%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU773^1 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:17 AM UTC 2026
% Result : Theorem 24.66s 4.09s
% Output : Refutation 24.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU773^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:26:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.22/0.31 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
% 0.87/0.59 % (1367102)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.87/0.59 % (1367107)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=674865698:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.87/0.59 % (1367108)lrs+10_16_si=on:nwc=1.5:random_seed=4216828653:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.87/0.59 % (1367109)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=290982594:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.87/0.59 % (1367110)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=2962315357: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)
% 0.87/0.59 % (1367109)Instruction limit reached!
% 0.87/0.59 % (1367109)------------------------------
% 0.87/0.59 % (1367109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.59 % (1367109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.59 % (1367109)CaDiCaL version: 2.1.3
% 0.87/0.59 % (1367109)Termination reason: Instruction limit
% 0.87/0.59 % (1367109)Termination phase: shuffling
% 0.87/0.59 % (1367109)Time elapsed: 0.004 s
% 0.87/0.59 % (1367109)Peak memory usage: 10 MB
% 0.87/0.59 % (1367109)Instructions burned: 4 (million)
% 0.87/0.59 % (1367108)Instruction limit reached!
% 0.87/0.59 % (1367108)------------------------------
% 0.87/0.59 % (1367108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.59 % (1367108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.59 % (1367108)CaDiCaL version: 2.1.3
% 0.87/0.59 % (1367108)Termination reason: Instruction limit
% 0.87/0.59 % (1367108)Termination phase: shuffling
% 0.87/0.59 % (1367108)Time elapsed: 0.016 s
% 0.87/0.59 % (1367108)Peak memory usage: 10 MB
% 0.87/0.59 % (1367108)Instructions burned: 18 (million)
% 0.87/0.59 % (1367107)Instruction limit reached!
% 0.87/0.59 % (1367107)------------------------------
% 0.87/0.59 % (1367107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.59 % (1367107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.59 % (1367107)CaDiCaL version: 2.1.3
% 0.87/0.59 % (1367107)Termination reason: Instruction limit
% 0.87/0.59 % (1367107)Termination phase: Preprocessing 3
% 0.87/0.59 % (1367107)Time elapsed: 0.039 s
% 0.87/0.59 % (1367107)Peak memory usage: 12 MB
% 0.87/0.59 % (1367107)Instructions burned: 87 (million)
% 0.87/0.59 % (1367112)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1116988796:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.87/0.59 % (1367113)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.87/0.59 % (1367113)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
% 0.87/0.59 % (1367118)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1617635637:i=2:hud=10:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.87/0.59 % (1367118)Instruction limit reached!
% 0.87/0.59 % (1367118)------------------------------
% 0.87/0.59 % (1367118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.59 % (1367118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.59 % (1367118)CaDiCaL version: 2.1.3
% 0.87/0.59 % (1367118)Termination reason: Instruction limit
% 0.87/0.59 % (1367118)Termination phase: shuffling
% 0.87/0.59 % (1367118)Time elapsed: 0.007 s
% 0.87/0.59 % (1367118)Peak memory usage: 10 MB
% 0.87/0.59 % (1367118)Instructions burned: 3 (million)
% 0.87/0.59 % (1367111)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=548286969:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.87/0.59 % (1367113)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=1244786275:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.87/0.59 % (1367111)Instruction limit reached!
% 0.87/0.59 % (1367111)------------------------------
% 0.87/0.59 % (1367111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.66 % (1367111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.66 % (1367111)CaDiCaL version: 2.1.3
% 1.61/0.66 % (1367111)Termination reason: Instruction limit
% 1.61/0.66 % (1367111)Termination phase: shuffling
% 1.61/0.66 % (1367111)Time elapsed: 0.010 s
% 1.61/0.66 % (1367111)Peak memory usage: 10 MB
% 1.61/0.66 % (1367111)Instructions burned: 24 (million)
% 1.61/0.66 % (1367121)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.61/0.66 % (1367119)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3642393237:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2998 on theBenchmark for (2998ds/5Mi)
% 1.61/0.66 % (1367121)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3273941306:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.61/0.66 % (1367119)Instruction limit reached!
% 1.61/0.66 % (1367119)------------------------------
% 1.61/0.66 % (1367119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.66 % (1367119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.66 % (1367119)CaDiCaL version: 2.1.3
% 1.61/0.66 % (1367119)Termination reason: Instruction limit
% 1.61/0.66 % (1367119)Termination phase: shuffling
% 1.61/0.66 % (1367119)Time elapsed: 0.005 s
% 1.61/0.66 % (1367119)Peak memory usage: 10 MB
% 1.61/0.66 % (1367119)Instructions burned: 5 (million)
% 1.61/0.66 % (1367126)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
% 1.61/0.66 % (1367126)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.61/0.66 % (1367121)Instruction limit reached!
% 1.61/0.66 % (1367121)------------------------------
% 1.61/0.66 % (1367121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.66 % (1367121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.66 % (1367121)CaDiCaL version: 2.1.3
% 1.61/0.66 % (1367121)Termination reason: Instruction limit
% 1.61/0.66 % (1367121)Termination phase: shuffling
% 1.61/0.66 % (1367121)Time elapsed: 0.007 s
% 1.61/0.66 % (1367121)Peak memory usage: 10 MB
% 1.61/0.66 % (1367121)Instructions burned: 8 (million)
% 1.61/0.66 % (1367126)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=377107351:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.61/0.66 % (1367126)Instruction limit reached!
% 1.61/0.66 % (1367126)------------------------------
% 1.61/0.66 % (1367126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.66 % (1367126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.66 % (1367126)CaDiCaL version: 2.1.3
% 1.61/0.66 % (1367126)Termination reason: Instruction limit
% 1.61/0.66 % (1367126)Termination phase: shuffling
% 1.61/0.66 % (1367126)Time elapsed: 0.013 s
% 1.61/0.66 % (1367126)Peak memory usage: 11 MB
% 1.61/0.66 % (1367126)Instructions burned: 29 (million)
% 1.61/0.66 % (1367129)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=4165333654:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.61/0.66 % (1367132)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.61/0.66 % (1367132)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=1052568803:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.61/0.66 % (1367131)lrs+10_1_si=on:cs=on:random_seed=776689209:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.61/0.66 % (1367124)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2686186797:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/12Mi)
% 1.61/0.66 % (1367132)Instruction limit reached!
% 1.61/0.66 % (1367132)------------------------------
% 1.61/0.66 % (1367132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.66 % (1367132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.99/0.73 % (1367132)CaDiCaL version: 2.1.3
% 1.99/0.73 % (1367132)Termination reason: Instruction limit
% 1.99/0.73 % (1367132)Termination phase: shuffling
% 1.99/0.73 % (1367132)Time elapsed: 0.002 s
% 1.99/0.73 % (1367132)Peak memory usage: 10 MB
% 1.99/0.73 % (1367132)Instructions burned: 4 (million)
% 1.99/0.73 % (1367131)Instruction limit reached!
% 1.99/0.73 % (1367131)------------------------------
% 1.99/0.73 % (1367131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.99/0.73 % (1367131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.99/0.73 % (1367131)CaDiCaL version: 2.1.3
% 1.99/0.73 % (1367131)Termination reason: Instruction limit
% 1.99/0.73 % (1367131)Termination phase: shuffling
% 1.99/0.73 % (1367131)Time elapsed: 0.007 s
% 1.99/0.73 % (1367131)Peak memory usage: 10 MB
% 1.99/0.73 % (1367131)Instructions burned: 8 (million)
% 1.99/0.73 % (1367124)Instruction limit reached!
% 1.99/0.73 % (1367124)------------------------------
% 1.99/0.73 % (1367124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.99/0.73 % (1367124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.99/0.73 % (1367124)CaDiCaL version: 2.1.3
% 1.99/0.73 % (1367124)Termination reason: Instruction limit
% 1.99/0.73 % (1367124)Termination phase: shuffling
% 1.99/0.73 % (1367124)Time elapsed: 0.011 s
% 1.99/0.73 % (1367124)Peak memory usage: 10 MB
% 1.99/0.73 % (1367124)Instructions burned: 13 (million)
% 1.99/0.73 % (1367112)Instruction limit reached!
% 1.99/0.73 % (1367112)------------------------------
% 1.99/0.73 % (1367112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.99/0.73 % (1367112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.99/0.73 % (1367112)CaDiCaL version: 2.1.3
% 1.99/0.73 % (1367112)Termination reason: Instruction limit
% 1.99/0.73 % (1367112)Termination phase: Preprocessing 3
% 1.99/0.73 % (1367112)Time elapsed: 0.090 s
% 1.99/0.73 % (1367112)Peak memory usage: 12 MB
% 1.99/0.73 % (1367112)Instructions burned: 76 (million)
% 1.99/0.73 % (1367137)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2503628651:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/38Mi)
% 1.99/0.73 % (1367137)Instruction limit reached!
% 1.99/0.73 % (1367137)------------------------------
% 1.99/0.73 % (1367137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.99/0.73 % (1367137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.99/0.73 % (1367137)CaDiCaL version: 2.1.3
% 1.99/0.73 % (1367137)Termination reason: Instruction limit
% 1.99/0.73 % (1367137)Termination phase: Property scanning
% 1.99/0.73 % (1367137)Time elapsed: 0.017 s
% 1.99/0.73 % (1367137)Peak memory usage: 11 MB
% 1.99/0.73 % (1367137)Instructions burned: 39 (million)
% 1.99/0.73 % (1367138)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=678900081:st=2:i=249:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/249Mi)
% 1.99/0.73 % (1367139)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4228020953:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/25Mi)
% 1.99/0.73 % (1367140)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2080857691:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2997 on theBenchmark for (2997ds/14Mi)
% 1.99/0.73 % (1367142)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=303376945:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/327Mi)
% 1.99/0.73 % (1367129)Instruction limit reached!
% 1.99/0.73 % (1367129)------------------------------
% 1.99/0.73 % (1367129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.99/0.73 % (1367129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.99/0.73 % (1367129)CaDiCaL version: 2.1.3
% 1.99/0.73 % (1367129)Termination reason: Instruction limit
% 1.99/0.73 % (1367129)Termination phase: Property scanning
% 1.99/0.73 % (1367129)Time elapsed: 0.069 s
% 1.99/0.73 % (1367129)Peak memory usage: 12 MB
% 1.99/0.73 % (1367129)Instructions burned: 86 (million)
% 1.99/0.73 % (1367140)Instruction limit reached!
% 1.99/0.73 % (1367140)------------------------------
% 1.99/0.73 % (1367140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.99/0.73 % (1367140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.81 % (1367140)CaDiCaL version: 2.1.3
% 2.63/0.81 % (1367140)Termination reason: Instruction limit
% 2.63/0.81 % (1367140)Termination phase: shuffling
% 2.63/0.81 % (1367140)Time elapsed: 0.013 s
% 2.63/0.81 % (1367140)Peak memory usage: 10 MB
% 2.63/0.81 % (1367140)Instructions burned: 14 (million)
% 2.63/0.81 % (1367113)Instruction limit reached!
% 2.63/0.81 % (1367113)------------------------------
% 2.63/0.81 % (1367113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.81 % (1367113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.81 % (1367113)CaDiCaL version: 2.1.3
% 2.63/0.81 % (1367113)Termination reason: Instruction limit
% 2.63/0.81 % (1367113)Termination phase: Property scanning
% 2.63/0.81 % (1367113)Time elapsed: 0.125 s
% 2.63/0.81 % (1367113)Peak memory usage: 12 MB
% 2.63/0.81 % (1367113)Instructions burned: 157 (million)
% 2.63/0.81 % (1367139)Instruction limit reached!
% 2.63/0.81 % (1367139)------------------------------
% 2.63/0.81 % (1367139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.81 % (1367139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.81 % (1367139)CaDiCaL version: 2.1.3
% 2.63/0.81 % (1367139)Termination reason: Instruction limit
% 2.63/0.81 % (1367139)Termination phase: shuffling
% 2.63/0.81 % (1367139)Time elapsed: 0.022 s
% 2.63/0.81 % (1367139)Peak memory usage: 10 MB
% 2.63/0.81 % (1367139)Instructions burned: 25 (million)
% 2.63/0.81 % (1367147)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4066899722:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/14Mi)
% 2.63/0.81 % (1367149)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1195813103:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.63/0.81 % (1367150)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1030992029:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.63/0.81 % (1367147)Instruction limit reached!
% 2.63/0.81 % (1367147)------------------------------
% 2.63/0.81 % (1367147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.81 % (1367147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.81 % (1367147)CaDiCaL version: 2.1.3
% 2.63/0.81 % (1367147)Termination reason: Instruction limit
% 2.63/0.81 % (1367147)Termination phase: shuffling
% 2.63/0.81 % (1367147)Time elapsed: 0.013 s
% 2.63/0.81 % (1367147)Peak memory usage: 10 MB
% 2.63/0.81 % (1367147)Instructions burned: 14 (million)
% 2.63/0.81 % (1367150)Instruction limit reached!
% 2.63/0.81 % (1367150)------------------------------
% 2.63/0.81 % (1367150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.81 % (1367150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.81 % (1367150)CaDiCaL version: 2.1.3
% 2.63/0.81 % (1367150)Termination reason: Instruction limit
% 2.63/0.81 % (1367150)Termination phase: shuffling
% 2.63/0.81 % (1367150)Time elapsed: 0.020 s
% 2.63/0.81 % (1367150)Peak memory usage: 11 MB
% 2.63/0.81 % (1367150)Instructions burned: 24 (million)
% 2.63/0.81 % (1367149)Instruction limit reached!
% 2.63/0.81 % (1367149)------------------------------
% 2.63/0.81 % (1367149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.81 % (1367149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.81 % (1367149)CaDiCaL version: 2.1.3
% 2.63/0.81 % (1367149)Termination reason: Instruction limit
% 2.63/0.81 % (1367149)Termination phase: shuffling
% 2.63/0.81 % (1367149)Time elapsed: 0.023 s
% 2.63/0.81 % (1367149)Peak memory usage: 11 MB
% 2.63/0.81 % (1367149)Instructions burned: 27 (million)
% 2.63/0.81 % (1367148)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1238868746:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 2.63/0.81 % (1367148)Instruction limit reached!
% 2.63/0.81 % (1367148)------------------------------
% 2.63/0.81 % (1367148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.81 % (1367148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.81 % (1367148)CaDiCaL version: 2.1.3
% 2.63/0.81 % (1367148)Termination reason: Instruction limit
% 2.63/0.81 % (1367148)Termination phase: shuffling
% 2.63/0.81 % (1367148)Time elapsed: 0.003 s
% 2.63/0.81 % (1367148)Peak memory usage: 10 MB
% 2.63/0.81 % (1367148)Instructions burned: 2 (million)
% 3.03/0.93 % (1367154)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1244556573:cond=on:i=60:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/60Mi)
% 3.03/0.93 % (1367155)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
% 3.03/0.93 % (1367155)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 3.03/0.93 % (1367156)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 3.03/0.93 % (1367155)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=3650796627:i=14:add=off:nm=40:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/14Mi)
% 3.03/0.93 % (1367156)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=350150789:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2996 on theBenchmark for (2996ds/8Mi)
% 3.03/0.93 % (1367156)Instruction limit reached!
% 3.03/0.93 % (1367156)------------------------------
% 3.03/0.93 % (1367156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.93 % (1367156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.93 % (1367156)CaDiCaL version: 2.1.3
% 3.03/0.93 % (1367156)Termination reason: Instruction limit
% 3.03/0.93 % (1367156)Termination phase: shuffling
% 3.03/0.93 % (1367156)Time elapsed: 0.007 s
% 3.03/0.93 % (1367156)Peak memory usage: 10 MB
% 3.03/0.93 % (1367156)Instructions burned: 8 (million)
% 3.03/0.93 % (1367155)Instruction limit reached!
% 3.03/0.93 % (1367155)------------------------------
% 3.03/0.93 % (1367155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.93 % (1367155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.93 % (1367155)CaDiCaL version: 2.1.3
% 3.03/0.93 % (1367155)Termination reason: Instruction limit
% 3.03/0.93 % (1367155)Termination phase: shuffling
% 3.03/0.93 % (1367155)Time elapsed: 0.013 s
% 3.03/0.93 % (1367155)Peak memory usage: 10 MB
% 3.03/0.93 % (1367155)Instructions burned: 15 (million)
% 3.03/0.93 % (1367158)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=1606852735:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2996 on theBenchmark for (2996ds/31Mi)
% 3.03/0.93 % (1367154)Instruction limit reached!
% 3.03/0.93 % (1367154)------------------------------
% 3.03/0.93 % (1367154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.93 % (1367154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.93 % (1367154)CaDiCaL version: 2.1.3
% 3.03/0.93 % (1367154)Termination reason: Instruction limit
% 3.03/0.93 % (1367154)Termination phase: Preprocessing 3
% 3.03/0.93 % (1367154)Time elapsed: 0.051 s
% 3.03/0.93 % (1367154)Peak memory usage: 12 MB
% 3.03/0.93 % (1367154)Instructions burned: 60 (million)
% 3.03/0.93 % (1367162)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1326694071:i=7:hud=5:bd=preordered:rtra=on:bet=on_2996 on theBenchmark for (2996ds/7Mi)
% 3.03/0.93 % (1367142)Instruction limit reached!
% 3.03/0.93 % (1367142)------------------------------
% 3.03/0.93 % (1367142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.93 % (1367142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.93 % (1367142)CaDiCaL version: 2.1.3
% 3.03/0.93 % (1367142)Termination reason: Instruction limit
% 3.03/0.93 % (1367142)Termination phase: Saturation
% 3.03/0.93 % (1367142)Time elapsed: 0.139 s
% 3.03/0.93 % (1367142)Peak memory usage: 16 MB
% 3.03/0.93 % (1367142)Instructions burned: 328 (million)
% 3.03/0.93 % (1367158)Instruction limit reached!
% 3.03/0.93 % (1367158)------------------------------
% 3.03/0.93 % (1367158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.93 % (1367158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.93 % (1367158)CaDiCaL version: 2.1.3
% 3.03/0.93 % (1367158)Termination reason: Instruction limit
% 3.03/0.93 % (1367158)Termination phase: shuffling
% 3.03/0.93 % (1367158)Time elapsed: 0.028 s
% 3.03/0.93 % (1367158)Peak memory usage: 11 MB
% 3.03/1.04 % (1367158)Instructions burned: 31 (million)
% 3.03/1.04 % (1367163)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=302873869:i=23:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/23Mi)
% 3.03/1.04 % (1367162)Instruction limit reached!
% 3.03/1.04 % (1367162)------------------------------
% 3.03/1.04 % (1367162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/1.04 % (1367162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.04 % (1367162)CaDiCaL version: 2.1.3
% 3.03/1.04 % (1367162)Termination reason: Instruction limit
% 3.03/1.04 % (1367162)Termination phase: shuffling
% 3.03/1.04 % (1367162)Time elapsed: 0.007 s
% 3.03/1.04 % (1367162)Peak memory usage: 10 MB
% 3.03/1.04 % (1367162)Instructions burned: 8 (million)
% 3.03/1.04 % (1367167)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=945993261:i=1240:rtra=on:ixr=off_2995 on theBenchmark for (2995ds/1240Mi)
% 3.03/1.04 % (1367163)Instruction limit reached!
% 3.03/1.04 % (1367163)------------------------------
% 3.03/1.04 % (1367163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/1.04 % (1367163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.04 % (1367163)CaDiCaL version: 2.1.3
% 3.03/1.04 % (1367163)Termination reason: Instruction limit
% 3.03/1.04 % (1367163)Termination phase: shuffling
% 3.03/1.04 % (1367163)Time elapsed: 0.020 s
% 3.03/1.04 % (1367163)Peak memory usage: 11 MB
% 3.03/1.04 % (1367163)Instructions burned: 24 (million)
% 3.03/1.04 % (1367166)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2250563910:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/20Mi)
% 3.03/1.04 % (1367169)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2277250309:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2995 on theBenchmark for (2995ds/143Mi)
% 3.03/1.04 % (1367170)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3024275449:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/193Mi)
% 3.03/1.04 % (1367138)Instruction limit reached!
% 3.03/1.04 % (1367138)------------------------------
% 3.03/1.04 % (1367138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/1.04 % (1367138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.04 % (1367138)CaDiCaL version: 2.1.3
% 3.03/1.04 % (1367138)Termination reason: Instruction limit
% 3.03/1.04 % (1367138)Termination phase: Saturation
% 3.03/1.04 % (1367138)Time elapsed: 0.199 s
% 3.03/1.04 % (1367138)Peak memory usage: 15 MB
% 3.03/1.04 % (1367138)Instructions burned: 249 (million)
% 3.03/1.04 % (1367166)Instruction limit reached!
