/2.35 thf(f4738,plain,(
% 13.04/2.35 (((setukpairinjL1 => sF36)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f896,f4728])).
% 13.04/2.35 thf(f4747,plain,(
% 13.04/2.35 (sF36 = $false) | ($false = ((setukpairinjL1 => $true)))),
% 13.04/2.35 inference(superposition,[],[f4738,f807])).
% 13.04/2.35 thf(f4750,plain,(
% 13.04/2.35 ($true = $false) | (sF36 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4747])).
% 13.04/2.35 thf(f4751,plain,(
% 13.04/2.35 (sF36 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4750])).
% 13.04/2.35 thf(f4755,plain,(
% 13.04/2.35 (((kfstsingleton => sF35)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f895,f4751])).
% 13.04/2.35 thf(f4762,plain,(
% 13.04/2.35 (sF35 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4755])).
% 13.04/2.35 thf(f4772,plain,(
% 13.04/2.35 (((theprop => sF34)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f893,f4762])).
% 13.04/2.35 thf(f4779,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => sF34)))),
% 13.04/2.35 inference(forward_demodulation,[],[f4772,f1149])).
% 13.04/2.35 thf(f4780,plain,(
% 13.04/2.35 ($false = sF34)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4779])).
% 13.04/2.35 thf(f4790,plain,(
% 13.04/2.35 ($false = ((kfstpairEq => sF33)))),
% 13.04/2.35 inference(backward_demodulation,[],[f891,f4780])).
% 13.04/2.35 thf(f4793,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => sF33)))),
% 13.04/2.35 inference(forward_demodulation,[],[f4790,f747])).
% 13.04/2.35 thf(f4798,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => $true)) = $false) | (sF33 = $false)),
% 13.04/2.35 inference(superposition,[],[f4793,f807])).
% 13.04/2.35 thf(f4801,plain,(
% 13.04/2.35 (sF33 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4798])).
% 13.04/2.35 thf(f4802,plain,(
% 13.04/2.35 (sF33 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4801])).
% 13.04/2.35 thf(f4806,plain,(
% 13.04/2.35 (((cartprodfstin => sF32)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f890,f4802])).
% 13.04/2.35 thf(f4813,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (kfst @ Y1) @ Y2)))))))) => sF32)))),
% 13.04/2.35 inference(forward_demodulation,[],[f4806,f766])).
% 13.04/2.35 thf(f4818,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (kfst @ Y1) @ Y2)))))))) => $true)) = $false) | ($false = sF32)),
% 13.04/2.35 inference(superposition,[],[f4813,f807])).
% 13.04/2.35 thf(f4821,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF32)),
% 13.04/2.35 inference(boolean_simplification,[],[f4818])).
% 13.04/2.35 thf(f4822,plain,(
% 13.04/2.35 ($false = sF32)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4821])).
% 13.04/2.35 thf(f4826,plain,(
% 13.04/2.35 ($false = ((setukpairinjL2 => sF31)))),
% 13.04/2.35 inference(backward_demodulation,[],[f888,f4822])).
% 13.04/2.35 thf(f4833,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))) => sF31)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4826,f633])).
% 13.04/2.35 thf(f4915,plain,(
% 13.04/2.35 ($false = sF31)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4833])).
% 13.04/2.35 thf(f4925,plain,(
% 13.04/2.35 ($false = ((setukpairinjL => sF30)))),
% 13.04/2.35 inference(backward_demodulation,[],[f887,f4915])).
% 13.04/2.35 thf(f4932,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => sF30)))),
% 13.04/2.35 inference(forward_demodulation,[],[f4925,f643])).
% 13.04/2.35 thf(f4935,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => $true))) | ($false = sF30)),
% 13.04/2.35 inference(superposition,[],[f4932,f807])).
% 13.04/2.35 thf(f4939,plain,(
% 13.04/2.35 ($false = sF30) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f4935])).
% 13.04/2.35 thf(f4940,plain,(
% 13.04/2.35 ($false = sF30)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f4939])).
% 13.04/2.35 thf(f4943,plain,(
% 13.04/2.35 ($false = ((setukpairinjR11 => sF29)))),
% 13.04/2.35 inference(backward_demodulation,[],[f885,f4940])).
% 13.04/2.35 thf(f4948,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => sF29)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4943,f781])).
% 13.04/2.35 thf(f4949,plain,(
% 13.04/2.35 ($false = sF29)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4948])).
% 13.04/2.35 thf(f4959,plain,(
% 13.04/2.35 ($false = ((setukpairinjR12 => sF28)))),
% 13.04/2.35 inference(backward_demodulation,[],[f883,f4949])).