% 3.03/1.04 % (1367166)------------------------------
% 3.03/1.04 % (1367166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/1.04 % (1367166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.04 % (1367166)CaDiCaL version: 2.1.3
% 3.03/1.04 % (1367166)Termination reason: Instruction limit
% 3.03/1.04 % (1367166)Termination phase: shuffling
% 3.03/1.04 % (1367166)Time elapsed: 0.017 s
% 3.03/1.04 % (1367166)Peak memory usage: 10 MB
% 3.03/1.04 % (1367166)Instructions burned: 20 (million)
% 3.03/1.04 % (1367172)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=206732368:i=42:hud=10:rtra=on_2995 on theBenchmark for (2995ds/42Mi)
% 3.03/1.04 % (1367176)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.03/1.04 % (1367176)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3632714260:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2995 on theBenchmark for (2995ds/7Mi)
% 3.03/1.04 % (1367177)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3833469320:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/181Mi)
% 3.03/1.04 % (1367176)Instruction limit reached!
% 3.03/1.04 % (1367176)------------------------------
% 3.03/1.04 % (1367176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/1.04 % (1367176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.04 % (1367176)CaDiCaL version: 2.1.3
% 3.03/1.04 % (1367176)Termination reason: Instruction limit
% 3.03/1.04 % (1367176)Termination phase: shuffling
% 3.03/1.04 % (1367176)Time elapsed: 0.006 s
% 3.03/1.04 % (1367176)Peak memory usage: 10 MB
% 5.36/1.20 % (1367176)Instructions burned: 7 (million)
% 5.36/1.20 % (1367172)Instruction limit reached!
% 5.36/1.20 % (1367172)------------------------------
% 5.36/1.20 % (1367172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.20 % (1367172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.20 % (1367172)CaDiCaL version: 2.1.3
% 5.36/1.20 % (1367172)Termination reason: Instruction limit
% 5.36/1.20 % (1367172)Termination phase: shuffling
% 5.36/1.20 % (1367172)Time elapsed: 0.037 s
% 5.36/1.20 % (1367172)Peak memory usage: 11 MB
% 5.36/1.20 % (1367172)Instructions burned: 42 (million)
% 5.36/1.20 % (1367181)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=340080477:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2995 on theBenchmark for (2995ds/169Mi)
% 5.36/1.20 % (1367182)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 5.36/1.20 % (1367182)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3088569154:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2995 on theBenchmark for (2995ds/6Mi)
% 5.36/1.20 % (1367182)Instruction limit reached!
% 5.36/1.20 % (1367182)------------------------------
% 5.36/1.20 % (1367182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.20 % (1367182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.20 % (1367182)CaDiCaL version: 2.1.3
% 5.36/1.20 % (1367182)Termination reason: Instruction limit
% 5.36/1.20 % (1367182)Termination phase: shuffling
% 5.36/1.20 % (1367182)Time elapsed: 0.006 s
% 5.36/1.20 % (1367182)Peak memory usage: 10 MB
% 5.36/1.20 % (1367182)Instructions burned: 6 (million)
% 5.36/1.20 % (1367169)Instruction limit reached!
% 5.36/1.20 % (1367169)------------------------------
% 5.36/1.20 % (1367169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.20 % (1367169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.20 % (1367169)CaDiCaL version: 2.1.3
% 5.36/1.20 % (1367169)Termination reason: Instruction limit
% 5.36/1.20 % (1367169)Termination phase: Twee Goal Transformation
% 5.36/1.20 % (1367169)Time elapsed: 0.122 s
% 5.36/1.20 % (1367169)Peak memory usage: 12 MB
% 5.36/1.20 % (1367169)Instructions burned: 143 (million)
% 5.36/1.20 % (1367185)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3259860568:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2994 on theBenchmark for (2994ds/22Mi)
% 5.36/1.20 % (1367170)Instruction limit reached!
% 5.36/1.20 % (1367170)------------------------------
% 5.36/1.20 % (1367170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.20 % (1367170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.20 % (1367170)CaDiCaL version: 2.1.3
% 5.36/1.20 % (1367170)Termination reason: Instruction limit
% 5.36/1.20 % (1367170)Termination phase: Property scanning
% 5.36/1.20 % (1367170)Time elapsed: 0.148 s
% 5.36/1.20 % (1367170)Peak memory usage: 12 MB
% 5.36/1.20 % (1367170)Instructions burned: 193 (million)
% 5.36/1.20 % (1367185)Instruction limit reached!
% 5.36/1.20 % (1367185)------------------------------
% 5.36/1.20 % (1367185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.20 % (1367185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.20 % (1367185)CaDiCaL version: 2.1.3
% 5.36/1.20 % (1367185)Termination reason: Instruction limit
% 5.36/1.20 % (1367185)Termination phase: shuffling
% 5.36/1.20 % (1367185)Time elapsed: 0.020 s
% 5.36/1.20 % (1367185)Peak memory usage: 11 MB
% 5.36/1.20 % (1367185)Instructions burned: 22 (million)
% 5.36/1.20 % (1367186)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=556224280:i=19:add=on:rtra=on_2994 on theBenchmark for (2994ds/19Mi)
% 5.36/1.20 % (1367186)Instruction limit reached!
% 5.36/1.20 % (1367186)------------------------------
% 5.36/1.20 % (1367186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.36/1.20 % (1367186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.20 % (1367186)CaDiCaL version: 2.1.3
% 5.36/1.20 % (1367186)Termination reason: Instruction limit
% 5.36/1.20 % (1367186)Termination phase: shuffling
% 5.36/1.20 % (1367186)Time elapsed: 0.016 s
% 6.29/1.40 % (1367186)Peak memory usage: 10 MB
% 6.29/1.40 % (1367186)Instructions burned: 20 (million)
% 6.29/1.40 % (1367188)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=2709875695:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/316Mi)
% 6.29/1.40 % (1367177)Instruction limit reached!
% 6.29/1.40 % (1367177)------------------------------
% 6.29/1.40 % (1367177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.29/1.40 % (1367177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/1.40 % (1367177)CaDiCaL version: 2.1.3
% 6.29/1.40 % (1367177)Termination reason: Instruction limit
% 6.29/1.40 % (1367177)Termination phase: Saturation
% 6.29/1.40 % (1367177)Time elapsed: 0.141 s
% 6.29/1.40 % (1367177)Peak memory usage: 13 MB
% 6.29/1.40 % (1367177)Instructions burned: 181 (million)
% 6.29/1.40 % (1367189)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=2510146729:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2994 on theBenchmark for (2994ds/853Mi)
% 6.29/1.40 % (1367191)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=1774202325:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2993 on theBenchmark for (2993ds/45Mi)
% 6.29/1.40 % (1367193)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3585107085:i=480:rtra=on_2993 on theBenchmark for (2993ds/480Mi)
% 6.29/1.40 % (1367181)Instruction limit reached!
% 6.29/1.40 % (1367181)------------------------------
% 6.29/1.40 % (1367181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.29/1.40 % (1367181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/1.40 % (1367181)CaDiCaL version: 2.1.3
% 6.29/1.40 % (1367181)Termination reason: Instruction limit
% 6.29/1.40 % (1367181)Termination phase: Property scanning
% 6.29/1.40 % (1367181)Time elapsed: 0.137 s
% 6.29/1.40 % (1367181)Peak memory usage: 12 MB
% 6.29/1.40 % (1367181)Instructions burned: 169 (million)
% 6.29/1.40 % (1367110)Instruction limit reached!
% 6.29/1.40 % (1367110)------------------------------
% 6.29/1.40 % (1367110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.29/1.40 % (1367110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/1.40 % (1367110)CaDiCaL version: 2.1.3
% 6.29/1.40 % (1367110)Termination reason: Instruction limit
% 6.29/1.40 % (1367110)Termination phase: Saturation
% 6.29/1.40 % (1367110)Time elapsed: 0.569 s
% 6.29/1.40 % (1367110)Peak memory usage: 21 MB
% 6.29/1.40 % (1367110)Instructions burned: 635 (million)
% 6.29/1.40 % (1367191)Instruction limit reached!
% 6.29/1.40 % (1367191)------------------------------
% 6.29/1.40 % (1367191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.29/1.40 % (1367191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/1.40 % (1367191)CaDiCaL version: 2.1.3
% 6.29/1.40 % (1367191)Termination reason: Instruction limit
% 6.29/1.40 % (1367191)Termination phase: shuffling
% 6.29/1.40 % (1367191)Time elapsed: 0.037 s
% 6.29/1.40 % (1367191)Peak memory usage: 11 MB
% 6.29/1.40 % (1367191)Instructions burned: 46 (million)
% 6.29/1.40 % (1367197)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=606299496:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2993 on theBenchmark for (2993ds/21Mi)
% 6.29/1.40 % (1367198)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 6.29/1.40 % (1367198)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3333565270:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/200Mi)
% 6.29/1.40 % (1367197)Instruction limit reached!
% 6.29/1.40 % (1367197)------------------------------
% 6.29/1.40 % (1367197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.29/1.40 % (1367197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/1.40 % (1367197)CaDiCaL version: 2.1.3
% 6.29/1.40 % (1367197)Termination reason: Instruction limit
% 6.29/1.40 % (1367197)Termination phase: shuffling
% 7.45/1.64 % (1367197)Time elapsed: 0.019 s
% 7.45/1.64 % (1367197)Peak memory usage: 10 MB
% 7.45/1.64 % (1367197)Instructions burned: 21 (million)
% 7.45/1.64 % (1367199)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1566802238:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2993 on theBenchmark for (2993ds/13Mi)
% 7.45/1.64 % (1367199)Instruction limit reached!
% 7.45/1.64 % (1367199)------------------------------
% 7.45/1.64 % (1367199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (1367199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (1367199)CaDiCaL version: 2.1.3
% 7.45/1.64 % (1367199)Termination reason: Instruction limit
% 7.45/1.64 % (1367199)Termination phase: shuffling
% 7.45/1.64 % (1367199)Time elapsed: 0.013 s
% 7.45/1.64 % (1367199)Peak memory usage: 10 MB
% 7.45/1.64 % (1367199)Instructions burned: 13 (million)
% 7.45/1.64 % (1367202)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=554392144:i=66:s2at=3:nm=2:rtra=on:rawr=on_2992 on theBenchmark for (2992ds/66Mi)
% 7.45/1.64 % (1367204)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2726454215:i=51:fsr=off:rtra=on_2992 on theBenchmark for (2992ds/51Mi)
% 7.45/1.64 % (1367202)Instruction limit reached!
% 7.45/1.64 % (1367202)------------------------------
% 7.45/1.64 % (1367202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (1367202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (1367202)CaDiCaL version: 2.1.3
% 7.45/1.64 % (1367202)Termination reason: Instruction limit
% 7.45/1.64 % (1367202)Termination phase: Property scanning
% 7.45/1.64 % (1367202)Time elapsed: 0.056 s
% 7.45/1.64 % (1367202)Peak memory usage: 11 MB
% 7.45/1.64 % (1367202)Instructions burned: 66 (million)
% 7.45/1.64 % (1367204)Instruction limit reached!
% 7.45/1.64 % (1367204)------------------------------
% 7.45/1.64 % (1367204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (1367204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (1367204)CaDiCaL version: 2.1.3
% 7.45/1.64 % (1367204)Termination reason: Instruction limit
% 7.45/1.64 % (1367204)Termination phase: Property scanning
% 7.45/1.64 % (1367204)Time elapsed: 0.044 s
% 7.45/1.64 % (1367204)Peak memory usage: 11 MB
% 7.45/1.64 % (1367204)Instructions burned: 51 (million)
% 7.45/1.64 % (1367207)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2163525574:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/31Mi)
% 7.45/1.64 % (1367208)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3905603297:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2991 on theBenchmark for (2991ds/137Mi)
% 7.45/1.64 % (1367198)Instruction limit reached!
% 7.45/1.64 % (1367198)------------------------------
% 7.45/1.64 % (1367198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (1367198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (1367198)CaDiCaL version: 2.1.3
% 7.45/1.64 % (1367198)Termination reason: Instruction limit
% 7.45/1.64 % (1367198)Termination phase: Saturation
% 7.45/1.64 % (1367198)Time elapsed: 0.162 s
% 7.45/1.64 % (1367198)Peak memory usage: 14 MB
% 7.45/1.64 % (1367198)Instructions burned: 200 (million)
% 7.45/1.64 % (1367207)Instruction limit reached!
% 7.45/1.64 % (1367207)------------------------------
% 7.45/1.64 % (1367207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (1367207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (1367207)CaDiCaL version: 2.1.3
% 7.45/1.64 % (1367207)Termination reason: Instruction limit
% 7.45/1.64 % (1367207)Termination phase: shuffling
% 7.45/1.64 % (1367207)Time elapsed: 0.027 s
% 7.45/1.64 % (1367207)Peak memory usage: 11 MB
% 7.45/1.64 % (1367207)Instructions burned: 32 (million)
% 7.45/1.64 % (1367188)Instruction limit reached!
% 7.45/1.64 % (1367188)------------------------------
% 7.45/1.64 % (1367188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.45/1.64 % (1367188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.64 % (1367188)CaDiCaL version: 2.1.3
% 7.45/1.64 % (1367188)Termination reason: Instruction limit
% 7.45/1.64 % (1367188)Termination phase: Saturation
% 7.45/1.64 % (1367188)Time elapsed: 0.255 s
% 8.62/1.83 % (1367188)Peak memory usage: 16 MB
% 8.62/1.83 % (1367188)Instructions burned: 317 (million)
% 8.62/1.83 % (1367211)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=1063809351:cond=on:i=34:hud=10:nm=10:rtra=on_2991 on theBenchmark for (2991ds/34Mi)
% 8.62/1.83 % (1367212)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1236004158:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2991 on theBenchmark for (2991ds/67Mi)
% 8.62/1.83 % (1367213)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 8.62/1.83 % (1367213)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3665225114:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2991 on theBenchmark for (2991ds/180Mi)
% 8.62/1.83 % (1367211)Instruction limit reached!
% 8.62/1.83 % (1367211)------------------------------
% 8.62/1.83 % (1367211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.62/1.83 % (1367211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/1.83 % (1367211)CaDiCaL version: 2.1.3
% 8.62/1.83 % (1367211)Termination reason: Instruction limit
% 8.62/1.83 % (1367211)Termination phase: shuffling
% 8.62/1.83 % (1367211)Time elapsed: 0.030 s
% 8.62/1.83 % (1367211)Peak memory usage: 11 MB
% 8.62/1.83 % (1367211)Instructions burned: 35 (million)
% 8.62/1.83 % (1367212)Instruction limit reached!
% 8.62/1.83 % (1367212)------------------------------
% 8.62/1.83 % (1367212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.62/1.83 % (1367212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/1.83 % (1367212)CaDiCaL version: 2.1.3
% 8.62/1.83 % (1367212)Termination reason: Instruction limit
% 8.62/1.83 % (1367212)Termination phase: Property scanning
% 8.62/1.83 % (1367212)Time elapsed: 0.055 s
% 8.62/1.83 % (1367212)Peak memory usage: 11 MB
% 8.62/1.83 % (1367212)Instructions burned: 68 (million)
% 8.62/1.83 % (1367208)Instruction limit reached!
% 8.62/1.83 % (1367208)------------------------------
% 8.62/1.83 % (1367208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.62/1.83 % (1367208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/1.83 % (1367208)CaDiCaL version: 2.1.3
% 8.62/1.83 % (1367208)Termination reason: Instruction limit
% 8.62/1.83 % (1367208)Termination phase: Twee Goal Transformation
% 8.62/1.83 % (1367208)Time elapsed: 0.111 s
% 8.62/1.83 % (1367208)Peak memory usage: 12 MB
% 8.62/1.83 % (1367208)Instructions burned: 138 (million)
% 8.62/1.83 % (1367167)Instruction limit reached!
% 8.62/1.83 % (1367167)------------------------------
% 8.62/1.83 % (1367167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.62/1.83 % (1367167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/1.83 % (1367167)CaDiCaL version: 2.1.3
% 8.62/1.83 % (1367167)Termination reason: Instruction limit
% 8.62/1.83 % (1367167)Termination phase: Saturation
% 8.62/1.83 % (1367167)Time elapsed: 0.549 s
% 8.62/1.83 % (1367167)Peak memory usage: 19 MB
% 8.62/1.83 % (1367167)Instructions burned: 1241 (million)
% 8.62/1.83 % (1367217)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=2254140481:st=2:i=246:sd=3:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/246Mi)
% 8.62/1.83 % (1367221)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2882100037:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/874Mi)
% 8.62/1.83 % (1367218)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=4014650227:cond=on:i=96:bd=all:rtra=on_2990 on theBenchmark for (2990ds/96Mi)
% 8.62/1.83 % (1367219)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1918963656:i=427:sd=1:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/427Mi)
% 8.62/1.83 % (1367213)Instruction limit reached!
% 8.62/1.83 % (1367213)------------------------------
% 8.62/1.83 % (1367213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.62/1.83 % (1367213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/1.83 % (1367213)CaDiCaL version: 2.1.3
% 8.62/1.83 % (1367213)Termination reason: Instruction limit
% 8.62/1.83 % (1367213)Termination phase: Saturation
% 8.62/1.83 % (1367213)Time elapsed: 0.140 s
% 8.62/1.83 % (1367213)Peak memory usage: 13 MB
% 8.62/1.83 % (1367213)Instructions burned: 180 (million)
% 8.62/1.83 % (1367218)Instruction limit reached!
% 8.62/1.83 % (1367218)------------------------------
% 8.62/1.83 % (1367218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/1.99 % (1367218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/1.99 % (1367218)CaDiCaL version: 2.1.3
% 9.68/1.99 % (1367218)Termination reason: Instruction limit
% 9.68/1.99 % (1367218)Termination phase: Property scanning
% 9.68/1.99 % (1367218)Time elapsed: 0.078 s
% 9.68/1.99 % (1367218)Peak memory usage: 12 MB
% 9.68/1.99 % (1367218)Instructions burned: 97 (million)
% 9.68/1.99 % (1367193)Instruction limit reached!
% 9.68/1.99 % (1367193)------------------------------
% 9.68/1.99 % (1367193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/1.99 % (1367193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/1.99 % (1367193)CaDiCaL version: 2.1.3
% 9.68/1.99 % (1367193)Termination reason: Instruction limit
% 9.68/1.99 % (1367193)Termination phase: Saturation
% 9.68/1.99 % (1367193)Time elapsed: 0.423 s
% 9.68/1.99 % (1367193)Peak memory usage: 19 MB
% 9.68/1.99 % (1367193)Instructions burned: 482 (million)
% 9.68/1.99 % (1367225)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=875305715:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/515Mi)
% 9.68/1.99 % (1367226)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=826786076:st=1.5:i=130:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/130Mi)
% 9.68/1.99 % (1367227)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=40456057:i=44:ep=R:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/44Mi)
% 9.68/1.99 % (1367227)Instruction limit reached!
% 9.68/1.99 % (1367227)------------------------------
% 9.68/1.99 % (1367227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/1.99 % (1367227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/1.99 % (1367227)CaDiCaL version: 2.1.3
% 9.68/1.99 % (1367227)Termination reason: Instruction limit
% 9.68/1.99 % (1367227)Termination phase: shuffling
% 9.68/1.99 % (1367227)Time elapsed: 0.036 s
% 9.68/1.99 % (1367227)Peak memory usage: 11 MB
% 9.68/1.99 % (1367227)Instructions burned: 44 (million)
% 9.68/1.99 % (1367217)Instruction limit reached!
% 9.68/1.99 % (1367217)------------------------------
% 9.68/1.99 % (1367217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/1.99 % (1367217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/1.99 % (1367217)CaDiCaL version: 2.1.3
% 9.68/1.99 % (1367217)Termination reason: Instruction limit
% 9.68/1.99 % (1367217)Termination phase: Saturation
% 9.68/1.99 % (1367217)Time elapsed: 0.196 s
% 9.68/1.99 % (1367217)Peak memory usage: 14 MB
% 9.68/1.99 % (1367217)Instructions burned: 247 (million)
% 9.68/1.99 % (1367231)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=1933218966:s2a=on:i=571:nm=16:rtra=on_2988 on theBenchmark for (2988ds/571Mi)
% 9.68/1.99 % (1367232)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1189955310:i=450:rtra=on:ixr=off:ntd=on_2988 on theBenchmark for (2988ds/450Mi)
% 9.68/1.99 % (1367226)Instruction limit reached!
% 9.68/1.99 % (1367226)------------------------------
% 9.68/1.99 % (1367226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/1.99 % (1367226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/1.99 % (1367226)CaDiCaL version: 2.1.3
% 9.68/1.99 % (1367226)Termination reason: Instruction limit
% 9.68/1.99 % (1367226)Termination phase: Property scanning
% 9.68/1.99 % (1367226)Time elapsed: 0.101 s
% 9.68/1.99 % (1367226)Peak memory usage: 12 MB
% 9.68/1.99 % (1367226)Instructions burned: 130 (million)
% 9.68/1.99 % (1367235)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3798032502:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/95Mi)
% 9.68/1.99 % (1367235)Instruction limit reached!
% 9.68/1.99 % (1367235)------------------------------
% 9.68/1.99 % (1367235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/1.99 % (1367235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/1.99 % (1367235)CaDiCaL version: 2.1.3
% 9.68/1.99 % (1367235)Termination reason: Instruction limit
% 9.68/1.99 % (1367235)Termination phase: Property scanning
% 9.68/1.99 % (1367235)Time elapsed: 0.076 s
% 9.68/1.99 % (1367235)Peak memory usage: 12 MB
% 9.68/1.99 % (1367235)Instructions burned: 95 (million)
% 12.23/2.25 % (1367237)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=1872619077:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2986 on theBenchmark for (2986ds/65Mi)
% 12.23/2.25 % (1367219)Instruction limit reached!
% 12.23/2.25 % (1367219)------------------------------
% 12.23/2.25 % (1367219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.23/2.25 % (1367219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.25 % (1367219)CaDiCaL version: 2.1.3
% 12.23/2.25 % (1367219)Termination reason: Instruction limit
% 12.23/2.25 % (1367219)Termination phase: Saturation
% 12.23/2.25 % (1367219)Time elapsed: 0.366 s
% 12.23/2.25 % (1367219)Peak memory usage: 17 MB
% 12.23/2.25 % (1367219)Instructions burned: 427 (million)
% 12.23/2.25 % (1367221)Instruction limit reached!
% 12.23/2.25 % (1367221)------------------------------
% 12.23/2.25 % (1367221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.23/2.25 % (1367221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.25 % (1367221)CaDiCaL version: 2.1.3
% 12.23/2.25 % (1367221)Termination reason: Instruction limit
% 12.23/2.25 % (1367221)Termination phase: Saturation
% 12.23/2.25 % (1367221)Time elapsed: 0.388 s
% 12.23/2.25 % (1367221)Peak memory usage: 17 MB
% 12.23/2.25 % (1367221)Instructions burned: 874 (million)
% 12.23/2.25 % (1367240)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=1460428911:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2986 on theBenchmark for (2986ds/5755Mi)
% 12.23/2.25 % (1367189)Instruction limit reached!
% 12.23/2.25 % (1367189)------------------------------
% 12.23/2.25 % (1367189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.23/2.25 % (1367189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.25 % (1367239)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=260525377: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_2986 on theBenchmark for (2986ds/105Mi)
% 12.23/2.25 % (1367189)CaDiCaL version: 2.1.3
% 12.23/2.25 % (1367189)Termination reason: Instruction limit
% 12.23/2.25 % (1367189)Termination phase: Saturation
% 12.23/2.25 % (1367189)Time elapsed: 0.771 s
% 12.23/2.25 % (1367189)Peak memory usage: 23 MB
% 12.23/2.25 % (1367189)Instructions burned: 853 (million)
% 12.23/2.25 % (1367237)Instruction limit reached!
% 12.23/2.25 % (1367237)------------------------------
% 12.23/2.25 % (1367237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.23/2.25 % (1367237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.25 % (1367237)CaDiCaL version: 2.1.3
% 12.23/2.25 % (1367237)Termination reason: Instruction limit
% 12.23/2.25 % (1367237)Termination phase: Property scanning
% 12.23/2.25 % (1367237)Time elapsed: 0.063 s
% 12.23/2.25 % (1367237)Peak memory usage: 11 MB
% 12.23/2.25 % (1367237)Instructions burned: 65 (million)
% 12.23/2.25 % (1367243)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=18826348:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/375Mi)
% 12.23/2.26 % (1367244)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2208672672:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2985 on theBenchmark for (2985ds/495Mi)
% 12.23/2.26 % (1367239)Instruction limit reached!
% 12.23/2.26 % (1367239)------------------------------
% 12.23/2.26 % (1367239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.23/2.26 % (1367239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.23/2.26 % (1367239)CaDiCaL version: 2.1.3
% 12.23/2.26 % (1367239)Termination reason: Instruction limit
% 12.23/2.26 % (1367239)Termination phase: Property scanning
% 12.23/2.26 % (1367239)Time elapsed: 0.082 s
% 12.23/2.26 % (1367239)Peak memory usage: 12 MB
% 12.23/2.26 % (1367239)Instructions burned: 106 (million)
% 12.23/2.26 % (1367225)Instruction limit reached!
% 12.23/2.26 % (1367225)------------------------------
% 12.23/2.26 % (1367225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.23/2.26 % (1367225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.26/2.48 % (1367225)CaDiCaL version: 2.1.3
% 13.26/2.48 % (1367225)Termination reason: Instruction limit
% 13.26/2.48 % (1367225)Termination phase: Saturation
% 13.26/2.48 % (1367225)Time elapsed: 0.419 s
% 13.26/2.48 % (1367225)Peak memory usage: 16 MB
% 13.26/2.48 % (1367225)Instructions burned: 516 (million)
% 13.26/2.48 % (1367247)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=3222332839:cond=on:i=34:hud=10:nm=10:rtra=on_2985 on theBenchmark for (2985ds/34Mi)
% 13.26/2.48 % (1367248)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2781058883:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2984 on theBenchmark for (2984ds/91Mi)
% 13.26/2.48 % (1367247)Instruction limit reached!
% 13.26/2.48 % (1367247)------------------------------
% 13.26/2.48 % (1367247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.26/2.48 % (1367247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.26/2.48 % (1367247)CaDiCaL version: 2.1.3
% 13.26/2.48 % (1367247)Termination reason: Instruction limit
% 13.26/2.48 % (1367247)Termination phase: shuffling
% 13.26/2.48 % (1367247)Time elapsed: 0.030 s
% 13.26/2.48 % (1367247)Peak memory usage: 11 MB
% 13.26/2.48 % (1367247)Instructions burned: 34 (million)
% 13.26/2.48 % (1367232)Instruction limit reached!
% 13.26/2.48 % (1367232)------------------------------
% 13.26/2.48 % (1367232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.26/2.48 % (1367232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.26/2.48 % (1367232)CaDiCaL version: 2.1.3
% 13.26/2.48 % (1367232)Termination reason: Instruction limit
% 13.26/2.48 % (1367232)Termination phase: Saturation
% 13.26/2.48 % (1367232)Time elapsed: 0.368 s
% 13.26/2.48 % (1367232)Peak memory usage: 19 MB
% 13.26/2.48 % (1367232)Instructions burned: 450 (million)
% 13.26/2.48 % (1367251)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=2728777164:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2984 on theBenchmark for (2984ds/66Mi)
% 13.26/2.48 % (1367252)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3143904433:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2984 on theBenchmark for (2984ds/22Mi)
% 13.26/2.48 % (1367248)Instruction limit reached!
% 13.26/2.48 % (1367248)------------------------------
% 13.26/2.48 % (1367248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.26/2.48 % (1367248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.26/2.48 % (1367248)CaDiCaL version: 2.1.3
% 13.26/2.48 % (1367248)Termination reason: Instruction limit
% 13.26/2.48 % (1367248)Termination phase: SInE selection
% 13.26/2.48 % (1367248)Time elapsed: 0.076 s
% 13.26/2.48 % (1367248)Peak memory usage: 12 MB
% 13.26/2.48 % (1367248)Instructions burned: 92 (million)
% 13.26/2.48 % (1367252)Instruction limit reached!
% 13.26/2.48 % (1367252)------------------------------
% 13.26/2.48 % (1367252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.26/2.48 % (1367252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.26/2.48 % (1367252)CaDiCaL version: 2.1.3
% 13.26/2.48 % (1367252)Termination reason: Instruction limit
% 13.26/2.48 % (1367252)Termination phase: shuffling
% 13.26/2.48 % (1367252)Time elapsed: 0.020 s
% 13.26/2.48 % (1367252)Peak memory usage: 10 MB
% 13.26/2.48 % (1367252)Instructions burned: 23 (million)
% 13.26/2.48 % (1367251)Instruction limit reached!
% 13.26/2.48 % (1367251)------------------------------
% 13.26/2.48 % (1367251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.26/2.48 % (1367251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.26/2.48 % (1367251)CaDiCaL version: 2.1.3
% 13.26/2.48 % (1367251)Termination reason: Instruction limit
% 13.26/2.48 % (1367251)Termination phase: Naming
% 13.26/2.48 % (1367251)Time elapsed: 0.053 s
% 13.26/2.48 % (1367251)Peak memory usage: 12 MB
% 13.26/2.48 % (1367251)Instructions burned: 67 (million)
% 13.26/2.48 % (1367255)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=2544697416:i=338:bd=all:ins=4:rtra=on_2983 on theBenchmark for (2983ds/338Mi)
% 13.26/2.48 % (1367256)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3615266141:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2983 on theBenchmark for (2983ds/28Mi)
% 13.26/2.48 % (1367257)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 14.87/2.76 % (1367257)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2670154448:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2983 on theBenchmark for (2983ds/137Mi)
% 14.87/2.76 % (1367256)Instruction limit reached!
% 14.87/2.76 % (1367256)------------------------------
% 14.87/2.76 % (1367256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.87/2.76 % (1367256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.87/2.76 % (1367256)CaDiCaL version: 2.1.3
% 14.87/2.76 % (1367256)Termination reason: Instruction limit
% 14.87/2.76 % (1367256)Termination phase: shuffling
% 14.87/2.76 % (1367256)Time elapsed: 0.025 s
% 14.87/2.76 % (1367256)Peak memory usage: 11 MB
% 14.87/2.76 % (1367256)Instructions burned: 29 (million)
% 14.87/2.76 % (1367231)Instruction limit reached!
% 14.87/2.76 % (1367231)------------------------------
% 14.87/2.76 % (1367231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.87/2.76 % (1367231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.87/2.76 % (1367231)CaDiCaL version: 2.1.3
% 14.87/2.76 % (1367231)Termination reason: Instruction limit
% 14.87/2.76 % (1367231)Termination phase: Saturation
% 14.87/2.76 % (1367231)Time elapsed: 0.503 s
% 14.87/2.76 % (1367231)Peak memory usage: 19 MB
% 14.87/2.76 % (1367231)Instructions burned: 571 (million)
% 14.87/2.76 % (1367261)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=3561268185:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2983 on theBenchmark for (2983ds/340Mi)
% 14.87/2.76 % (1367243)Instruction limit reached!
% 14.87/2.76 % (1367243)------------------------------
% 14.87/2.76 % (1367243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.87/2.76 % (1367243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.87/2.76 % (1367243)CaDiCaL version: 2.1.3
% 14.87/2.76 % (1367243)Termination reason: Instruction limit
% 14.87/2.76 % (1367243)Termination phase: Saturation
% 14.87/2.76 % (1367243)Time elapsed: 0.308 s
% 14.87/2.76 % (1367243)Peak memory usage: 16 MB
% 14.87/2.76 % (1367243)Instructions burned: 375 (million)
% 14.87/2.76 % (1367262)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=2724877093:i=227:sd=1:bd=all:rtra=on:ss=axioms_2983 on theBenchmark for (2983ds/227Mi)
% 14.87/2.76 % (1367257)Instruction limit reached!
% 14.87/2.76 % (1367257)------------------------------
% 14.87/2.76 % (1367257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.87/2.76 % (1367257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.87/2.76 % (1367257)CaDiCaL version: 2.1.3
% 14.87/2.76 % (1367257)Termination reason: Instruction limit
% 14.87/2.76 % (1367257)Termination phase: Property scanning
% 14.87/2.76 % (1367257)Time elapsed: 0.108 s
% 14.87/2.76 % (1367257)Peak memory usage: 12 MB
% 14.87/2.76 % (1367257)Instructions burned: 138 (million)
% 14.87/2.76 % (1367264)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 14.87/2.76 % (1367264)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=231801619:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/373Mi)
% 14.87/2.76 % (1367266)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=2470914135:i=116:ep=RSTC:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/116Mi)
% 14.87/2.76 % (1367266)Instruction limit reached!
% 14.87/2.76 % (1367266)------------------------------
% 14.87/2.76 % (1367266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.87/2.76 % (1367266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.87/2.76 % (1367266)CaDiCaL version: 2.1.3
% 14.87/2.76 % (1367266)Termination reason: Instruction limit
% 14.87/2.76 % (1367266)Termination phase: Property scanning
% 14.87/2.76 % (1367266)Time elapsed: 0.100 s
% 14.87/2.76 % (1367266)Peak memory usage: 14 MB
% 14.87/2.76 % (1367266)Instructions burned: 117 (million)
% 14.87/2.76 % (1367244)Instruction limit reached!
% 14.87/2.76 % (1367244)------------------------------
% 14.87/2.76 % (1367244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.87/2.76 % (1367244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.87/2.76 % (1367244)CaDiCaL version: 2.1.3
% 19.68/3.29 % (1367244)Termination reason: Instruction limit
% 19.68/3.29 % (1367244)Termination phase: Saturation
% 19.68/3.29 % (1367244)Time elapsed: 0.464 s
% 19.68/3.29 % (1367244)Peak memory usage: 18 MB
% 19.68/3.29 % (1367244)Instructions burned: 495 (million)
% 19.68/3.29 % (1367255)Instruction limit reached!
% 19.68/3.29 % (1367255)------------------------------
% 19.68/3.29 % (1367255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.68/3.29 % (1367255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.68/3.29 % (1367255)CaDiCaL version: 2.1.3
% 19.68/3.29 % (1367255)Termination reason: Instruction limit
% 19.68/3.29 % (1367255)Termination phase: Saturation
% 19.68/3.29 % (1367255)Time elapsed: 0.276 s
% 19.68/3.29 % (1367255)Peak memory usage: 19 MB
% 19.68/3.29 % (1367255)Instructions burned: 340 (million)
% 19.68/3.29 % (1367262)Instruction limit reached!
% 19.68/3.29 % (1367262)------------------------------
% 19.68/3.29 % (1367262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.68/3.29 % (1367262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.68/3.29 % (1367262)CaDiCaL version: 2.1.3
% 19.68/3.29 % (1367262)Termination reason: Instruction limit
% 19.68/3.29 % (1367262)Termination phase: Saturation
% 19.68/3.29 % (1367262)Time elapsed: 0.189 s
% 19.68/3.29 % (1367262)Peak memory usage: 15 MB
% 19.68/3.29 % (1367262)Instructions burned: 231 (million)
% 19.68/3.29 % (1367269)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3453170678:i=575:rtra=on_2980 on theBenchmark for (2980ds/575Mi)
% 19.68/3.29 % (1367270)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3019454473:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2980 on theBenchmark for (2980ds/270Mi)
% 19.68/3.29 % (1367271)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=2531827499: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_2980 on theBenchmark for (2980ds/9840Mi)
% 19.68/3.29 % (1367272)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=712363262:i=421:rtra=on:ss=axioms_2980 on theBenchmark for (2980ds/421Mi)
% 19.68/3.29 % (1367261)Instruction limit reached!
% 19.68/3.29 % (1367261)------------------------------
% 19.68/3.29 % (1367261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.68/3.29 % (1367261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.68/3.29 % (1367261)CaDiCaL version: 2.1.3
% 19.68/3.29 % (1367261)Termination reason: Instruction limit
% 19.68/3.29 % (1367261)Termination phase: Saturation
% 19.68/3.29 % (1367261)Time elapsed: 0.286 s
% 19.68/3.29 % (1367261)Peak memory usage: 15 MB
% 19.68/3.29 % (1367261)Instructions burned: 341 (million)
% 19.68/3.29 % (1367277)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
% 19.68/3.29 % (1367277)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=27923612:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2979 on theBenchmark for (2979ds/270Mi)
% 19.68/3.29 % (1367264)Instruction limit reached!
% 19.68/3.29 % (1367264)------------------------------
% 19.68/3.29 % (1367264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.68/3.29 % (1367264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.68/3.29 % (1367264)CaDiCaL version: 2.1.3
% 19.68/3.29 % (1367264)Termination reason: Instruction limit
% 19.68/3.29 % (1367264)Termination phase: Saturation
% 19.68/3.29 % (1367264)Time elapsed: 0.301 s
% 19.68/3.29 % (1367264)Peak memory usage: 14 MB
% 19.68/3.29 % (1367264)Instructions burned: 374 (million)
% 19.68/3.29 % (1367279)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3830869728:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2979 on theBenchmark for (2979ds/31Mi)
% 19.68/3.29 % (1367279)Instruction limit reached!
% 19.68/3.29 % (1367279)------------------------------
% 19.68/3.29 % (1367279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.68/3.29 % (1367279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.68/3.29 % (1367279)CaDiCaL version: 2.1.3
% 22.30/3.70 % (1367279)Termination reason: Instruction limit
% 22.30/3.70 % (1367279)Termination phase: shuffling
% 22.30/3.70 % (1367279)Time elapsed: 0.027 s
% 22.30/3.70 % (1367279)Peak memory usage: 11 MB
% 22.30/3.70 % (1367279)Instructions burned: 32 (million)
% 22.30/3.70 % (1367270)Instruction limit reached!
% 22.30/3.70 % (1367270)------------------------------
% 22.30/3.70 % (1367270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.30/3.70 % (1367270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.30/3.70 % (1367270)CaDiCaL version: 2.1.3
% 22.30/3.70 % (1367270)Termination reason: Instruction limit
% 22.30/3.70 % (1367270)Termination phase: Saturation
% 22.30/3.70 % (1367270)Time elapsed: 0.208 s
% 22.30/3.70 % (1367270)Peak memory usage: 14 MB
% 22.30/3.70 % (1367270)Instructions burned: 270 (million)
% 22.30/3.70 % (1367281)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 22.30/3.70 % (1367281)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
% 22.30/3.70 % (1367281)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=885553685:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2978 on theBenchmark for (2978ds/1440Mi)
% 22.30/3.70 % (1367282)dis+10_2_sil=128000:si=on:random_seed=1377268992:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2978 on theBenchmark for (2978ds/339Mi)
% 22.30/3.70 % (1367277)Instruction limit reached!
% 22.30/3.70 % (1367277)------------------------------
% 22.30/3.70 % (1367277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.30/3.70 % (1367277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.30/3.70 % (1367277)CaDiCaL version: 2.1.3
% 22.30/3.70 % (1367277)Termination reason: Instruction limit
% 22.30/3.70 % (1367277)Termination phase: Saturation
% 22.30/3.70 % (1367277)Time elapsed: 0.215 s
% 22.30/3.70 % (1367277)Peak memory usage: 15 MB
% 22.30/3.70 % (1367277)Instructions burned: 271 (million)
% 22.30/3.70 % (1367285)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1294682394:i=111:add=on:fgj=on:rtra=on:fdi=1024_2977 on theBenchmark for (2977ds/111Mi)
% 22.30/3.70 % (1367272)Instruction limit reached!
% 22.30/3.70 % (1367272)------------------------------
% 22.30/3.70 % (1367272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.30/3.70 % (1367272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.30/3.70 % (1367272)CaDiCaL version: 2.1.3
% 22.30/3.70 % (1367272)Termination reason: Instruction limit
% 22.30/3.70 % (1367272)Termination phase: Saturation
% 22.30/3.70 % (1367272)Time elapsed: 0.346 s
% 22.30/3.70 % (1367272)Peak memory usage: 16 MB
% 22.30/3.70 % (1367272)Instructions burned: 421 (million)
% 22.30/3.70 % (1367287)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=220525187:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2976 on theBenchmark for (2976ds/122Mi)
% 22.30/3.70 % (1367285)Instruction limit reached!
% 22.30/3.70 % (1367285)------------------------------
% 22.30/3.70 % (1367285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.30/3.70 % (1367285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.30/3.70 % (1367285)CaDiCaL version: 2.1.3
% 22.30/3.70 % (1367285)Termination reason: Instruction limit
% 22.30/3.70 % (1367285)Termination phase: Property scanning
% 22.30/3.70 % (1367285)Time elapsed: 0.088 s
% 22.30/3.70 % (1367285)Peak memory usage: 12 MB
% 22.30/3.70 % (1367285)Instructions burned: 111 (million)
% 22.30/3.70 % (1367289)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=2855746227:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2976 on theBenchmark for (2976ds/136Mi)
% 22.30/3.70 % (1367269)Instruction limit reached!