% 13.04/2.35 thf(f4966,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => sF28)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f4959,f757])).
% 13.04/2.35 thf(f4969,plain,(
% 13.04/2.35 ($false = sF28)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4966])).
% 13.04/2.35 thf(f4983,plain,(
% 13.04/2.35 (((setukpairinjR1 => sF27)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f881,f4969])).
% 13.04/2.35 thf(f4986,plain,(
% 13.04/2.35 (sF27 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f4983])).
% 13.04/2.35 thf(f5000,plain,(
% 13.04/2.35 (((upairequniteq => sF26)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f879,f4986])).
% 13.04/2.35 thf(f5003,plain,(
% 13.04/2.35 (sF26 = $false) | (((upairequniteq => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f5000,f807])).
% 13.04/2.35 thf(f5006,plain,(
% 13.04/2.35 (sF26 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5003])).
% 13.04/2.35 thf(f5007,plain,(
% 13.04/2.35 (sF26 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5006])).
% 13.04/2.35 thf(f5013,plain,(
% 13.04/2.35 (((setukpairinjR2 => sF25)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f878,f5007])).
% 13.04/2.35 thf(f5016,plain,(
% 13.04/2.35 (sF25 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f5013])).
% 13.04/2.35 thf(f5026,plain,(
% 13.04/2.35 ($false = ((setukpairinjR => sF24)))),
% 13.04/2.35 inference(backward_demodulation,[],[f877,f5016])).
% 13.04/2.35 thf(f5031,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => sF24)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f5026,f710])).
% 13.04/2.35 thf(f5047,plain,(
% 13.04/2.35 (sF24 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f5031])).
% 13.04/2.35 thf(f5057,plain,(
% 13.04/2.35 (((ksndsingleton => sF23)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f876,f5047])).
% 13.04/2.35 thf(f5068,plain,(
% 13.04/2.35 ($false = sF23) | (((ksndsingleton => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f5057,f807])).
% 13.04/2.35 thf(f5072,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF23)),
% 13.04/2.35 inference(boolean_simplification,[],[f5068])).
% 13.04/2.35 thf(f5073,plain,(
% 13.04/2.35 ($false = sF23)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5072])).
% 13.04/2.35 thf(f5076,plain,(
% 13.04/2.35 ($false = ((ksndpairEq => sF22)))),
% 13.04/2.35 inference(backward_demodulation,[],[f874,f5073])).
% 13.04/2.35 thf(f5081,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => sF22)))),
% 13.04/2.35 inference(forward_demodulation,[],[f5076,f731])).
% 13.04/2.35 thf(f5088,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => $true))) | (sF22 = $false)),
% 13.04/2.35 inference(superposition,[],[f5081,f807])).
% 13.04/2.35 thf(f5091,plain,(
% 13.04/2.35 (sF22 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5088])).
% 13.04/2.35 thf(f5092,plain,(
% 13.04/2.35 (sF22 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5091])).
% 13.04/2.35 thf(f5096,plain,(
% 13.04/2.35 ($false = ((kpairsurjEq => sF21)))),
% 13.04/2.35 inference(backward_demodulation,[],[f873,f5092])).
% 13.04/2.35 thf(f5101,plain,(
% 13.04/2.35 (((kpairsurjEq => (cartprodsndin => sF20))) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f5096,f872])).
% 13.04/2.35 thf(f5108,plain,(
% 13.04/2.35 ($false = sF20) | ($false = ((kpairsurjEq => (cartprodsndin => $true))))),
% 13.04/2.35 inference(superposition,[],[f5101,f807])).
% 13.04/2.35 thf(f5113,plain,(
% 13.04/2.35 (((kpairsurjEq => $true)) = $false) | ($false = sF20)),
% 13.04/2.35 inference(boolean_simplification,[],[f5108])).
% 13.04/2.35 thf(f5114,plain,(
% 13.04/2.35 ($true = $false) | ($false = sF20)),
% 13.04/2.35 inference(boolean_simplification,[],[f5113])).
% 13.04/2.35 thf(f5115,plain,(
% 13.04/2.35 ($false = sF20)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5114])).
% 13.04/2.35 thf(f5123,plain,(
% 13.04/2.35 (((cartprodpairmemEL => sF19)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f870,f5115])).
% 13.04/2.35 thf(f5150,plain,(
% 13.04/2.35 (sF19 = $false) | (((cartprodpairmemEL => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f5123,f807])).
% 13.04/2.35 thf(f5154,plain,(
% 13.04/2.35 ($true = $false) | (sF19 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5150])).