% 22.30/3.70 % (1367269)------------------------------
% 22.30/3.70 % (1367269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.30/3.70 % (1367269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.30/3.70 % (1367269)CaDiCaL version: 2.1.3
% 22.30/3.70 % (1367269)Termination reason: Instruction limit
% 22.30/3.70 % (1367269)Termination phase: Saturation
% 24.30/4.00 % (1367269)Time elapsed: 0.476 s
% 24.30/4.00 % (1367269)Peak memory usage: 17 MB
% 24.30/4.00 % (1367269)Instructions burned: 576 (million)
% 24.30/4.00 % (1367291)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3507930839:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2975 on theBenchmark for (2975ds/232Mi)
% 24.30/4.00 % (1367282)Instruction limit reached!
% 24.30/4.00 % (1367282)------------------------------
% 24.30/4.00 % (1367282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.30/4.00 % (1367282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.30/4.00 % (1367282)CaDiCaL version: 2.1.3
% 24.30/4.00 % (1367282)Termination reason: Instruction limit
% 24.30/4.00 % (1367282)Termination phase: Saturation
% 24.30/4.00 % (1367282)Time elapsed: 0.270 s
% 24.30/4.00 % (1367282)Peak memory usage: 15 MB
% 24.30/4.00 % (1367282)Instructions burned: 339 (million)
% 24.30/4.00 % (1367287)Instruction limit reached!
% 24.30/4.00 % (1367287)------------------------------
% 24.30/4.00 % (1367287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.30/4.00 % (1367287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.30/4.00 % (1367287)CaDiCaL version: 2.1.3
% 24.30/4.00 % (1367287)Termination reason: Instruction limit
% 24.30/4.00 % (1367287)Termination phase: Property scanning
% 24.30/4.00 % (1367287)Time elapsed: 0.108 s
% 24.30/4.00 % (1367287)Peak memory usage: 12 MB
% 24.30/4.00 % (1367287)Instructions burned: 123 (million)
% 24.30/4.00 % (1367294)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 24.30/4.00 % (1367293)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=3339359649:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2975 on theBenchmark for (2975ds/1254Mi)
% 24.30/4.00 % (1367294)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=88366219:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2975 on theBenchmark for (2975ds/281Mi)
% 24.30/4.00 % (1367289)Instruction limit reached!
% 24.30/4.00 % (1367289)------------------------------
% 24.30/4.00 % (1367289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.30/4.00 % (1367289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.30/4.00 % (1367289)CaDiCaL version: 2.1.3
% 24.30/4.00 % (1367289)Termination reason: Instruction limit
% 24.30/4.00 % (1367289)Termination phase: Property scanning
% 24.30/4.00 % (1367289)Time elapsed: 0.107 s
% 24.30/4.00 % (1367289)Peak memory usage: 12 MB
% 24.30/4.00 % (1367289)Instructions burned: 136 (million)
% 24.30/4.00 % (1367297)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3452925115:i=619:add=on:rtra=on_2974 on theBenchmark for (2974ds/619Mi)
% 24.30/4.00 % (1367291)Instruction limit reached!
% 24.30/4.00 % (1367291)------------------------------
% 24.30/4.00 % (1367291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.30/4.00 % (1367291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.30/4.00 % (1367291)CaDiCaL version: 2.1.3
% 24.30/4.00 % (1367291)Termination reason: Instruction limit
% 24.30/4.00 % (1367291)Termination phase: Saturation
% 24.30/4.00 % (1367291)Time elapsed: 0.190 s
% 24.30/4.00 % (1367291)Peak memory usage: 15 MB
% 24.30/4.00 % (1367291)Instructions burned: 233 (million)
% 24.30/4.00 % (1367299)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=2689038155:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2973 on theBenchmark for (2973ds/865Mi)
% 24.30/4.00 % (1367294)Instruction limit reached!
% 24.30/4.00 % (1367294)------------------------------
% 24.30/4.00 % (1367294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.30/4.00 % (1367294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.30/4.00 % (1367294)CaDiCaL version: 2.1.3
% 24.30/4.00 % (1367294)Termination reason: Instruction limit
% 24.30/4.00 % (1367294)Termination phase: Saturation
% 24.30/4.00 % (1367294)Time elapsed: 0.216 s
% 24.30/4.00 % (1367294)Peak memory usage: 13 MB
% 24.30/4.00 % (1367294)Instructions burned: 281 (million)
% 24.30/4.00 % (1367301)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2864164541:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2972 on theBenchmark for (2972ds/212Mi)
% 24.30/4.00 % (1367301)Instruction limit reached!
% 24.66/4.09 % (1367301)------------------------------
% 24.66/4.09 % (1367301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367301)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367301)Termination reason: Instruction limit
% 24.66/4.09 % (1367301)Termination phase: Saturation
% 24.66/4.09 % (1367301)Time elapsed: 0.181 s
% 24.66/4.09 % (1367301)Peak memory usage: 14 MB
% 24.66/4.09 % (1367301)Instructions burned: 212 (million)
% 24.66/4.09 % (1367303)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=530632741:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2970 on theBenchmark for (2970ds/130Mi)
% 24.66/4.09 % (1367297)Instruction limit reached!
% 24.66/4.09 % (1367297)------------------------------
% 24.66/4.09 % (1367297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367297)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367297)Termination reason: Instruction limit
% 24.66/4.09 % (1367297)Termination phase: Saturation
% 24.66/4.09 % (1367297)Time elapsed: 0.485 s
% 24.66/4.09 % (1367297)Peak memory usage: 16 MB
% 24.66/4.09 % (1367297)Instructions burned: 619 (million)
% 24.66/4.09 % (1367305)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=409296332:st=1.5:i=346:rtra=on:ss=axioms_2969 on theBenchmark for (2969ds/346Mi)
% 24.66/4.09 % (1367303)Instruction limit reached!
% 24.66/4.09 % (1367303)------------------------------
% 24.66/4.09 % (1367303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367303)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367303)Termination reason: Instruction limit
% 24.66/4.09 % (1367303)Termination phase: Property scanning
% 24.66/4.09 % (1367303)Time elapsed: 0.112 s
% 24.66/4.09 % (1367303)Peak memory usage: 12 MB
% 24.66/4.09 % (1367303)Instructions burned: 130 (million)
% 24.66/4.09 % (1367307)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=2835837520:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2968 on theBenchmark for (2968ds/152Mi)
% 24.66/4.09 % (1367307)Instruction limit reached!
% 24.66/4.09 % (1367307)------------------------------
% 24.66/4.09 % (1367307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367307)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367307)Termination reason: Instruction limit
% 24.66/4.09 % (1367307)Termination phase: Property scanning
% 24.66/4.09 % (1367307)Time elapsed: 0.138 s
% 24.66/4.09 % (1367307)Peak memory usage: 13 MB
% 24.66/4.09 % (1367307)Instructions burned: 152 (million)
% 24.66/4.09 % (1367281)Instruction limit reached!
% 24.66/4.09 % (1367281)------------------------------
% 24.66/4.09 % (1367281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367281)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367281)Termination reason: Instruction limit
% 24.66/4.09 % (1367281)Termination phase: Saturation
% 24.66/4.09 % (1367281)Time elapsed: 1.136 s
% 24.66/4.09 % (1367281)Peak memory usage: 28 MB
% 24.66/4.09 % (1367281)Instructions burned: 1440 (million)
% 24.66/4.09 % (1367309)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1552720676:i=75:ep=R:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/75Mi)
% 24.66/4.09 % (1367299)Instruction limit reached!
% 24.66/4.09 % (1367299)------------------------------
% 24.66/4.09 % (1367299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367299)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367299)Termination reason: Instruction limit
% 24.66/4.09 % (1367299)Termination phase: Saturation
% 24.66/4.09 % (1367299)Time elapsed: 0.671 s
% 24.66/4.09 % (1367299)Peak memory usage: 18 MB
% 24.66/4.09 % (1367299)Instructions burned: 866 (million)
% 24.66/4.09 % (1367305)Instruction limit reached!
% 24.66/4.09 % (1367305)------------------------------
% 24.66/4.09 % (1367305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367305)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367305)Termination reason: Instruction limit
% 24.66/4.09 % (1367305)Termination phase: Saturation
% 24.66/4.09 % (1367305)Time elapsed: 0.271 s
% 24.66/4.09 % (1367305)Peak memory usage: 16 MB
% 24.66/4.09 % (1367305)Instructions burned: 346 (million)
% 24.66/4.09 % (1367310)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=3334093052:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2966 on theBenchmark for (2966ds/387Mi)
% 24.66/4.09 % (1367313)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=1682904711:i=161:piset=and:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/161Mi)
% 24.66/4.09 % (1367312)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=1460256927:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2966 on theBenchmark for (2966ds/148Mi)
% 24.66/4.09 % (1367309)Instruction limit reached!
% 24.66/4.09 % (1367309)------------------------------
% 24.66/4.09 % (1367309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367309)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367309)Termination reason: Instruction limit
% 24.66/4.09 % (1367309)Termination phase: Property scanning
% 24.66/4.09 % (1367309)Time elapsed: 0.068 s
% 24.66/4.09 % (1367309)Peak memory usage: 11 MB
% 24.66/4.09 % (1367309)Instructions burned: 76 (million)
% 24.66/4.09 % (1367317)lrs+10_1_sil=128000:si=on:random_seed=2389740396:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2965 on theBenchmark for (2965ds/888Mi)
% 24.66/4.09 % (1367312)Instruction limit reached!
% 24.66/4.09 % (1367312)------------------------------
% 24.66/4.09 % (1367312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367312)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367312)Termination reason: Instruction limit
% 24.66/4.09 % (1367312)Termination phase: Saturation
% 24.66/4.09 % (1367312)Time elapsed: 0.115 s
% 24.66/4.09 % (1367312)Peak memory usage: 13 MB
% 24.66/4.09 % (1367312)Instructions burned: 148 (million)
% 24.66/4.09 % (1367313)Instruction limit reached!
% 24.66/4.09 % (1367313)------------------------------
% 24.66/4.09 % (1367313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367313)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367313)Termination reason: Instruction limit
% 24.66/4.09 % (1367313)Termination phase: Saturation
% 24.66/4.09 % (1367313)Time elapsed: 0.126 s
% 24.66/4.09 % (1367313)Peak memory usage: 13 MB
% 24.66/4.09 % (1367313)Instructions burned: 161 (million)
% 24.66/4.09 % (1367319)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=1357912266:i=136:add=on:ins=4:rtra=on:sup=off_2964 on theBenchmark for (2964ds/136Mi)
% 24.66/4.09 % (1367320)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=100198272:i=88:s2at=3:nm=2:rtra=on:rawr=on_2964 on theBenchmark for (2964ds/88Mi)
% 24.66/4.09 % (1367293) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1367102-1367293"...
% 24.66/4.09 % (1367320)Instruction limit reached!
% 24.66/4.09 % (1367320)------------------------------
% 24.66/4.09 % (1367320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367320)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367320)Termination reason: Instruction limit
% 24.66/4.09 % (1367320)Termination phase: SInE selection
% 24.66/4.09 % (1367320)Time elapsed: 0.069 s
% 24.66/4.09 % (1367320)Peak memory usage: 11 MB
% 24.66/4.09 % (1367320)Instructions burned: 88 (million)
% 24.66/4.09 % (1367310)Instruction limit reached!
% 24.66/4.09 % (1367310)------------------------------
% 24.66/4.09 % (1367310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367310)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367319)Instruction limit reached!
% 24.66/4.09 % (1367319)------------------------------
% 24.66/4.09 % (1367319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.09 % (1367310)Termination reason: Instruction limit
% 24.66/4.09 % (1367310)Termination phase: Saturation
% 24.66/4.09 % (1367310)Time elapsed: 0.295 s
% 24.66/4.09 % (1367310)Peak memory usage: 16 MB
% 24.66/4.09 % (1367319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.09 % (1367310)Instructions burned: 388 (million)
% 24.66/4.09 % (1367319)CaDiCaL version: 2.1.3
% 24.66/4.09 % (1367319)Termination reason: Instruction limit
% 24.66/4.09 % (1367319)Termination phase: Property scanning
% 24.66/4.09 % (1367319)Time elapsed: 0.111 s
% 24.66/4.09 % (1367319)Peak memory usage: 12 MB
% 24.66/4.09 % (1367319)Instructions burned: 136 (million)
% 24.66/4.09 % (1367323)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=3385532352:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2963 on theBenchmark for (2963ds/93Mi)
% 24.66/4.09 % (1367324)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3413077347:i=2186:rtra=on:ixr=off_2963 on theBenchmark for (2963ds/2186Mi)
% 24.66/4.09 % (1367325)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3150834069:s2a=on:i=240:rtra=on:ntd=on_2963 on theBenchmark for (2963ds/240Mi)
% 24.66/4.09 % (1367293)...printing done.
% 24.66/4.09 % (1367293)Refutation found. Thanks to Tanya!
% 24.66/4.09 % SZS status Theorem for theBenchmark
% 24.66/4.09 % SZS output start Proof for theBenchmark
% 24.66/4.09 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 24.66/4.09 thf(func_def_0, type, in: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 24.66/4.09 thf(func_def_3, type, setextAx: $o).
% 24.66/4.09 thf(func_def_5, type, emptysetAx: $o).
% 24.66/4.09 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 24.66/4.09 thf(func_def_7, type, setadjoinAx: $o).
% 24.66/4.09 thf(func_def_8, type, powerset: ($i > $i)).
% 24.66/4.09 thf(func_def_9, type, powersetAx: $o).
% 24.66/4.09 thf(func_def_10, type, setunion: ($i > $i)).
% 24.66/4.09 thf(func_def_11, type, setunionAx: $o).
% 24.66/4.09 thf(func_def_13, type, omega0Ax: $o).
% 24.66/4.09 thf(func_def_14, type, omegaSAx: $o).
% 24.66/4.09 thf(func_def_15, type, omegaIndAx: $o).
% 24.66/4.09 thf(func_def_16, type, replAx: $o).
% 24.66/4.09 thf(func_def_17, type, foundationAx: $o).
% 24.66/4.09 thf(func_def_18, type, wellorderingAx: $o).
% 24.66/4.09 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 24.66/4.09 thf(func_def_20, type, descrp: $o).
% 24.66/4.09 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 24.66/4.09 thf(func_def_22, type, dsetconstrI: $o).
% 24.66/4.09 thf(func_def_23, type, dsetconstrEL: $o).
% 24.66/4.09 thf(func_def_24, type, dsetconstrER: $o).
% 24.66/4.09 thf(func_def_25, type, exuE1: $o).
% 24.66/4.09 thf(func_def_26, type, prop2set: ($o > $i)).
% 24.66/4.09 thf(func_def_27, type, prop2setE: $o).
% 24.66/4.09 thf(func_def_28, type, emptysetE: $o).
% 24.66/4.09 thf(func_def_29, type, emptysetimpfalse: $o).
% 24.66/4.09 thf(func_def_30, type, notinemptyset: $o).
% 24.66/4.09 thf(func_def_31, type, exuE3e: $o).
% 24.66/4.09 thf(func_def_32, type, setext: $o).
% 24.66/4.09 thf(func_def_33, type, emptyI: $o).
% 24.66/4.09 thf(func_def_34, type, noeltsimpempty: $o).
% 24.66/4.09 thf(func_def_35, type, setbeta: $o).
% 24.66/4.09 thf(func_def_36, type, nonempty: ($i > $o)).
% 24.66/4.09 thf(func_def_37, type, nonemptyE1: $o).
% 24.66/4.09 thf(func_def_38, type, nonemptyI: $o).
% 24.66/4.09 thf(func_def_39, type, nonemptyI1: $o).
% 24.66/4.09 thf(func_def_40, type, setadjoinIL: $o).
% 24.66/4.09 thf(func_def_41, type, emptyinunitempty: $o).
% 24.66/4.09 thf(func_def_42, type, setadjoinIR: $o).
% 24.66/4.09 thf(func_def_43, type, setadjoinE: $o).
% 24.66/4.09 thf(func_def_44, type, setadjoinOr: $o).
% 24.66/4.09 thf(func_def_45, type, setoftrueEq: $o).
% 24.66/4.09 thf(func_def_46, type, powersetI: $o).
% 24.66/4.09 thf(func_def_47, type, emptyinPowerset: $o).
% 24.66/4.09 thf(func_def_48, type, emptyInPowerset: $o).
% 24.66/4.09 thf(func_def_49, type, powersetE: $o).
% 24.66/4.09 thf(func_def_50, type, setunionI: $o).
% 24.66/4.09 thf(func_def_51, type, setunionE: $o).
% 24.66/4.09 thf(func_def_52, type, subPowSU: $o).
% 24.66/4.09 thf(func_def_53, type, exuE2: $o).
% 24.66/4.09 thf(func_def_54, type, nonemptyImpWitness: $o).
% 24.66/4.09 thf(func_def_55, type, uniqinunit: $o).
% 24.66/4.09 thf(func_def_56, type, notinsingleton: $o).
% 24.66/4.09 thf(func_def_57, type, eqinunit: $o).
% 24.66/4.09 thf(func_def_58, type, singletonsswitch: $o).
% 24.66/4.09 thf(func_def_59, type, upairsetE: $o).
% 24.66/4.09 thf(func_def_60, type, upairsetIL: $o).
% 24.66/4.09 thf(func_def_61, type, upairsetIR: $o).
% 24.66/4.09 thf(func_def_62, type, emptyE1: $o).
% 24.66/4.09 thf(func_def_63, type, vacuousDall: $o).
% 24.66/4.09 thf(func_def_64, type, quantDeMorgan1: $o).
% 24.66/4.09 thf(func_def_65, type, quantDeMorgan2: $o).
% 24.66/4.09 thf(func_def_66, type, quantDeMorgan3: $o).
% 24.66/4.09 thf(func_def_67, type, quantDeMorgan4: $o).
% 24.66/4.09 thf(func_def_68, type, prop2setI: $o).
% 24.66/4.09 thf(func_def_69, type, set2prop: ($i > $o)).
% 24.66/4.09 thf(func_def_70, type, prop2set2propI: $o).
% 24.66/4.09 thf(func_def_71, type, notdexE: $o).
% 24.66/4.09 thf(func_def_72, type, notdallE: $o).
% 24.66/4.09 thf(func_def_73, type, exuI1: $o).
% 24.66/4.09 thf(func_def_74, type, exuI3: $o).
% 24.66/4.09 thf(func_def_75, type, exuI2: $o).
% 24.66/4.09 thf(func_def_76, type, inCongP: $o).
% 24.66/4.09 thf(func_def_77, type, in__Cong: $o).
% 24.66/4.09 thf(func_def_78, type, exuE3u: $o).
% 24.66/4.09 thf(func_def_79, type, exu__Cong: $o).
% 24.66/4.09 thf(func_def_80, type, emptyset__Cong: $o).
% 24.66/4.09 thf(func_def_81, type, setadjoin__Cong: $o).
% 24.66/4.09 thf(func_def_82, type, powerset__Cong: $o).
% 24.66/4.09 thf(func_def_83, type, setunion__Cong: $o).
% 24.66/4.09 thf(func_def_84, type, omega__Cong: $o).
% 24.66/4.09 thf(func_def_85, type, exuEu: $o).
% 24.66/4.09 thf(func_def_86, type, descr__Cong: $o).
% 24.66/4.09 thf(func_def_87, type, dsetconstr__Cong: $o).
% 24.66/4.09 thf(func_def_88, type, subset: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_91, type, subsetI1: $o).
% 24.66/4.09 thf(func_def_92, type, eqimpsubset2: $o).
% 24.66/4.09 thf(func_def_93, type, eqimpsubset1: $o).
% 24.66/4.09 thf(func_def_94, type, subsetI2: $o).
% 24.66/4.09 thf(func_def_95, type, emptysetsubset: $o).
% 24.66/4.09 thf(func_def_96, type, subsetE: $o).
% 24.66/4.09 thf(func_def_97, type, subsetE2: $o).
% 24.66/4.09 thf(func_def_98, type, notsubsetI: $o).
% 24.66/4.09 thf(func_def_99, type, notequalI1: $o).
% 24.66/4.09 thf(func_def_100, type, notequalI2: $o).
% 24.66/4.09 thf(func_def_101, type, subsetRefl: $o).
% 24.66/4.09 thf(func_def_102, type, subsetTrans: $o).
% 24.66/4.09 thf(func_def_103, type, setadjoinSub: $o).
% 24.66/4.09 thf(func_def_104, type, setadjoinSub2: $o).
% 24.66/4.09 thf(func_def_105, type, subset2powerset: $o).
% 24.66/4.09 thf(func_def_106, type, setextsub: $o).
% 24.66/4.09 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 24.66/4.09 thf(func_def_108, type, powersetI1: $o).
% 24.66/4.09 thf(func_def_109, type, powersetE1: $o).
% 24.66/4.09 thf(func_def_110, type, inPowerset: $o).
% 24.66/4.09 thf(func_def_111, type, powersetsubset: $o).
% 24.66/4.09 thf(func_def_112, type, sepInPowerset: $o).
% 24.66/4.09 thf(func_def_113, type, sepSubset: $o).
% 24.66/4.09 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 24.66/4.09 thf(func_def_115, type, binunionIL: $o).
% 24.66/4.09 thf(func_def_116, type, upairset2IR: $o).
% 24.66/4.09 thf(func_def_117, type, binunionIR: $o).
% 24.66/4.09 thf(func_def_118, type, binunionEcases: $o).
% 24.66/4.09 thf(func_def_119, type, binunionE: $o).
% 24.66/4.09 thf(func_def_120, type, binunionLsub: $o).
% 24.66/4.09 thf(func_def_121, type, binunionRsub: $o).
% 24.66/4.09 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 24.66/4.09 thf(func_def_123, type, binintersectI: $o).
% 24.66/4.09 thf(func_def_124, type, binintersectSubset5: $o).
% 24.66/4.09 thf(func_def_125, type, binintersectEL: $o).
% 24.66/4.09 thf(func_def_126, type, binintersectLsub: $o).
% 24.66/4.09 thf(func_def_127, type, binintersectSubset2: $o).
% 24.66/4.09 thf(func_def_128, type, binintersectSubset3: $o).
% 24.66/4.09 thf(func_def_129, type, binintersectER: $o).
% 24.66/4.09 thf(func_def_130, type, disjointsetsI1: $o).
% 24.66/4.09 thf(func_def_131, type, binintersectRsub: $o).
% 24.66/4.09 thf(func_def_132, type, binintersectSubset4: $o).
% 24.66/4.09 thf(func_def_133, type, binintersectSubset1: $o).
% 24.66/4.09 thf(func_def_134, type, bs114d: $o).
% 24.66/4.09 thf(func_def_135, type, regular: ($i > $o)).
% 24.66/4.09 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 24.66/4.09 thf(func_def_137, type, setminusI: $o).
% 24.66/4.09 thf(func_def_138, type, setminusEL: $o).
% 24.66/4.09 thf(func_def_139, type, setminusER: $o).
% 24.66/4.09 thf(func_def_140, type, setminusSubset2: $o).
% 24.66/4.09 thf(func_def_141, type, setminusERneg: $o).
% 24.66/4.09 thf(func_def_142, type, setminusELneg: $o).
% 24.66/4.09 thf(func_def_143, type, setminusILneg: $o).
% 24.66/4.09 thf(func_def_144, type, setminusIRneg: $o).
% 24.66/4.09 thf(func_def_145, type, setminusLsub: $o).
% 24.66/4.09 thf(func_def_146, type, setminusSubset1: $o).
% 24.66/4.09 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 24.66/4.09 thf(func_def_148, type, symdiffE: $o).
% 24.66/4.09 thf(func_def_149, type, symdiffI1: $o).
% 24.66/4.09 thf(func_def_150, type, symdiffI2: $o).
% 24.66/4.09 thf(func_def_151, type, symdiffIneg1: $o).
% 24.66/4.09 thf(func_def_152, type, symdiffIneg2: $o).
% 24.66/4.09 thf(func_def_153, type, iskpair: ($i > $o)).
% 24.66/4.09 thf(func_def_154, type, secondinupair: $o).
% 24.66/4.09 thf(func_def_155, type, setukpairIL: $o).
% 24.66/4.09 thf(func_def_156, type, setukpairIR: $o).
% 24.66/4.09 thf(func_def_157, type, kpairiskpair: $o).
% 24.66/4.09 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 24.66/4.09 thf(func_def_159, type, kpairp: $o).
% 24.66/4.09 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 24.66/4.09 thf(func_def_161, type, singletonsubset: $o).
% 24.66/4.09 thf(func_def_162, type, singletoninpowerset: $o).
% 24.66/4.09 thf(func_def_163, type, singletoninpowunion: $o).
% 24.66/4.09 thf(func_def_164, type, upairset2E: $o).
% 24.66/4.09 thf(func_def_165, type, upairsubunion: $o).
% 24.66/4.09 thf(func_def_166, type, upairinpowunion: $o).
% 24.66/4.09 thf(func_def_167, type, ubforcartprodlem1: $o).
% 24.66/4.09 thf(func_def_168, type, ubforcartprodlem2: $o).
% 24.66/4.09 thf(func_def_169, type, ubforcartprodlem3: $o).
% 24.66/4.09 thf(func_def_170, type, cartprodpairin: $o).
% 24.66/4.09 thf(func_def_171, type, cartprodmempair1: $o).
% 24.66/4.09 thf(func_def_172, type, cartprodmempair: $o).
% 24.66/4.09 thf(func_def_173, type, setunionE2: $o).
% 24.66/4.09 thf(func_def_174, type, setunionsingleton1: $o).
% 24.66/4.09 thf(func_def_175, type, setunionsingleton2: $o).
% 24.66/4.09 thf(func_def_176, type, setunionsingleton: $o).
% 24.66/4.09 thf(func_def_177, type, singleton: ($i > $o)).
% 24.66/4.09 thf(func_def_178, type, singletonprop: $o).
% 24.66/4.09 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 24.66/4.09 thf(func_def_180, type, ex1E1: $o).
% 24.66/4.09 thf(func_def_181, type, ex1I: $o).
% 24.66/4.09 thf(func_def_182, type, ex1I2: $o).
% 24.66/4.09 thf(func_def_183, type, singletonsuniq: $o).
% 24.66/4.09 thf(func_def_184, type, atmost1p: ($i > $o)).
% 24.66/4.09 thf(func_def_185, type, atleast2p: ($i > $o)).
% 24.66/4.09 thf(func_def_186, type, atmost2p: ($i > $o)).
% 24.66/4.09 thf(func_def_187, type, upairsetp: ($i > $o)).
% 24.66/4.09 thf(func_def_188, type, setukpairinjL1: $o).
% 24.66/4.09 thf(func_def_189, type, kfstsingleton: $o).
% 24.66/4.09 thf(func_def_190, type, theprop: $o).
% 24.66/4.09 thf(func_def_191, type, kfst: ($i > $i)).
% 24.66/4.09 thf(func_def_192, type, kfstpairEq: $o).
% 24.66/4.09 thf(func_def_193, type, cartprodfstin: $o).
% 24.66/4.09 thf(func_def_194, type, setukpairinjL2: $o).
% 24.66/4.09 thf(func_def_195, type, setukpairinjL: $o).
% 24.66/4.09 thf(func_def_196, type, setukpairinjR11: $o).
% 24.66/4.09 thf(func_def_197, type, setukpairinjR12: $o).
% 24.66/4.09 thf(func_def_198, type, setukpairinjR1: $o).
% 24.66/4.09 thf(func_def_199, type, upairequniteq: $o).
% 24.66/4.09 thf(func_def_200, type, setukpairinjR2: $o).
% 24.66/4.09 thf(func_def_201, type, setukpairinjR: $o).
% 24.66/4.09 thf(func_def_202, type, ksndsingleton: $o).
% 24.66/4.09 thf(func_def_203, type, ksnd: ($i > $i)).
% 24.66/4.09 thf(func_def_204, type, ksndpairEq: $o).
% 24.66/4.09 thf(func_def_205, type, kpairsurjEq: $o).
% 24.66/4.09 thf(func_def_206, type, cartprodsndin: $o).
% 24.66/4.09 thf(func_def_207, type, cartprodpairmemEL: $o).
% 24.66/4.09 thf(func_def_208, type, cartprodpairmemER: $o).
% 24.66/4.09 thf(func_def_209, type, cartprodmempaircEq: $o).
% 24.66/4.09 thf(func_def_210, type, cartprodfstpairEq: $o).
% 24.66/4.09 thf(func_def_211, type, cartprodsndpairEq: $o).
% 24.66/4.09 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 24.66/4.09 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 24.66/4.09 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 24.66/4.09 thf(func_def_215, type, dpsetconstrI: $o).
% 24.66/4.09 thf(func_def_216, type, dpsetconstrSub: $o).
% 24.66/4.09 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 24.66/4.09 thf(func_def_218, type, dpsetconstrERa: $o).
% 24.66/4.09 thf(func_def_219, type, dpsetconstrEL1: $o).
% 24.66/4.09 thf(func_def_220, type, dpsetconstrEL2: $o).
% 24.66/4.09 thf(func_def_221, type, dpsetconstrER: $o).
% 24.66/4.09 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 24.66/4.09 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 24.66/4.09 thf(func_def_224, type, funcImageSingleton: $o).
% 24.66/4.09 thf(func_def_225, type, apProp: $o).
% 24.66/4.09 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 24.66/4.09 thf(func_def_227, type, app: $o).
% 24.66/4.09 thf(func_def_228, type, infuncsetfunc: $o).
% 24.66/4.09 thf(func_def_229, type, ap2p: $o).
% 24.66/4.09 thf(func_def_230, type, funcinfuncset: $o).
% 24.66/4.09 thf(func_def_231, type, lamProp: $o).
% 24.66/4.09 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 24.66/4.09 thf(func_def_233, type, lamp: $o).
% 24.66/4.09 thf(func_def_234, type, lam2p: $o).
% 24.66/4.09 thf(func_def_235, type, brelnall1: $o).
% 24.66/4.09 thf(func_def_236, type, brelnall2: $o).
% 24.66/4.09 thf(func_def_237, type, ex1E2: $o).
% 24.66/4.09 thf(func_def_238, type, funcGraphProp1: $o).
% 24.66/4.09 thf(func_def_239, type, funcGraphProp3: $o).
% 24.66/4.09 thf(func_def_240, type, funcGraphProp2: $o).
% 24.66/4.09 thf(func_def_241, type, funcextLem: $o).
% 24.66/4.09 thf(func_def_242, type, funcGraphProp4: $o).
% 24.66/4.09 thf(func_def_243, type, subbreln: $o).
% 24.66/4.09 thf(func_def_244, type, eqbreln: $o).
% 24.66/4.09 thf(func_def_245, type, funcext: $o).
% 24.66/4.09 thf(func_def_246, type, funcext2: $o).
% 24.66/4.09 thf(func_def_247, type, ap2apEq1: $o).
% 24.66/4.09 thf(func_def_248, type, ap2apEq2: $o).
% 24.66/4.09 thf(func_def_249, type, beta1: $o).
% 24.66/4.09 thf(func_def_250, type, eta1: $o).
% 24.66/4.09 thf(func_def_251, type, lam2lamEq: $o).
% 24.66/4.09 thf(func_def_252, type, beta2: $o).
% 24.66/4.09 thf(func_def_253, type, eta2: $o).
% 24.66/4.09 thf(func_def_254, type, iffalseProp1: $o).
% 24.66/4.09 thf(func_def_255, type, iffalseProp2: $o).
% 24.66/4.09 thf(func_def_256, type, iftrueProp1: $o).
% 24.66/4.09 thf(func_def_257, type, iftrueProp2: $o).
% 24.66/4.09 thf(func_def_258, type, ifSingleton: $o).
% 24.66/4.09 thf(func_def_259, type, if: ($i > $o > $i > $i > $i)).
% 24.66/4.09 thf(func_def_260, type, ifp: $o).
% 24.66/4.09 thf(func_def_261, type, theeq: $o).
% 24.66/4.09 thf(func_def_262, type, iftrue: $o).
% 24.66/4.09 thf(func_def_263, type, iffalse: $o).
% 24.66/4.09 thf(func_def_264, type, iftrueorfalse: $o).
% 24.66/4.09 thf(func_def_265, type, binintersectT_lem: $o).
% 24.66/4.09 thf(func_def_266, type, binunionT_lem: $o).
% 24.66/4.09 thf(func_def_267, type, powersetT_lem: $o).
% 24.66/4.09 thf(func_def_268, type, setminusT_lem: $o).
% 24.66/4.09 thf(func_def_269, type, complementT_lem: $o).
% 24.66/4.09 thf(func_def_270, type, setextT: $o).
% 24.66/4.09 thf(func_def_271, type, subsetTI: $o).
% 24.66/4.09 thf(func_def_272, type, powersetTI1: $o).
% 24.66/4.09 thf(func_def_273, type, powersetTE1: $o).
% 24.66/4.09 thf(func_def_274, type, complementTI1: $o).
% 24.66/4.09 thf(func_def_275, type, complementTE1: $o).
% 24.66/4.09 thf(func_def_276, type, binintersectTELcontra: $o).
% 24.66/4.09 thf(func_def_277, type, binintersectTERcontra: $o).
% 24.66/4.09 thf(func_def_278, type, contrasubsetT: $o).
% 24.66/4.09 thf(func_def_279, type, contrasubsetT1: $o).
% 24.66/4.09 thf(func_def_280, type, contrasubsetT2: $o).
% 24.66/4.09 thf(func_def_281, type, contrasubsetT3: $o).
% 24.66/4.09 thf(func_def_282, type, doubleComplementI1: $o).
% 24.66/4.09 thf(func_def_283, type, doubleComplementE1: $o).
% 24.66/4.09 thf(func_def_284, type, doubleComplementSub1: $o).
% 24.66/4.09 thf(func_def_285, type, doubleComplementSub2: $o).
% 24.66/4.09 thf(func_def_286, type, doubleComplementEq: $o).
% 24.66/4.09 thf(func_def_287, type, complementTnotintersectT: $o).
% 24.66/4.09 thf(func_def_288, type, complementImpComplementIntersect: $o).
% 24.66/4.09 thf(func_def_289, type, complementSubsetComplementIntersect: $o).
% 24.66/4.09 thf(func_def_290, type, complementInPowersetComplementIntersect: $o).
% 24.66/4.09 thf(func_def_291, type, contraSubsetComplement: $o).
% 24.66/4.09 thf(func_def_292, type, complementTcontraSubset: $o).
% 24.66/4.09 thf(func_def_293, type, binunionTILcontra: $o).
% 24.66/4.09 thf(func_def_294, type, binunionTIRcontra: $o).
% 24.66/4.09 thf(func_def_295, type, inIntersectImpInUnion: $o).
% 24.66/4.09 thf(func_def_296, type, inIntersectImpInUnion2: $o).
% 24.66/4.09 thf(func_def_297, type, inIntersectImpInIntersectUnions: $o).
% 24.66/4.09 thf(func_def_298, type, intersectInPowersetIntersectUnions: $o).
% 24.66/4.09 thf(func_def_299, type, inComplementUnionImpNotIn1: $o).
% 24.66/4.09 thf(func_def_300, type, inComplementUnionImpInComplement1: $o).
% 24.66/4.09 thf(func_def_301, type, binunionTE: $o).
% 24.66/4.09 thf(func_def_302, type, binunionTEcontra: $o).
% 24.66/4.09 thf(func_def_303, type, demorgan2a1: $o).
% 24.66/4.09 thf(func_def_304, type, complementUnionInPowersetComplement: $o).
% 24.66/4.09 thf(func_def_305, type, demorgan2a2: $o).
% 24.66/4.09 thf(func_def_306, type, demorgan1a: $o).
% 24.66/4.09 thf(func_def_307, type, demorgan1b: $o).
% 24.66/4.09 thf(func_def_308, type, demorgan1: $o).
% 24.66/4.09 thf(func_def_309, type, demorgan2a: $o).
% 24.66/4.09 thf(func_def_310, type, demorgan2b2: $o).
% 24.66/4.09 thf(func_def_311, type, demorgan2b: $o).
% 24.66/4.09 thf(func_def_312, type, demorgan2: $o).
% 24.66/4.09 thf(func_def_313, type, woz13rule0: $o).
% 24.66/4.09 thf(func_def_314, type, woz13rule1: $o).
% 24.66/4.09 thf(func_def_315, type, woz13rule2: $o).
% 24.66/4.09 thf(func_def_316, type, woz13rule3: $o).
% 24.66/4.09 thf(func_def_317, type, woz13rule4: $o).
% 24.66/4.09 thf(func_def_318, type, woz1_1: $o).
% 24.66/4.09 thf(func_def_319, type, woz1_2: $o).
% 24.66/4.09 thf(func_def_320, type, woz1_3: $o).
% 24.66/4.09 thf(func_def_321, type, woz1_4: $o).
% 24.66/4.09 thf(func_def_322, type, woz1_5: $o).
% 24.66/4.09 thf(func_def_323, type, breln1: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_324, type, breln1all2: $o).
% 24.66/4.09 thf(func_def_325, type, breln1Set: ($i > $i)).
% 24.66/4.09 thf(func_def_326, type, breln1SetBreln1: $o).
% 24.66/4.09 thf(func_def_327, type, transitive: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_328, type, antisymmetric: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_329, type, reflexive: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_330, type, refltransitive: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_331, type, refllinearorder: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_332, type, reflwellordering: ($i > $i > $o)).
% 24.66/4.09 thf(func_def_333, type, choice2fnsingleton: $o).
% 24.66/4.09 thf(func_def_334, type, setOfPairsIsBReln1: $o).
% 24.66/4.09 thf(func_def_335, type, breln1all1: $o).
% 24.66/4.09 thf(func_def_336, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 24.66/4.09 thf(func_def_337, type, vIMP: ($o > $o > $o)).
% 24.66/4.09 thf(func_def_338, type, db1: !>[X0: $tType]:(X0)).
% 24.66/4.09 thf(func_def_339, type, db0: !>[X0: $tType]:(X0)).
% 24.66/4.09 thf(func_def_340, type, db2: !>[X0: $tType]:(X0)).
% 24.66/4.09 thf(func_def_341, type, vNOT: ($o > $o)).
% 24.66/4.09 thf(func_def_342, type, db3: !>[X0: $tType]:(X0)).
% 24.66/4.09 thf(func_def_343, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 24.66/4.09 thf(func_def_344, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 24.66/4.09 thf(func_def_345, type, db4: !>[X0: $tType]:(X0)).
% 24.66/4.09 thf(func_def_346, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 24.66/4.09 thf(func_def_347, type, vAND: ($o > $o > $o)).
% 24.66/4.09 thf(func_def_348, type, vOR: ($o > $o > $o)).
% 24.66/4.09 thf(func_def_349, type, vIFF: ($o > $o > $o)).
% 24.66/4.09 thf(func_def_350, type, db5: !>[X0: $tType]:(X0)).
% 24.66/4.09 thf(func_def_353, type, db6: !>[X0: $tType]:(X0)).
% 24.66/4.09 thf(func_def_354, type, sF0: $o).
% 24.66/4.09 thf(func_def_355, type, sF1: $o).
% 24.66/4.09 thf(func_def_356, type, sF2: $o).
% 24.66/4.09 thf(func_def_357, type, sF3: $o).
% 24.66/4.09 thf(func_def_358, type, sF4: $o).
% 24.66/4.09 thf(func_def_359, type, sF5: $o).
% 24.66/4.09 thf(func_def_360, type, sF6: $o).
% 24.66/4.09 thf(func_def_361, type, sF7: $o).
% 24.66/4.09 thf(func_def_362, type, sF8: $o).
% 24.66/4.09 thf(func_def_363, type, sF9: $o).
% 24.66/4.09 thf(func_def_364, type, sF10: $o).
% 24.66/4.09 thf(func_def_365, type, sF11: $o).
% 24.66/4.09 thf(func_def_366, type, sF12: $o).
% 24.66/4.09 thf(func_def_367, type, sF13: $o).
% 24.66/4.09 thf(func_def_368, type, sF14: $o).
% 24.66/4.09 thf(func_def_369, type, sF15: $o).
% 24.66/4.09 thf(func_def_370, type, sF16: $o).
% 24.66/4.09 thf(func_def_371, type, sF17: $o).
% 24.66/4.09 thf(func_def_372, type, sF18: $o).
% 24.66/4.09 thf(func_def_373, type, sF19: $o).
% 24.66/4.09 thf(func_def_374, type, sF20: $o).
% 24.66/4.09 thf(func_def_375, type, sF21: $o).
% 24.66/4.09 thf(func_def_376, type, sF22: $o).
% 24.66/4.09 thf(func_def_377, type, sF23: $o).
% 24.66/4.09 thf(func_def_378, type, sF24: $o).
% 24.66/4.09 thf(func_def_379, type, sF25: $o).
% 24.66/4.09 thf(func_def_380, type, sF26: $o).
% 24.66/4.09 thf(func_def_381, type, sF27: $o).
% 24.66/4.09 thf(func_def_382, type, sF28: $o).
% 24.66/4.09 thf(func_def_383, type, sF29: $o).
% 24.66/4.09 thf(func_def_384, type, sF30: $o).
% 24.66/4.09 thf(func_def_385, type, sF31: $o).
% 24.66/4.09 thf(func_def_386, type, sF32: $o).
% 24.66/4.09 thf(func_def_387, type, sF33: $o).
% 24.66/4.09 thf(func_def_388, type, sF34: $o).
% 24.66/4.09 thf(func_def_389, type, sF35: $o).