% 13.04/2.35 thf(f5155,plain,(
% 13.04/2.35 (sF19 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5154])).
% 13.04/2.35 thf(f5158,plain,(
% 13.04/2.35 (((cartprodpairmemER => sF18)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f868,f5155])).
% 13.04/2.35 thf(f5167,plain,(
% 13.04/2.35 ($false = ((cartprodpairmemER => $true))) | (sF18 = $false)),
% 13.04/2.35 inference(superposition,[],[f5158,f807])).
% 13.04/2.35 thf(f5170,plain,(
% 13.04/2.35 (sF18 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5167])).
% 13.04/2.35 thf(f5171,plain,(
% 13.04/2.35 (sF18 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5170])).
% 13.04/2.35 thf(f5175,plain,(
% 13.04/2.35 ($false = ((cartprodmempaircEq => sF17)))),
% 13.04/2.35 inference(backward_demodulation,[],[f867,f5171])).
% 13.04/2.35 thf(f5180,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF17)))),
% 13.04/2.35 inference(forward_demodulation,[],[f5175,f1148])).
% 13.04/2.35 thf(f5194,plain,(
% 13.04/2.35 (sF17 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f5180])).
% 13.04/2.35 thf(f5204,plain,(
% 13.04/2.35 ($false = ((cartprodfstpairEq => sF16)))),
% 13.04/2.35 inference(backward_demodulation,[],[f866,f5194])).
% 13.04/2.35 thf(f5209,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => sF16)))),
% 13.04/2.35 inference(forward_demodulation,[],[f5204,f800])).
% 13.04/2.35 thf(f5250,plain,(
% 13.04/2.35 (sF16 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => $true)))),
% 13.04/2.35 inference(superposition,[],[f5209,f807])).
% 13.04/2.35 thf(f5255,plain,(
% 13.04/2.35 (sF16 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5250])).
% 13.04/2.35 thf(f5256,plain,(
% 13.04/2.35 (sF16 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5255])).
% 13.04/2.35 thf(f5262,plain,(
% 13.04/2.35 ($false = ((cartprodsndpairEq => sF15)))),
% 13.04/2.35 inference(backward_demodulation,[],[f865,f5256])).
% 13.04/2.35 thf(f5265,plain,(
% 13.04/2.35 (sF15 = $false) | ($false = ((cartprodsndpairEq => $true)))),
% 13.04/2.35 inference(superposition,[],[f5262,f807])).
% 13.04/2.35 thf(f5269,plain,(
% 13.04/2.35 ($true = $false) | (sF15 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5265])).
% 13.04/2.35 thf(f5270,plain,(
% 13.04/2.35 (sF15 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5269])).
% 13.04/2.35 thf(f5277,plain,(
% 13.04/2.35 ($false = ((cartprodpairsurjEq => sF14)))),
% 13.04/2.35 inference(backward_demodulation,[],[f864,f5270])).
% 13.04/2.35 thf(f5278,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => sF14)))),
% 13.04/2.35 inference(forward_demodulation,[],[f5277,f622])).
% 13.04/2.35 thf(f5279,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => (dpsetconstrI => sF13))) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f5278,f863])).
% 13.04/2.35 thf(f5380,plain,(
% 13.04/2.35 (sF13 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => (dpsetconstrI => $true))) = $false)),
% 13.04/2.35 inference(superposition,[],[f5279,f807])).
% 13.04/2.35 thf(f5389,plain,(
% 13.04/2.35 (sF13 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => $true)) = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5380])).
% 13.04/2.35 thf(f5390,plain,(
% 13.04/2.35 (sF13 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5389])).
% 13.04/2.35 thf(f5391,plain,(
% 13.04/2.35 (sF13 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5390])).
% 13.04/2.35 thf(f5400,plain,(
% 13.04/2.35 (((dpsetconstrSub => sF12)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f862,f5391])).
% 13.04/2.35 thf(f5416,plain,(
% 13.04/2.35 (sF12 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f5400])).
% 13.04/2.35 thf(f5426,plain,(
% 13.04/2.35 (((setOfPairsIsBReln => sF11)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f860,f5416])).
% 13.04/2.35 thf(f5431,plain,(
% 13.04/2.35 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) => sF11)))),
% 13.04/2.35 inference(forward_demodulation,[],[f5426,f1179])).
% 13.04/2.35 thf(f5463,plain,(
% 13.04/2.35 (sF11 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f5431])).
% 13.04/2.35 thf(f5477,plain,(
% 13.04/2.35 (((dpsetconstrERa => sF10)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f859,f5463])).