% 24.66/4.09 thf(func_def_390, type, sF36: $o).
% 24.66/4.09 thf(func_def_391, type, sF37: $o).
% 24.66/4.09 thf(func_def_392, type, sF38: $o).
% 24.66/4.09 thf(func_def_393, type, sF39: $o).
% 24.66/4.09 thf(func_def_394, type, sF40: $o).
% 24.66/4.09 thf(func_def_395, type, sF41: $o).
% 24.66/4.09 thf(func_def_396, type, sF42: $o).
% 24.66/4.09 thf(func_def_397, type, sF43: $o).
% 24.66/4.09 thf(func_def_398, type, sF44: $o).
% 24.66/4.09 thf(func_def_399, type, sF45: $o).
% 24.66/4.09 thf(func_def_400, type, sF46: $o).
% 24.66/4.09 thf(func_def_401, type, sF47: $o).
% 24.66/4.09 thf(func_def_402, type, sF48: $o).
% 24.66/4.09 thf(func_def_403, type, sF49: $o).
% 24.66/4.09 thf(func_def_404, type, sF50: $o).
% 24.66/4.09 thf(func_def_405, type, sF51: $o).
% 24.66/4.09 thf(func_def_406, type, sF52: $o).
% 24.66/4.09 thf(func_def_407, type, sF53: $o).
% 24.66/4.09 thf(func_def_408, type, sF54: $o).
% 24.66/4.09 thf(func_def_409, type, sF55: $o).
% 24.66/4.09 thf(func_def_410, type, sF56: $o).
% 24.66/4.09 thf(func_def_411, type, sF57: $o).
% 24.66/4.09 thf(func_def_412, type, sF58: $o).
% 24.66/4.09 thf(func_def_413, type, sF59: $o).
% 24.66/4.09 thf(func_def_414, type, sF60: $o).
% 24.66/4.09 thf(func_def_415, type, sF61: $o).
% 24.66/4.09 thf(func_def_416, type, sF62: $o).
% 24.66/4.09 thf(func_def_417, type, sF63: $o).
% 24.66/4.09 thf(func_def_418, type, sF64: $o).
% 24.66/4.09 thf(func_def_419, type, sF65: $o).
% 24.66/4.09 thf(func_def_420, type, sF66: $o).
% 24.66/4.09 thf(func_def_421, type, sF67: $o).
% 24.66/4.09 thf(func_def_422, type, sF68: $o).
% 24.66/4.09 thf(func_def_423, type, sF69: $o).
% 24.66/4.09 thf(func_def_424, type, sF70: $o).
% 24.66/4.09 thf(func_def_425, type, sF71: $o).
% 24.66/4.09 thf(func_def_426, type, sF72: $o).
% 24.66/4.09 thf(func_def_427, type, sF73: $o).
% 24.66/4.09 thf(func_def_428, type, sF74: $o).
% 24.66/4.09 thf(func_def_429, type, sF75: $o).
% 24.66/4.09 thf(func_def_430, type, sF76: $o).
% 24.66/4.09 thf(func_def_431, type, sF77: $o).
% 24.66/4.09 thf(func_def_432, type, sF78: $o).
% 24.66/4.09 thf(func_def_433, type, sF79: $o).
% 24.66/4.09 thf(func_def_434, type, sF80: $o).
% 24.66/4.09 thf(func_def_435, type, sF81: $o).
% 24.66/4.09 thf(func_def_436, type, sF82: $o).
% 24.66/4.09 thf(func_def_437, type, sF83: $o).
% 24.66/4.09 thf(func_def_438, type, sF84: $o).
% 24.66/4.09 thf(func_def_439, type, sF85: $o).
% 24.66/4.09 thf(func_def_440, type, sF86: $o).
% 24.66/4.09 thf(func_def_441, type, sF87: $o).
% 24.66/4.09 thf(func_def_442, type, sF88: $o).
% 24.66/4.09 thf(func_def_443, type, sF89: $o).
% 24.66/4.09 thf(func_def_444, type, sF90: $o).
% 24.66/4.09 thf(func_def_445, type, sF91: $o).
% 24.66/4.09 thf(func_def_446, type, sF92: $o).
% 24.66/4.09 thf(func_def_447, type, sF93: $o).
% 24.66/4.09 thf(func_def_448, type, sF94: $o).
% 24.66/4.09 thf(func_def_449, type, sF95: $o).
% 24.66/4.09 thf(func_def_450, type, sF96: $o).
% 24.66/4.09 thf(func_def_451, type, sF97: $o).
% 24.66/4.09 thf(func_def_452, type, sF98: $o).
% 24.66/4.09 thf(func_def_453, type, sF99: $o).
% 24.66/4.09 thf(func_def_454, type, sF100: $o).
% 24.66/4.09 thf(func_def_455, type, sF101: $o).
% 24.66/4.09 thf(func_def_456, type, sF102: $o).
% 24.66/4.09 thf(func_def_457, type, sF103: $o).
% 24.66/4.09 thf(func_def_458, type, sF104: $o).
% 24.66/4.09 thf(func_def_459, type, sF105: $o).
% 24.66/4.09 thf(func_def_460, type, sF106: $o).
% 24.66/4.09 thf(func_def_461, type, sF107: $o).
% 24.66/4.09 thf(func_def_462, type, sF108: $o).
% 24.66/4.09 thf(func_def_463, type, sF109: $o).
% 24.66/4.09 thf(func_def_464, type, sF110: $o).
% 24.66/4.09 thf(func_def_465, type, sF111: $o).
% 24.66/4.09 thf(func_def_466, type, sF112: $o).
% 24.66/4.09 thf(func_def_467, type, sF113: $o).
% 24.66/4.09 thf(func_def_468, type, sF114: $o).
% 24.66/4.09 thf(func_def_469, type, sF115: $o).
% 24.66/4.09 thf(func_def_470, type, sF116: $o).
% 24.66/4.09 thf(func_def_471, type, sF117: $o).
% 24.66/4.09 thf(func_def_472, type, sF118: $o).
% 24.66/4.09 thf(func_def_473, type, sF119: $o).
% 24.66/4.09 thf(func_def_474, type, sF120: $o).
% 24.66/4.09 thf(func_def_475, type, sF121: $o).
% 24.66/4.09 thf(func_def_476, type, sF122: $o).
% 24.66/4.09 thf(func_def_477, type, sF123: $o).
% 24.66/4.09 thf(func_def_478, type, sF124: $o).
% 24.66/4.09 thf(func_def_479, type, sF125: $o).
% 24.66/4.09 thf(func_def_480, type, sF126: $o).
% 24.66/4.09 thf(func_def_481, type, sF127: $o).
% 24.66/4.09 thf(func_def_482, type, sF128: $o).
% 24.66/4.09 thf(func_def_483, type, sF129: $o).
% 24.66/4.09 thf(func_def_484, type, sF130: $o).
% 24.66/4.09 thf(func_def_485, type, sF131: $o).
% 24.66/4.09 thf(func_def_486, type, sF132: $o).
% 24.66/4.09 thf(func_def_487, type, sF133: $o).
% 24.66/4.09 thf(func_def_488, type, sF134: $o).
% 24.66/4.09 thf(func_def_489, type, sF135: $o).
% 24.66/4.09 thf(func_def_490, type, sF136: $o).
% 24.66/4.09 thf(func_def_491, type, sF137: $o).
% 24.66/4.09 thf(func_def_492, type, sF138: $o).
% 24.66/4.09 thf(func_def_493, type, sF139: $o).
% 24.66/4.09 thf(func_def_494, type, sF140: $o).
% 24.66/4.09 thf(func_def_495, type, sF141: $o).
% 24.66/4.09 thf(func_def_496, type, sF142: $o).
% 24.66/4.09 thf(func_def_497, type, sF143: $o).
% 24.66/4.09 thf(func_def_498, type, sF144: $o).
% 24.66/4.09 thf(func_def_499, type, sF145: $o).
% 24.66/4.09 thf(func_def_500, type, sF146: $o).
% 24.66/4.09 thf(func_def_501, type, sF147: $o).
% 24.66/4.09 thf(func_def_502, type, sF148: $o).
% 24.66/4.09 thf(func_def_503, type, sF149: $o).
% 24.66/4.09 thf(func_def_504, type, sF150: $o).
% 24.66/4.09 thf(func_def_505, type, sF151: $o).
% 24.66/4.09 thf(func_def_506, type, sF152: $o).
% 24.66/4.09 thf(func_def_507, type, sF153: $o).
% 24.66/4.09 thf(func_def_508, type, sF154: $o).
% 24.66/4.09 thf(func_def_509, type, sF155: $o).
% 24.66/4.09 thf(func_def_510, type, sF156: $o).
% 24.66/4.09 thf(func_def_511, type, sF157: $o).
% 24.66/4.09 thf(func_def_512, type, sF158: $o).
% 24.66/4.09 thf(func_def_513, type, sF159: $o).
% 24.66/4.09 thf(func_def_514, type, sF160: $o).
% 24.66/4.09 thf(func_def_515, type, sF161: $o).
% 24.66/4.09 thf(func_def_516, type, sF162: $o).
% 24.66/4.09 thf(func_def_517, type, sF163: $o).
% 24.66/4.09 thf(func_def_518, type, sF164: $o).
% 24.66/4.09 thf(func_def_519, type, sF165: $o).
% 24.66/4.09 thf(func_def_520, type, sF166: $o).
% 24.66/4.09 thf(func_def_521, type, sF167: $o).
% 24.66/4.09 thf(func_def_522, type, sF168: $o).
% 24.66/4.09 thf(func_def_523, type, sF169: $o).
% 24.66/4.09 thf(func_def_524, type, sF170: $o).
% 24.66/4.09 thf(func_def_525, type, sF171: $o).
% 24.66/4.09 thf(func_def_526, type, sF172: $o).
% 24.66/4.09 thf(func_def_527, type, sF173: $o).
% 24.66/4.09 thf(func_def_528, type, sF174: $o).
% 24.66/4.09 thf(func_def_529, type, sF175: $o).
% 24.66/4.09 thf(func_def_530, type, sF176: $o).
% 24.66/4.09 thf(func_def_531, type, sF177: $o).
% 24.66/4.09 thf(func_def_532, type, sF178: $o).
% 24.66/4.09 thf(func_def_533, type, sF179: $o).
% 24.66/4.09 thf(func_def_534, type, sF180: $o).
% 24.66/4.09 thf(func_def_535, type, sF181: $o).
% 24.66/4.09 thf(func_def_536, type, sF182: $o).
% 24.66/4.09 thf(func_def_537, type, sF183: $o).
% 24.66/4.09 thf(func_def_538, type, sF184: $o).
% 24.66/4.09 thf(func_def_539, type, sF185: $o).
% 24.66/4.09 thf(func_def_540, type, sF186: $o).
% 24.66/4.09 thf(func_def_541, type, sF187: $o).
% 24.66/4.09 thf(func_def_542, type, sF188: $o).
% 24.66/4.09 thf(func_def_543, type, sF189: $o).
% 24.66/4.09 thf(func_def_544, type, sF190: $o).
% 24.66/4.09 thf(func_def_545, type, sF191: $o).
% 24.66/4.09 thf(func_def_546, type, sF192: $o).
% 24.66/4.09 thf(func_def_547, type, sF193: $o).
% 24.66/4.09 thf(func_def_548, type, sF194: $o).
% 24.66/4.09 thf(func_def_549, type, sF195: $o).
% 24.66/4.09 thf(func_def_550, type, sF196: $o).
% 24.66/4.09 thf(func_def_551, type, sF197: $o).
% 24.66/4.09 thf(func_def_552, type, sF198: $o).
% 24.66/4.09 thf(func_def_553, type, sF199: $o).
% 24.66/4.09 thf(func_def_554, type, sF200: $o).
% 24.66/4.09 thf(func_def_555, type, sF201: $o).
% 24.66/4.09 thf(func_def_556, type, sF202: $o).
% 24.66/4.09 thf(func_def_557, type, sF203: $o).
% 24.66/4.09 thf(func_def_558, type, sF204: $o).
% 24.66/4.09 thf(func_def_559, type, sF205: $o).
% 24.66/4.09 thf(func_def_560, type, sF206: $o).
% 24.66/4.09 thf(func_def_561, type, sF207: $o).
% 24.66/4.09 thf(func_def_562, type, sF208: $o).
% 24.66/4.09 thf(func_def_563, type, sF209: $o).
% 24.66/4.09 thf(func_def_564, type, sF210: $o).
% 24.66/4.09 thf(func_def_565, type, sF211: $o).
% 24.66/4.09 thf(func_def_566, type, sF212: $o).
% 24.66/4.09 thf(func_def_567, type, sF213: $o).
% 24.66/4.09 thf(func_def_568, type, sF214: $o).
% 24.66/4.09 thf(func_def_569, type, sF215: $o).
% 24.66/4.09 thf(func_def_570, type, sF216: $o).
% 24.66/4.09 thf(func_def_571, type, sF217: $o).
% 24.66/4.09 thf(func_def_572, type, sF218: $o).
% 24.66/4.09 thf(func_def_573, type, sF219: $o).
% 24.66/4.09 thf(func_def_574, type, sF220: $o).
% 24.66/4.09 thf(func_def_575, type, sF221: $o).
% 24.66/4.09 thf(func_def_576, type, sF222: $o).
% 24.66/4.09 thf(func_def_577, type, sF223: $o).
% 24.66/4.09 thf(func_def_578, type, sF224: $o).
% 24.66/4.09 thf(func_def_579, type, sF225: $o).
% 24.66/4.09 thf(func_def_580, type, sF226: $o).
% 24.66/4.09 thf(func_def_581, type, sF227: $o).
% 24.66/4.09 thf(func_def_582, type, sF228: $o).
% 24.66/4.09 thf(func_def_583, type, sF229: $o).
% 24.66/4.09 thf(func_def_584, type, sF230: $o).
% 24.66/4.09 thf(func_def_585, type, sF231: $o).
% 24.66/4.09 thf(func_def_586, type, sF232: $o).
% 24.66/4.09 thf(func_def_587, type, sF233: $o).
% 24.66/4.09 thf(func_def_588, type, sF234: $o).
% 24.66/4.09 thf(func_def_589, type, sF235: $o).
% 24.66/4.09 thf(func_def_590, type, sF236: $o).
% 24.66/4.09 thf(func_def_591, type, sF237: $o).
% 24.66/4.09 thf(func_def_592, type, sF238: $o).
% 24.66/4.09 thf(func_def_593, type, sF239: $o).
% 24.66/4.09 thf(func_def_594, type, sF240: $o).
% 24.66/4.09 thf(func_def_595, type, sF241: $o).
% 24.66/4.09 thf(func_def_596, type, sF242: $o).
% 24.66/4.09 thf(func_def_597, type, sF243: $o).
% 24.66/4.09 thf(func_def_598, type, sF244: $o).
% 24.66/4.09 thf(func_def_599, type, sF245: $o).
% 24.66/4.09 thf(func_def_600, type, sF246: $o).
% 24.66/4.09 thf(func_def_601, type, sF247: $o).
% 24.66/4.09 thf(func_def_602, type, sF248: $o).
% 24.66/4.09 thf(func_def_603, type, sF249: $o).
% 24.66/4.09 thf(func_def_604, type, sF250: $o).
% 24.66/4.09 thf(func_def_605, type, sF251: $o).
% 24.66/4.09 thf(func_def_606, type, sF252: $o).
% 24.66/4.09 thf(func_def_607, type, sF253: $o).
% 24.66/4.09 thf(func_def_608, type, sF254: $o).
% 24.66/4.09 thf(func_def_609, type, sF255: $o).
% 24.66/4.09 thf(func_def_610, type, sF256: $o).
% 24.66/4.09 thf(func_def_611, type, sF257: $o).
% 24.66/4.09 thf(func_def_612, type, sF258: $o).
% 24.66/4.09 thf(func_def_613, type, sF259: $o).
% 24.66/4.09 thf(func_def_614, type, sF260: $o).
% 24.66/4.09 thf(func_def_615, type, sF261: $o).
% 24.66/4.09 thf(func_def_616, type, sF262: $o).
% 24.66/4.09 thf(func_def_617, type, sF263: $o).
% 24.66/4.09 thf(func_def_618, type, sF264: $o).
% 24.66/4.09 thf(func_def_619, type, sF265: $o).
% 24.66/4.09 thf(func_def_620, type, sF266: $o).
% 24.66/4.09 thf(func_def_621, type, sF267: $o).
% 24.66/4.09 thf(func_def_622, type, sF268: $o).
% 24.66/4.09 thf(func_def_623, type, sF269: $o).
% 24.66/4.09 thf(func_def_624, type, sF270: $o).
% 24.66/4.09 thf(func_def_625, type, sF271: $o).
% 24.66/4.09 thf(func_def_626, type, sF272: $o).
% 24.66/4.09 thf(func_def_627, type, sF273: $o).
% 24.66/4.09 thf(func_def_628, type, sF274: $o).
% 24.66/4.09 thf(func_def_629, type, sF275: $o).
% 24.66/4.09 thf(func_def_630, type, sF276: $o).
% 24.66/4.09 thf(func_def_631, type, sF277: $o).
% 24.66/4.09 thf(func_def_632, type, sF278: $o).
% 24.66/4.09 thf(func_def_633, type, sF279: $o).
% 24.66/4.09 thf(func_def_634, type, sF280: $o).
% 24.66/4.09 thf(func_def_635, type, sF281: $o).
% 24.66/4.09 thf(func_def_636, type, sF282: $o).
% 24.66/4.09 thf(func_def_637, type, sF283: $o).
% 24.66/4.09 thf(func_def_638, type, sF284: $o).
% 24.66/4.09 thf(func_def_639, type, sF285: $o).
% 24.66/4.09 thf(func_def_640, type, sF286: $o).
% 24.66/4.09 thf(func_def_641, type, sF287: $o).
% 24.66/4.09 thf(func_def_642, type, sF288: $o).
% 24.66/4.09 thf(func_def_643, type, sF289: $o).
% 24.66/4.09 thf(func_def_644, type, sF290: $o).
% 24.66/4.09 thf(func_def_647, type, sK293: ($i > $i)).
% 24.66/4.09 thf(f1,axiom,(
% 24.66/4.09 ((^[X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu)).
% 24.66/4.09 thf(f2,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) <=> (in @ X2 @ X0)) => (X0 = X1)) = setextAx)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx)).
% 24.66/4.09 thf(f3,axiom,(
% 24.66/4.09 (emptysetAx = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx)).
% 24.66/4.09 thf(f4,axiom,(
% 24.66/4.09 (setadjoinAx = ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) | (X2 = X0)) <=> (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx)).
% 24.66/4.09 thf(f5,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))) = powersetAx)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx)).
% 24.66/4.09 thf(f7,axiom,(
% 24.66/4.09 (omega0Ax = ((in @ emptyset @ omega)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax)).
% 24.66/4.09 thf(f8,axiom,(
% 24.66/4.09 (omegaSAx = ! [X0 : $i] : ((in @ X0 @ omega) => (in @ (setadjoin @ X0 @ X0) @ omega)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx)).
% 24.66/4.09 thf(f14,axiom,(
% 24.66/4.09 (! [X2 : $i,X1 : ($i > $o),X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))) = dsetconstrI)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI)).
% 24.66/4.09 thf(f15,axiom,(
% 24.66/4.09 (dsetconstrEL = ! [X1 : ($i > $o),X2 : $i,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL)).
% 24.66/4.09 thf(f16,axiom,(
% 24.66/4.09 (! [X0 : $i,X2 : $i,X1 : ($i > $o)] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (X1 @ X2)) = dsetconstrER)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 24.66/4.09 thf(f18,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $o] : ((in @ X1 @ (prop2set @ X0)) => X0) = prop2setE)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE)).
% 24.66/4.09 thf(f19,axiom,(
% 24.66/4.09 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 24.66/4.09 thf(f20,axiom,(
% 24.66/4.09 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse)).
% 24.66/4.09 thf(f21,axiom,(
% 24.66/4.09 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset)).
% 24.66/4.09 thf(f22,axiom,(
% 24.66/4.09 (exuE3e = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (X0 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e)).
% 24.66/4.09 thf(f23,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))) = setext)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 24.66/4.09 thf(f24,axiom,(
% 24.66/4.09 (emptyI = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI)).
% 24.66/4.09 thf(f25,axiom,(
% 24.66/4.09 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = noeltsimpempty)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty)).
% 24.66/4.09 thf(f27,axiom,(
% 24.66/4.09 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty)).
% 24.66/4.09 thf(f28,axiom,(
% 24.66/4.09 (nonemptyE1 = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1)).
% 24.66/4.09 thf(f29,axiom,(
% 24.66/4.09 (nonemptyI = ! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI)).