% 13.04/2.35 thf(f5480,plain,(
% 13.04/2.35 (((dpsetconstrERa => $true)) = $false) | (sF10 = $false)),
% 13.04/2.35 inference(superposition,[],[f5477,f807])).
% 13.04/2.35 thf(f5483,plain,(
% 13.04/2.35 ($true = $false) | (sF10 = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5480])).
% 13.04/2.35 thf(f5484,plain,(
% 13.04/2.35 (sF10 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5483])).
% 13.04/2.35 thf(f5488,plain,(
% 13.04/2.35 ($false = ((dpsetconstrEL1 => sF9)))),
% 13.04/2.35 inference(backward_demodulation,[],[f857,f5484])).
% 13.04/2.35 thf(f5495,plain,(
% 13.04/2.35 ((((!! @ $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 @ Y0 @ Y1)))))))))))) => sF9)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f5488,f1166])).
% 13.04/2.35 thf(f5498,plain,(
% 13.04/2.35 (sF9 = $false)),
% 13.04/2.35 inference(imp_proxy_clausification,[],[f5495])).
% 13.04/2.35 thf(f5514,plain,(
% 13.04/2.35 (((dpsetconstrEL2 => sF8)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f856,f5498])).
% 13.04/2.35 thf(f5515,plain,(
% 13.04/2.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y1) @ (dpsetconstr @ Y2 @ Y0 @ Y3)) => (in @ Y1 @ Y0)))))))))))) => sF8)) = $false)),
% 13.04/2.35 inference(forward_demodulation,[],[f5514,f1187])).
% 13.04/2.35 thf(f5518,plain,(
% 13.04/2.35 (sF8 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y1) @ (dpsetconstr @ Y2 @ Y0 @ Y3)) => (in @ Y1 @ Y0)))))))))))) => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f5515,f807])).
% 13.04/2.35 thf(f5521,plain,(
% 13.04/2.35 (sF8 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5518])).
% 13.04/2.35 thf(f5522,plain,(
% 13.04/2.35 (sF8 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5521])).
% 13.04/2.35 thf(f5526,plain,(
% 13.04/2.35 (((dpsetconstrER => sF7)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f855,f5522])).
% 13.04/2.35 thf(f5535,plain,(
% 13.04/2.35 ($false = ((dpsetconstrER => $true))) | (sF7 = $false)),
% 13.04/2.35 inference(superposition,[],[f5526,f807])).
% 13.04/2.35 thf(f5538,plain,(
% 13.04/2.35 (sF7 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5535])).
% 13.04/2.35 thf(f5539,plain,(
% 13.04/2.35 (sF7 = $false)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5538])).
% 13.04/2.35 thf(f5543,plain,(
% 13.04/2.35 (((funcImageSingleton => sF6)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f854,f5539])).
% 13.04/2.35 thf(f5554,plain,(
% 13.04/2.35 ($false = sF6) | (((funcImageSingleton => $true)) = $false)),
% 13.04/2.35 inference(superposition,[],[f5543,f807])).
% 13.04/2.35 thf(f5557,plain,(
% 13.04/2.35 ($false = sF6) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5554])).
% 13.04/2.35 thf(f5558,plain,(
% 13.04/2.35 ($false = sF6)),
% 13.04/2.35 inference(trivial_inequality_removal,[],[f5557])).
% 13.04/2.35 thf(f5562,plain,(
% 13.04/2.35 (((apProp => sF5)) = $false)),
% 13.04/2.35 inference(backward_demodulation,[],[f853,f5558])).
% 13.04/2.35 thf(f5571,plain,(
% 13.04/2.35 (sF5 = $false) | ($false = ((apProp => $true)))),
% 13.04/2.35 inference(superposition,[],[f5562,f807])).
% 13.04/2.35 thf(f5574,plain,(
% 13.04/2.35 (sF5 = $false) | ($true = $false)),
% 13.04/2.35 inference(boolean_simplification,[],[f5571])).
% 13.04/2.35 thf(f5575,plain,(
% 13.04/2.35 (sF5 = $false)),
% 13.04/2.36 inference(trivial_inequality_removal,[],[f5574])).
% 13.04/2.36 thf(f5579,plain,(
% 13.04/2.36 ($false = ((app => sF4)))),
% 13.04/2.36 inference(backward_demodulation,[],[f851,f5575])).
% 13.04/2.36 thf(f5588,plain,(
% 13.04/2.36 ($false = sF4)),
% 13.04/2.36 inference(imp_proxy_clausification,[],[f5579])).