% 24.66/4.09 thf(f30,axiom,(
% 24.66/4.09 (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)) = nonemptyI1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1)).
% 24.66/4.09 thf(f31,axiom,(
% 24.66/4.09 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL)).
% 24.66/4.09 thf(f32,axiom,(
% 24.66/4.09 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty)).
% 24.66/4.09 thf(f33,axiom,(
% 24.66/4.09 (setadjoinIR = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR)).
% 24.66/4.09 thf(f36,axiom,(
% 24.66/4.09 (setoftrueEq = ! [X0 : $i] : (X0 = ((dsetconstr @ X0 @ (^[X1 : $i] : ($true))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq)).
% 24.66/4.09 thf(f37,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 24.66/4.09 thf(f38,axiom,(
% 24.66/4.09 (emptyinPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset)).
% 24.66/4.09 thf(f39,axiom,(
% 24.66/4.09 (emptyInPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset)).
% 24.66/4.09 thf(f40,axiom,(
% 24.66/4.09 (powersetE = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 24.66/4.09 thf(f42,axiom,(
% 24.66/4.09 (setunionE = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE)).
% 24.66/4.09 thf(f43,axiom,(
% 24.66/4.09 (subPowSU = ! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU)).
% 24.66/4.09 thf(f44,axiom,(
% 24.66/4.09 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2))) = exuE2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2)).
% 24.66/4.09 thf(f45,axiom,(
% 24.66/4.09 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 24.66/4.09 thf(f46,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 24.66/4.09 thf(f47,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))) = notinsingleton)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton)).
% 24.66/4.09 thf(f49,axiom,(
% 24.66/4.09 (singletonsswitch = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch)).
% 24.66/4.09 thf(f51,axiom,(
% 24.66/4.09 (upairsetIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL)).
% 24.66/4.09 thf(f52,axiom,(
% 24.66/4.09 (upairsetIR = ! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR)).
% 24.66/4.09 thf(f53,axiom,(
% 24.66/4.09 (emptyE1 = ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((((dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))) = emptyset) => $false)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1)).
% 24.66/4.09 thf(f54,axiom,(
% 24.66/4.09 (vacuousDall = ! [X1 : $i,X0 : ($i > $o)] : ((in @ X1 @ emptyset) => (X0 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall)).
% 24.66/4.09 thf(f55,axiom,(
% 24.66/4.09 (quantDeMorgan1 = ! [X1 : ($i > $o),X0 : $i] : (~ ! [X2 : $i] : ((in @ X2 @ X0) => (X1 @ X2)) => ? [X2 : $i] : ((in @ X2 @ X0) & ~(X1 @ X2))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1)).
% 24.66/4.09 thf(f56,axiom,(
% 24.66/4.09 (quantDeMorgan2 = ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2)) => ~ ? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2)).
% 24.66/4.09 thf(f59,axiom,(
% 24.66/4.09 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI)).
% 24.66/4.09 thf(f61,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : ($i > $o)] : (~ ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2))) = notdexE)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE)).
% 24.66/4.09 thf(f63,axiom,(
% 24.66/4.09 (exuI1 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1)).
% 24.66/4.09 thf(f64,axiom,(
% 24.66/4.09 (! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1)))))) = exuI3)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3)).
% 24.66/4.09 thf(f65,axiom,(
% 24.66/4.09 (! [X0 : ($i > $o)] : (? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2)) => (exu @ (^[X1 : $i] : ((X0 @ X1))))) = exuI2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2)).
% 24.66/4.09 thf(f67,axiom,(
% 24.66/4.09 (in__Cong = ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => ((in @ X3 @ X1) <=> (in @ X2 @ X0)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong)).
% 24.66/4.09 thf(f68,axiom,(
% 24.66/4.09 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuE3u)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u)).
% 24.66/4.09 thf(f70,axiom,(
% 24.66/4.09 ((emptyset = emptyset) = emptyset__Cong)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong)).
% 24.66/4.09 thf(f71,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X3 : $i,X2 : $i] : ((X2 = X3) => (((setadjoin @ X0 @ X2)) = ((setadjoin @ X1 @ X3))))) = setadjoin__Cong)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong)).
% 24.66/4.09 thf(f72,axiom,(
% 24.66/4.09 (powerset__Cong = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((powerset @ X0)) = ((powerset @ X1)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong)).
% 24.66/4.09 thf(f73,axiom,(
% 24.66/4.09 (setunion__Cong = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setunion @ X0)) = ((setunion @ X1)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong)).
% 24.66/4.09 thf(f74,axiom,(
% 24.66/4.09 ((omega = omega) = omega__Cong)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong)).
% 24.66/4.09 thf(f75,axiom,(
% 24.66/4.09 (exuEu = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu)).
% 24.66/4.09 thf(f78,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 24.66/4.09 thf(f79,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2)).
% 24.66/4.09 thf(f80,axiom,(
% 24.66/4.09 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1)).
% 24.66/4.09 thf(f81,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 24.66/4.09 thf(f82,axiom,(
% 24.66/4.09 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset)).
% 24.66/4.09 thf(f85,axiom,(
% 24.66/4.09 (notsubsetI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI)).
% 24.66/4.09 thf(f86,axiom,(
% 24.66/4.09 (notequalI1 = ! [X0 : $i,X1 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1)).
% 24.66/4.09 thf(f88,axiom,(
% 24.66/4.09 (! [X0 : $i] : (subset @ X0 @ X0) = subsetRefl)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl)).
% 24.66/4.09 thf(f89,axiom,(
% 24.66/4.09 (subsetTrans = ! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans)).
% 24.66/4.09 thf(f90,axiom,(
% 24.66/4.09 (setadjoinSub = ! [X1 : $i,X0 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub)).
% 24.66/4.09 thf(f92,axiom,(
% 24.66/4.09 (subset2powerset = ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset)).
% 24.66/4.09 thf(f94,axiom,(
% 24.66/4.09 (subsetemptysetimpeq = ! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq)).
% 24.66/4.09 thf(f95,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1)).
% 24.66/4.09 thf(f96,axiom,(
% 24.66/4.09 (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1)).
% 24.66/4.09 thf(f97,axiom,(
% 24.66/4.09 (inPowerset = ! [X0 : $i] : (in @ X0 @ (powerset @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset)).
% 24.66/4.09 thf(f98,axiom,(
% 24.66/4.09 (powersetsubset = ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset)).
% 24.66/4.09 thf(f99,axiom,(
% 24.66/4.09 (sepInPowerset = ! [X0 : $i,X1 : ($i > $o)] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ (powerset @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset)).
% 24.66/4.09 thf(f100,axiom,(
% 24.66/4.09 (! [X1 : ($i > $o),X0 : $i] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ X0) = sepSubset)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset)).
% 24.66/4.09 thf(f101,axiom,(
% 24.66/4.09 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))) = binunionIL)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL)).
% 24.66/4.09 thf(f102,axiom,(
% 24.66/4.09 (upairset2IR = ! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR)).
% 24.66/4.09 thf(f103,axiom,(
% 24.66/4.09 (binunionIR = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR)).
% 24.66/4.09 thf(f105,axiom,(
% 24.66/4.09 (binunionE = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X1) | (in @ X2 @ X0))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE)).
% 24.66/4.09 thf(f106,axiom,(
% 24.66/4.09 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub)).
% 24.66/4.09 thf(f107,axiom,(
% 24.66/4.09 (binunionRsub = ! [X1 : $i,X0 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub)).
% 24.66/4.09 thf(f108,axiom,(
% 24.66/4.09 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI)).
% 24.66/4.09 thf(f109,axiom,(
% 24.66/4.09 (! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X2 @ X0) => ((subset @ X2 @ X1) => (subset @ X2 @ (binintersect @ X0 @ X1)))) = binintersectSubset5)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5)).
% 24.66/4.09 thf(f110,axiom,(
% 24.66/4.09 (binintersectEL = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL)).
% 24.66/4.09 thf(f111,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0) = binintersectLsub)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub)).
% 24.66/4.09 thf(f112,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X0 @ X1)) = X0)) = binintersectSubset2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2)).
% 24.66/4.09 thf(f113,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0)) = binintersectSubset3)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3)).
% 24.66/4.09 thf(f114,axiom,(
% 24.66/4.09 (binintersectER = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)).
% 24.66/4.09 thf(f115,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (((binintersect @ X0 @ X1)) = emptyset)) = disjointsetsI1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1)).
% 24.66/4.09 thf(f116,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1) = binintersectRsub)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub)).
% 24.66/4.09 thf(f117,axiom,(
% 24.66/4.09 (binintersectSubset4 = ! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X0 @ X1)) = X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4)).
% 24.66/4.09 thf(f118,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)) = binintersectSubset1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1)).
% 24.66/4.09 thf(f119,axiom,(
% 24.66/4.09 (bs114d = ! [X0 : $i,X2 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X2))) = ((binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d)).
% 24.66/4.09 thf(f120,axiom,(
% 24.66/4.09 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI)).
% 24.66/4.09 thf(f121,axiom,(
% 24.66/4.09 (setminusEL = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL)).
% 24.66/4.09 thf(f122,axiom,(
% 24.66/4.09 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER)).
% 24.66/4.09 thf(f123,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((setminus @ X0 @ X1)) = emptyset)) = setminusSubset2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2)).
% 24.66/4.09 thf(f124,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i,X2 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = setminusERneg)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg)).
% 24.66/4.09 thf(f125,axiom,(
% 24.66/4.09 (setminusELneg = ! [X2 : $i,X1 : $i,X0 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg)).
% 24.66/4.09 thf(f126,axiom,(
% 24.66/4.09 (setminusILneg = ! [X2 : $i,X0 : $i,X1 : $i] : (~(in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X0 @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg)).
% 24.66/4.09 thf(f127,axiom,(
% 24.66/4.09 (setminusIRneg = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg)).
% 24.66/4.09 thf(f128,axiom,(
% 24.66/4.09 (setminusLsub = ! [X1 : $i,X0 : $i] : (subset @ (setminus @ X0 @ X1) @ X0))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub)).
% 24.66/4.09 thf(f129,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1)) = setminusSubset1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1)).
% 24.66/4.09 thf(f132,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (symdiff @ X0 @ X1)))) = symdiffI2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2)).
% 24.66/4.09 thf(f133,axiom,(
% 24.66/4.09 (symdiffIneg1 = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => ~(in @ X2 @ (symdiff @ X0 @ X1)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1)).
% 24.66/4.09 thf(f134,axiom,(
% 24.66/4.09 (symdiffIneg2 = ! [X0 : $i,X2 : $i,X1 : $i] : (~(in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(in @ X2 @ (symdiff @ X0 @ X1)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2)).
% 24.66/4.09 thf(f135,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair)).
% 24.66/4.09 thf(f136,axiom,(
% 24.66/4.09 (setukpairIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL)).
% 24.66/4.09 thf(f137,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = setukpairIR)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR)).
% 24.66/4.09 thf(f138,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair)).
% 24.66/4.09 thf(f139,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)) = kpairp)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp)).
% 24.66/4.09 thf(f140,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((in @ X1 @ X0) => (subset @ (setadjoin @ X1 @ emptyset) @ X0)) = singletonsubset)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset)).
% 24.66/4.09 thf(f141,axiom,(
% 24.66/4.09 (singletoninpowerset = ! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset)).
% 24.66/4.09 thf(f142,axiom,(
% 24.66/4.09 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))) = singletoninpowunion)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion)).
% 24.66/4.09 thf(f145,axiom,(
% 24.66/4.09 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))) = upairinpowunion)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion)).
% 24.66/4.09 thf(f146,axiom,(
% 24.66/4.09 (ubforcartprodlem1 = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1)).
% 24.66/4.09 thf(f147,axiom,(
% 24.66/4.09 (ubforcartprodlem2 = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2)).
% 24.66/4.09 thf(f148,axiom,(
% 24.66/4.09 (ubforcartprodlem3 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3)).
% 24.66/4.09 thf(f150,axiom,(
% 24.66/4.09 (cartprodmempair1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 24.66/4.09 thf(f152,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0))) = setunionE2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2)).
% 24.66/4.09 thf(f153,axiom,(
% 24.66/4.09 (setunionsingleton1 = ! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1)).
% 24.66/4.09 thf(f154,axiom,(
% 24.66/4.09 (setunionsingleton2 = ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2)).
% 24.66/4.09 thf(f155,axiom,(
% 24.66/4.09 (! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset))) = X0) = setunionsingleton)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton)).
% 24.66/4.09 thf(f157,axiom,(
% 24.66/4.09 (ex1E1 = ! [X1 : ($i > $o),X0 : $i] : ((ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) => ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1)).
% 24.66/4.09 thf(f158,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X3) => (X3 = X2))) => (ex1 @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))) = ex1I)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I)).
% 24.66/4.09 thf(f159,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))))) = ex1I2)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2)).
% 24.66/4.09 thf(f160,axiom,(
% 24.66/4.09 (singletonsuniq = ! [X0 : $i,X1 : $i] : ((((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X1 @ emptyset))) => (X0 = X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq)).
% 24.66/4.09 thf(f161,axiom,(
% 24.66/4.09 (setukpairinjL1 = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1)).
% 24.66/4.09 thf(f162,axiom,(
% 24.66/4.09 (! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : ((in @ (setadjoin @ X1 @ emptyset) @ X0)))))) = kfstsingleton)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton)).
% 24.66/4.09 thf(f164,axiom,(
% 24.66/4.09 (kfstpairEq = ! [X1 : $i,X0 : $i] : (((kfst @ (kpair @ X0 @ X1))) = X0))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq)).
% 24.66/4.09 thf(f165,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (kfst @ X2) @ X0)) = cartprodfstin)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin)).
% 24.66/4.09 thf(f167,axiom,(
% 24.66/4.09 (! [X0 : $i,X3 : $i,X1 : $i,X2 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X0 = X2)) = setukpairinjL)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL)).
% 24.66/4.09 thf(f169,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = ((setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)))) = setukpairinjR12)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12)).
% 24.66/4.09 thf(f170,axiom,(
% 24.66/4.09 (! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = ((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) => ((X2 = X3) => (X1 = X3))) = setukpairinjR1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1)).
% 24.66/4.09 thf(f173,axiom,(
% 24.66/4.09 (! [X1 : $i,X2 : $i,X0 : $i,X3 : $i] : ((((kpair @ X0 @ X1)) = ((kpair @ X2 @ X3))) => (X1 = X3)) = setukpairinjR)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR)).
% 24.66/4.09 thf(f174,axiom,(
% 24.66/4.09 (! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : ((X0 = ((kpair @ (kfst @ X0) @ X1)))))))) = ksndsingleton)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton)).
% 24.66/4.09 thf(f175,axiom,(
% 24.66/4.09 (ksndpairEq = ! [X1 : $i,X0 : $i] : (((ksnd @ (kpair @ X0 @ X1))) = X1))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq)).
% 24.66/4.09 thf(f179,axiom,(
% 24.66/4.09 (cartprodpairmemER = ! [X2 : $i,X3 : $i,X1 : $i,X0 : $i] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) => (in @ X3 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER)).
% 24.66/4.09 thf(f180,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kpair @ X2 @ X3)) = ((kpair @ X2 @ X3))))) = cartprodmempaircEq)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq)).
% 24.66/4.09 thf(f181,axiom,(
% 24.66/4.09 (cartprodfstpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kfst @ (kpair @ X2 @ X3))) = X2))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq)).
% 24.66/4.09 thf(f182,axiom,(
% 24.66/4.09 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((ksnd @ (kpair @ X2 @ X3))) = X3))) = cartprodsndpairEq)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq)).
% 24.66/4.09 thf(f183,axiom,(
% 24.66/4.09 (cartprodpairsurjEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (((kpair @ (kfst @ X2) @ (ksnd @ X2))) = X2)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq)).
% 24.66/4.09 thf(f184,axiom,(
% 24.66/4.09 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 24.66/4.09 thf(f186,axiom,(
% 24.66/4.09 (dpsetconstrSub = ! [X2 : ($i > $i > $o),X0 : $i,X1 : $i] : (subset @ (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : ((X2 @ X3 @ X4)))) @ (cartprod @ X0 @ X1)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub)).
% 24.66/4.09 thf(f191,axiom,(
% 24.66/4.09 (dpsetconstrER = ! [X4 : $i,X2 : ($i > $i > $o),X1 : $i,X0 : $i,X3 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (X2 @ X3 @ X4)))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER)).
% 24.66/4.09 thf(f193,axiom,(
% 24.66/4.09 (! [X0 : $i,X2 : $i,X1 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) @ X1))) = apProp)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apProp)).
% 24.66/4.09 thf(f196,axiom,(
% 24.66/4.09 (ap2p = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p)).
% 24.66/4.09 thf(f197,axiom,(
% 24.66/4.09 (! [X0 : $i,X2 : $i,X1 : $i] : ((func @ X0 @ X1 @ X2) => (in @ X2 @ (funcSet @ X0 @ X1))) = funcinfuncset)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset)).
% 24.66/4.09 thf(f203,axiom,(
% 24.66/4.09 (ex1E2 = ! [X0 : $i,X1 : ($i > $o)] : ((ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3)))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2)).
% 24.66/4.09 thf(f204,axiom,(
% 24.66/4.09 (funcGraphProp1 = ! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1)).
% 24.66/4.09 thf(f208,axiom,(
% 24.66/4.09 (funcGraphProp4 = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X2) => (((ap @ X0 @ X1 @ X2 @ X3)) = X4))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp4)).
% 24.66/4.09 thf(f209,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))) = subbreln)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln)).
% 24.66/4.09 thf(f213,axiom,(
% 24.66/4.09 (ap2apEq1 = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ X2 @ X3)) = ((ap @ X0 @ X1 @ X2 @ X3))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq1)).
% 24.66/4.09 thf(f214,axiom,(
% 24.66/4.09 (ap2apEq2 = ! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ X2 @ X3)) = ((ap @ X0 @ X1 @ X2 @ X3))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq2)).
% 24.66/4.09 thf(f215,axiom,(
% 24.66/4.09 (! [X2 : ($i > $i),X0 : $i,X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3)) = ((X2 @ X3))))) = beta1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1)).
% 24.66/4.09 thf(f216,axiom,(
% 24.66/4.09 (eta1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => (X2 = ((lam @ X0 @ X1 @ (^[X3 : $i] : ((ap @ X0 @ X1 @ X2 @ X3))))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta1)).
% 24.66/4.09 thf(f217,axiom,(
% 24.66/4.09 (lam2lamEq = ! [X1 : $i,X2 : ($i > $i),X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (((lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3))))) = ((lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3))))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2lamEq)).
% 24.66/4.09 thf(f220,axiom,(
% 24.66/4.09 (iffalseProp1 = ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X1 & (X4 = X2)) | (~X1 & (X4 = X3))))))))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp1)).
% 24.66/4.09 thf(f222,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (in @ X2 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X1 & (X4 = X2)) | ((X4 = X3) & ~X1)))))))) = iftrueProp1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp1)).
% 24.66/4.09 thf(f225,axiom,(
% 24.66/4.09 (! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (if @ X0 @ X1 @ X2 @ X3) @ X0))) = ifp)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifp)).
% 24.66/4.09 thf(f226,axiom,(
% 24.66/4.09 (! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))) = theeq)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq)).
% 24.66/4.09 thf(f230,axiom,(
% 24.66/4.09 (binintersectT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem)).
% 24.66/4.09 thf(f231,axiom,(
% 24.66/4.09 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem)).
% 24.66/4.09 thf(f232,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) = powersetT_lem)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem)).
% 24.66/4.09 thf(f233,axiom,(
% 24.66/4.09 (setminusT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X0)))))),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem)).
% 24.66/4.09 thf(f234,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 24.66/4.09 thf(f237,axiom,(
% 24.66/4.09 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))) = powersetTI1)),
% 24.66/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTI1)).
% 24.66/4.09 thf(f238,axiom,(
% 24.66/4.09 (powersetTE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X1 @ (powerset @ X2)) => ((in @ X3 @ X1) => (in @ X3 @ X2)))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTE1)).
% 24.66/4.10 thf(f241,axiom,(
% 24.66/4.10 (binintersectTELcontra = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ X1) => ~(in @ X3 @ (binintersect @ X1 @ X2)))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTELcontra)).
% 24.66/4.10 thf(f247,axiom,(
% 24.66/4.10 (doubleComplementI1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1)).
% 24.66/4.10 thf(f250,axiom,(
% 24.66/4.10 (doubleComplementSub2 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1)))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub2)).
% 24.66/4.10 thf(f251,axiom,(
% 24.66/4.10 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (X1 = ((setminus @ X0 @ (setminus @ X0 @ X1))))) = doubleComplementEq)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq)).
% 24.66/4.10 thf(f253,axiom,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = complementImpComplementIntersect)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect)).