% 13.04/2.36 thf(f5598,plain,(
% 13.04/2.36 (((infuncsetfunc => sF3)) = $false)),
% 13.04/2.36 inference(backward_demodulation,[],[f850,f5588])).
% 13.04/2.36 thf(f5605,plain,(
% 13.04/2.36 (((infuncsetfunc => (ap2p => sF2))) = $false)),
% 13.04/2.36 inference(forward_demodulation,[],[f5598,f848])).
% 13.04/2.36 thf(f5610,plain,(
% 13.04/2.36 ($false = sF2) | (((infuncsetfunc => (ap2p => $true))) = $false)),
% 13.04/2.36 inference(superposition,[],[f5605,f807])).
% 13.04/2.36 thf(f5618,plain,(
% 13.04/2.36 (((infuncsetfunc => $true)) = $false) | ($false = sF2)),
% 13.04/2.36 inference(boolean_simplification,[],[f5610])).
% 13.04/2.36 thf(f5619,plain,(
% 13.04/2.36 ($true = $false) | ($false = sF2)),
% 13.04/2.36 inference(boolean_simplification,[],[f5618])).
% 13.04/2.36 thf(f5620,plain,(
% 13.04/2.36 ($false = sF2)),
% 13.04/2.36 inference(trivial_inequality_removal,[],[f5619])).
% 13.04/2.36 thf(f5627,plain,(
% 13.04/2.36 ($false = ((funcinfuncset => sF1)))),
% 13.04/2.36 inference(backward_demodulation,[],[f846,f5620])).
% 13.04/2.36 thf(f5644,plain,(
% 13.04/2.36 (sF1 = $false) | (((funcinfuncset => $true)) = $false)),
% 13.04/2.36 inference(superposition,[],[f5627,f807])).
% 13.04/2.36 thf(f5649,plain,(
% 13.04/2.36 (sF1 = $false) | ($true = $false)),
% 13.04/2.36 inference(boolean_simplification,[],[f5644])).
% 13.04/2.36 thf(f5650,plain,(
% 13.04/2.36 (sF1 = $false)),
% 13.04/2.36 inference(trivial_inequality_removal,[],[f5649])).
% 13.04/2.36 thf(f5656,plain,(
% 13.04/2.36 (((lamProp => sF0)) = $false)),
% 13.04/2.36 inference(backward_demodulation,[],[f845,f5650])).
% 13.04/2.36 thf(f5657,plain,(
% 13.04/2.36 ($false = sF0)),
% 13.04/2.36 inference(imp_proxy_clausification,[],[f5656])).
% 13.04/2.36 thf(f5658,plain,(
% 13.04/2.36 (lamProp = $true)),
% 13.04/2.36 inference(imp_proxy_clausification,[],[f5656])).
% 13.04/2.36 thf(f5667,plain,(
% 13.04/2.36 ($false = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => ((subset @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))) @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y6 : $i]: (= @ (Y0 @ Y6)))))))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y6 : $i]: (= @ (Y0 @ Y6))))))))))))))))))))))))),
% 13.04/2.36 inference(backward_demodulation,[],[f1158,f5657])).
% 13.04/2.36 thf(f5671,plain,(
% 13.04/2.36 ($true = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => ((subset @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))) @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y6 : $i]: (= @ (Y0 @ Y6)))))))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y6 : $i]: (= @ (Y0 @ Y6))))))))))))))))))))))))),
% 13.04/2.36 inference(backward_demodulation,[],[f1139,f5658])).
% 13.04/2.36 thf(f5676,plain,(
% 13.04/2.36 ($true = $false)),
% 13.04/2.36 inference(forward_demodulation,[],[f5671,f5667])).
% 13.04/2.36 thf(f5677,plain,(
% 13.04/2.36 $false),
% 13.04/2.36 inference(trivial_inequality_removal,[],[f5676])).
% 13.04/2.36 % SZS output end Proof for theBenchmark
% 13.04/2.36 % (3583589)------------------------------
% 13.04/2.36 % (3583589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.04/2.36 % (3583589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.04/2.36 % (3583589)CaDiCaL version: 2.1.3
% 13.04/2.36 % (3583589)Termination reason: Refutation
% 13.04/2.36 % (3583589)Time elapsed: 0.332 s
% 13.04/2.36 % (3583589)Peak memory usage: 17 MB
% 13.04/2.36 % (3583589)Instructions burned: 620 (million)
% 13.04/2.36 % (3583392)Success in time 2.003 s
% 13.04/2.36 % Vampire exiting
%------------------------------------------------------------------------------