% 24.66/4.10 thf(f254,axiom,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) = complementSubsetComplementIntersect)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect)).
% 24.66/4.10 thf(f255,axiom,(
% 24.66/4.10 (complementInPowersetComplementIntersect = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementInPowersetComplementIntersect)).
% 24.66/4.10 thf(f263,axiom,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))) = intersectInPowersetIntersectUnions)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions)).
% 24.66/4.10 thf(f268,axiom,(
% 24.66/4.10 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))) = demorgan2a1)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a1)).
% 24.66/4.10 thf(f269,axiom,(
% 24.66/4.10 (complementUnionInPowersetComplement = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementUnionInPowersetComplement)).
% 24.66/4.10 thf(f271,axiom,(
% 24.66/4.10 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))) = demorgan1a)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1a)).
% 24.66/4.10 thf(f273,axiom,(
% 24.66/4.10 (demorgan1 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1)).
% 24.66/4.10 thf(f275,axiom,(
% 24.66/4.10 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => ((in @ X3 @ (setminus @ X0 @ X2)) => (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))))))) = demorgan2b2)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2b2)).
% 24.66/4.10 thf(f277,axiom,(
% 24.66/4.10 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (((setminus @ X0 @ (binunion @ X1 @ X2))) = ((binintersect @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))) = demorgan2)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2)).
% 24.66/4.10 thf(f278,axiom,(
% 24.66/4.10 (woz13rule0 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (binintersect @ X1 @ X2)) => (in @ X3 @ X0)))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule0)).
% 24.66/4.10 thf(f280,axiom,(
% 24.66/4.10 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))) = woz13rule2)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule2)).
% 24.66/4.10 thf(f283,axiom,(
% 24.66/4.10 (woz1_1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_1)).
% 24.66/4.10 thf(f285,axiom,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))) = woz1_3)),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_3)).
% 24.66/4.10 thf(f287,axiom,(
% 24.66/4.10 (woz1_5 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_5)).
% 24.66/4.10 thf(f288,axiom,(
% 24.66/4.10 (breln1 = (^[X0 : $i, X1 : $i] : ((breln @ X0 @ X0 @ X1))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1)).
% 24.66/4.10 thf(f294,conjecture,(
% 24.66/4.10 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (subset @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.66/4.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln1)).
% 24.66/4.10 thf(f295,negated_conjecture,(
% 24.66/4.10 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => ! [X1 : $i,X0 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (subset @ X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.66/4.10 inference(negated_conjecture,[status(cth)],[f294])).
% 24.66/4.10 thf(f298,plain,(
% 24.66/4.10 (! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))) = theeq)),
% 24.66/4.10 inference(rectify,[],[f226])).
% 24.66/4.10 thf(f299,plain,(
% 24.66/4.10 (theeq = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f298])).
% 24.66/4.10 thf(f300,plain,(
% 24.66/4.10 (powerset__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f72])).
% 24.66/4.10 thf(f303,plain,(
% 24.66/4.10 (ubforcartprodlem3 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 24.66/4.10 inference(rectify,[],[f148])).
% 24.66/4.10 thf(f304,plain,(
% 24.66/4.10 (ubforcartprodlem3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f303])).
% 24.66/4.10 thf(f307,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ X0)) => ((in @ X3 @ (setminus @ X1 @ X2)) => (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))))))) = demorgan2b2)),
% 24.66/4.10 inference(rectify,[],[f275])).
% 24.66/4.10 thf(f308,plain,(
% 24.66/4.10 (demorgan2b2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ Y1)) => ((in @ Y3 @ (setminus @ Y0 @ Y2)) => (in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f307])).
% 24.66/4.10 thf(f309,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X3) => (X3 = X2))) => (ex1 @ X0 @ (^[X4 : $i] : ((X1 @ X4))))))) = ex1I)),
% 24.66/4.10 inference(rectify,[],[f158])).
% 24.66/4.10 thf(f310,plain,(
% 24.66/4.10 (ex1I = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f309])).
% 24.66/4.10 thf(f317,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 24.66/4.10 inference(rectify,[],[f95])).
% 24.66/4.10 thf(f318,plain,(
% 24.66/4.10 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f317])).
% 24.66/4.10 thf(f319,plain,(
% 24.66/4.10 (iffalseProp1 = ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X1 & (X4 = X2)) | (~X1 & (X4 = X3))))))))))),
% 24.66/4.10 inference(rectify,[],[f220])).
% 24.66/4.10 thf(f320,plain,(
% 24.66/4.10 (iffalseProp1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((Y3 = Y4) & (~ Y1)) | ((Y0 = Y4) & Y1))))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f319])).
% 24.66/4.10 thf(f325,plain,(
% 24.66/4.10 (binintersectTELcontra = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ X1) => ~(in @ X3 @ (binintersect @ X1 @ X2)))))))),
% 24.66/4.10 inference(rectify,[],[f241])).
% 24.66/4.10 thf(f326,plain,(
% 24.66/4.10 (binintersectTELcontra = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2)))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f325])).
% 24.66/4.10 thf(f327,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))) = powersetI)),
% 24.66/4.10 inference(rectify,[],[f37])).
% 24.66/4.10 thf(f328,plain,(
% 24.66/4.10 (powersetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f327])).
% 24.66/4.10 thf(f329,plain,(
% 24.66/4.10 (ap2p = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X2 @ X1 @ X3) @ X2))))),
% 24.66/4.10 inference(rectify,[],[f196])).
% 24.66/4.10 thf(f330,plain,(
% 24.66/4.10 (ap2p = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f329])).
% 24.66/4.10 thf(f331,plain,(
% 24.66/4.10 (singletoninpowerset = ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))))),
% 24.66/4.10 inference(rectify,[],[f141])).
% 24.66/4.10 thf(f332,plain,(
% 24.66/4.10 (singletoninpowerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f331])).
% 24.66/4.10 thf(f337,plain,(
% 24.66/4.10 (binunionRsub = ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X1 @ X0)))),
% 24.66/4.10 inference(rectify,[],[f107])).
% 24.66/4.10 thf(f338,plain,(
% 24.66/4.10 (binunionRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f337])).
% 24.66/4.10 thf(f339,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1)) = setminusSubset1)),
% 24.66/4.10 inference(rectify,[],[f129])).
% 24.66/4.10 thf(f340,plain,(
% 24.66/4.10 (setminusSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f339])).
% 24.66/4.10 thf(f349,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ (binintersect @ X2 @ X1)))) = binintersectI)),
% 24.66/4.10 inference(rectify,[],[f108])).
% 24.66/4.10 thf(f350,plain,(
% 24.66/4.10 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f349])).
% 24.66/4.10 thf(f351,plain,(
% 24.66/4.10 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 24.66/4.10 inference(rectify,[],[f31])).
% 24.66/4.10 thf(f352,plain,(
% 24.66/4.10 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f351])).
% 24.66/4.10 thf(f353,plain,(
% 24.66/4.10 (! [X0 : ($i > $o)] : (? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2)) => (exu @ (^[X3 : $i] : ((X0 @ X3))))) = exuI2)),
% 24.66/4.10 inference(rectify,[],[f65])).
% 24.66/4.10 thf(f354,plain,(
% 24.66/4.10 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f353])).
% 24.66/4.10 thf(f355,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X1 @ X4) & (in @ X4 @ X0)) => (ex1 @ X0 @ (^[X5 : $i] : ((X1 @ X5)))))) = ex1I2)),
% 24.66/4.10 inference(rectify,[],[f159])).
% 24.66/4.10 thf(f356,plain,(
% 24.66/4.10 (ex1I2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f355])).
% 24.66/4.10 thf(f357,plain,(
% 24.66/4.10 (quantDeMorgan2 = ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2)) => ~ ? [X3 : $i] : ((in @ X3 @ X0) & (X1 @ X3))))),
% 24.66/4.10 inference(rectify,[],[f56])).
% 24.66/4.10 thf(f358,plain,(
% 24.66/4.10 (quantDeMorgan2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f357])).
% 24.66/4.10 thf(f359,plain,(
% 24.66/4.10 (setminusELneg = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ (setminus @ X2 @ X1)) => (~(in @ X0 @ X1) => ~(in @ X0 @ X2))))),
% 24.66/4.10 inference(rectify,[],[f125])).
% 24.66/4.10 thf(f360,plain,(
% 24.66/4.10 (setminusELneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f359])).
% 24.66/4.10 thf(f363,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 24.66/4.10 inference(rectify,[],[f138])).
% 24.66/4.10 thf(f364,plain,(
% 24.66/4.10 (kpairiskpair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f363])).
% 24.66/4.10 thf(f365,plain,(
% 24.66/4.10 (! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (if @ X2 @ X0 @ X1 @ X3) @ X2))) = ifp)),
% 24.66/4.10 inference(rectify,[],[f225])).
% 24.66/4.10 thf(f366,plain,(
% 24.66/4.10 (ifp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (if @ Y0 @ Y2 @ Y1 @ Y3) @ Y0)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f365])).
% 24.66/4.10 thf(f371,plain,(
% 24.66/4.10 (omegaSAx = ! [X0 : $i] : ((in @ X0 @ omega) => (in @ (setadjoin @ X0 @ X0) @ omega)))),
% 24.66/4.10 inference(rectify,[],[f8])).
% 24.66/4.10 thf(f372,plain,(
% 24.66/4.10 (omegaSAx = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega))))))),
% 24.66/4.10 inference(fool_elimination,[],[f371])).
% 24.66/4.10 thf(f377,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X2 @ X0)) = ((kpair @ X1 @ X3))) => (X0 = X3)) = setukpairinjR)),
% 24.66/4.10 inference(rectify,[],[f173])).
% 24.66/4.10 thf(f378,plain,(
% 24.66/4.10 (setukpairinjR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y2 @ Y0)) => (Y3 = Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f377])).
% 24.66/4.10 thf(f383,plain,(
% 24.66/4.10 (! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3))) => (exu @ (^[X4 : $i] : ((X0 @ X4)))))) = exuI3)),
% 24.66/4.10 inference(rectify,[],[f64])).
% 24.66/4.10 thf(f384,plain,(
% 24.66/4.10 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f383])).
% 24.66/4.10 thf(f387,plain,(
% 24.66/4.10 (upairset2IR = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 24.66/4.10 inference(rectify,[],[f102])).
% 24.66/4.10 thf(f388,plain,(
% 24.66/4.10 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f387])).
% 24.66/4.10 thf(f391,plain,(
% 24.66/4.10 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X3 : $i] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuE3u)),
% 24.66/4.10 inference(rectify,[],[f68])).
% 24.66/4.10 thf(f392,plain,(
% 24.66/4.10 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f391])).
% 24.66/4.10 thf(f393,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) => (in @ X3 @ (setminus @ X1 @ X0)))))) = demorgan2a1)),
% 24.66/4.10 inference(rectify,[],[f268])).
% 24.66/4.10 thf(f394,plain,(
% 24.66/4.10 (demorgan2a1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ Y1))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f393])).
% 24.66/4.10 thf(f395,plain,(
% 24.66/4.10 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 24.66/4.10 inference(rectify,[],[f21])).
% 24.66/4.10 thf(f396,plain,(
% 24.66/4.10 (notinemptyset = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 24.66/4.10 inference(fool_elimination,[],[f395])).
% 24.66/4.10 thf(f399,plain,(
% 24.66/4.10 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 24.66/4.10 inference(rectify,[],[f82])).
% 24.66/4.10 thf(f400,plain,(
% 24.66/4.10 (emptysetsubset = ((!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0)))))),
% 24.66/4.10 inference(fool_elimination,[],[f399])).
% 24.66/4.10 thf(f401,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 24.66/4.10 inference(rectify,[],[f78])).
% 24.66/4.10 thf(f402,plain,(
% 24.66/4.10 (subsetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f401])).
% 24.66/4.10 thf(f403,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X0) = binintersectRsub)),
% 24.66/4.10 inference(rectify,[],[f116])).
% 24.66/4.10 thf(f404,plain,(
% 24.66/4.10 (binintersectRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f403])).
% 24.66/4.10 thf(f405,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0) = binintersectLsub)),
% 24.66/4.10 inference(rectify,[],[f111])).
% 24.66/4.10 thf(f406,plain,(
% 24.66/4.10 (binintersectLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f405])).
% 24.66/4.10 thf(f409,plain,(
% 24.66/4.10 (! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : ! [X3 : $i] : ((X2 = X3) <=> (X0 @ X3))) = exuE2)),
% 24.66/4.10 inference(rectify,[],[f44])).
% 24.66/4.10 thf(f410,plain,(
% 24.66/4.10 (exuE2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f409])).
% 24.66/4.10 thf(f411,plain,(
% 24.66/4.10 (emptyInPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 24.66/4.10 inference(rectify,[],[f39])).
% 24.66/4.10 thf(f412,plain,(
% 24.66/4.10 (emptyInPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 24.66/4.10 inference(fool_elimination,[],[f411])).
% 24.66/4.10 thf(f419,plain,(
% 24.66/4.10 (omega__Cong = ((omega = omega)))),
% 24.66/4.10 inference(fool_elimination,[],[f74])).
% 24.66/4.10 thf(f422,plain,(
% 24.66/4.10 (woz13rule0 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (binintersect @ X0 @ X2)) => (in @ X3 @ X1)))))),
% 24.66/4.10 inference(rectify,[],[f278])).
% 24.66/4.10 thf(f423,plain,(
% 24.66/4.10 (woz13rule0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y1 @ Y2)) => (in @ Y3 @ Y0))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f422])).
% 24.66/4.10 thf(f428,plain,(
% 24.66/4.10 (kfstpairEq = ! [X0 : $i,X1 : $i] : (((kfst @ (kpair @ X1 @ X0))) = X1))),
% 24.66/4.10 inference(rectify,[],[f164])).
% 24.66/4.10 thf(f429,plain,(
% 24.66/4.10 (kfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f428])).
% 24.66/4.10 thf(f432,plain,(
% 24.66/4.10 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 24.66/4.10 inference(rectify,[],[f19])).
% 24.66/4.10 thf(f433,plain,(
% 24.66/4.10 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f432])).
% 24.66/4.10 thf(f434,plain,(
% 24.66/4.10 (cartprodmempair1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)))))),
% 24.66/4.10 inference(rectify,[],[f150])).
% 24.66/4.10 thf(f435,plain,(
% 24.66/4.10 (cartprodmempair1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((kpair @ Y3 @ Y4) = Y0)))) & (in @ Y3 @ Y2)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f434])).
% 24.66/4.10 thf(f436,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))) = intersectInPowersetIntersectUnions)),
% 24.66/4.10 inference(rectify,[],[f263])).
% 24.66/4.10 thf(f437,plain,(
% 24.66/4.10 (intersectInPowersetIntersectUnions = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y0 @ Y3) @ (binunion @ Y2 @ Y3)))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f436])).
% 24.66/4.10 thf(f438,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $o] : ((in @ X0 @ (prop2set @ X1)) => X1) = prop2setE)),
% 24.66/4.10 inference(rectify,[],[f18])).
% 24.66/4.10 thf(f439,plain,(
% 24.66/4.10 (prop2setE = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f438])).
% 24.66/4.10 thf(f452,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ? [X2 : $i] : ((in @ X0 @ X2) & (in @ X2 @ X1))) = setunionE2)),
% 24.66/4.10 inference(rectify,[],[f152])).
% 24.66/4.10 thf(f453,plain,(
% 24.66/4.10 (setunionE2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f452])).
% 24.66/4.10 thf(f454,plain,(
% 24.66/4.10 (cartprodpairmemER = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((in @ (kpair @ X0 @ X1) @ (cartprod @ X3 @ X2)) => (in @ X1 @ X2)))),
% 24.66/4.10 inference(rectify,[],[f179])).
% 24.66/4.10 thf(f455,plain,(
% 24.66/4.10 (cartprodpairmemER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y1))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f454])).
% 24.66/4.10 thf(f458,plain,(
% 24.66/4.10 (symdiffIneg1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ((in @ X0 @ X1) => ~(in @ X0 @ (symdiff @ X2 @ X1)))))),
% 24.66/4.10 inference(rectify,[],[f133])).
% 24.66/4.10 thf(f459,plain,(
% 24.66/4.10 (symdiffIneg1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f458])).
% 24.66/4.10 thf(f460,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) = complementSubsetComplementIntersect)),
% 24.66/4.10 inference(rectify,[],[f254])).
% 24.66/4.10 thf(f461,plain,(
% 24.66/4.10 (complementSubsetComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (subset @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f460])).
% 24.66/4.10 thf(f462,plain,(
% 24.66/4.10 (emptysetAx = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 24.66/4.10 inference(rectify,[],[f3])).
% 24.66/4.10 thf(f463,plain,(
% 24.66/4.10 (emptysetAx = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 24.66/4.10 inference(fool_elimination,[],[f462])).
% 24.66/4.10 thf(f466,plain,(
% 24.66/4.10 (woz1_5 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))))),
% 24.66/4.10 inference(rectify,[],[f287])).
% 24.66/4.10 thf(f467,plain,(
% 24.66/4.10 (woz1_5 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ (binunion @ Y0 @ Y2)) @ (powerset @ (setminus @ Y1 @ Y0)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f466])).
% 24.66/4.10 thf(f468,plain,(
% 24.66/4.10 (complementUnionInPowersetComplement = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))))),
% 24.66/4.10 inference(rectify,[],[f269])).
% 24.66/4.10 thf(f469,plain,(
% 24.66/4.10 (complementUnionInPowersetComplement = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ (binunion @ Y0 @ Y2)) @ (powerset @ (setminus @ Y1 @ Y0)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f468])).
% 24.66/4.10 thf(f470,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $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 = X1) => (X1 = X3))) = setukpairinjR1)),
% 24.66/4.10 inference(rectify,[],[f170])).
% 24.66/4.10 thf(f471,plain,(
% 24.66/4.10 (setukpairinjR1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y0)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f470])).
% 24.66/4.10 thf(f472,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X2 @ X1))))) = upairinpowunion)),
% 24.66/4.10 inference(rectify,[],[f145])).
% 24.66/4.10 thf(f473,plain,(
% 24.66/4.10 (upairinpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f472])).
% 24.66/4.10 thf(f476,plain,(
% 24.66/4.10 (woz1_1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))),
% 24.66/4.10 inference(rectify,[],[f283])).
% 24.66/4.10 thf(f477,plain,(
% 24.66/4.10 (woz1_1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f476])).
% 24.66/4.10 thf(f478,plain,(
% 24.66/4.10 (complementInPowersetComplementIntersect = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ (setminus @ X1 @ (binintersect @ X0 @ X2)))))))),
% 24.66/4.10 inference(rectify,[],[f255])).
% 24.66/4.10 thf(f479,plain,(
% 24.66/4.10 (complementInPowersetComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f478])).
% 24.66/4.10 thf(f482,plain,(
% 24.66/4.10 (setukpairIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 24.66/4.10 inference(rectify,[],[f136])).
% 24.66/4.10 thf(f483,plain,(
% 24.66/4.10 (setukpairIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f482])).
% 24.66/4.10 thf(f484,plain,(
% 24.66/4.10 ((^[X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 24.66/4.10 inference(rectify,[],[f1])).
% 24.66/4.10 thf(f485,plain,(
% 24.66/4.10 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 24.66/4.10 inference(fool_elimination,[],[f484])).
% 24.66/4.10 thf(f486,plain,(
% 24.66/4.10 (symdiffIneg2 = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X1 @ X0) => (~(in @ X1 @ X2) => ~(in @ X1 @ (symdiff @ X0 @ X2)))))),
% 24.66/4.10 inference(rectify,[],[f134])).
% 24.66/4.10 thf(f487,plain,(
% 24.66/4.10 (symdiffIneg2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f486])).
% 24.66/4.10 thf(f490,plain,(
% 24.66/4.10 (in__Cong = ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X2 @ X1) <=> (in @ X3 @ X0)))))),
% 24.66/4.10 inference(rectify,[],[f67])).
% 24.66/4.10 thf(f491,plain,(
% 24.66/4.10 (in__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f490])).
% 24.66/4.10 thf(f492,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = complementImpComplementIntersect)),
% 24.66/4.10 inference(rectify,[],[f253])).
% 24.66/4.10 thf(f493,plain,(
% 24.66/4.10 (complementImpComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f492])).
% 24.66/4.10 thf(f496,plain,(
% 24.66/4.10 (! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : ((X0 = ((kpair @ (kfst @ X0) @ X1)))))))) = ksndsingleton)),
% 24.66/4.10 inference(rectify,[],[f174])).
% 24.66/4.10 thf(f497,plain,(
% 24.66/4.10 (ksndsingleton = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f496])).
% 24.66/4.10 thf(f500,plain,(
% 24.66/4.10 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 24.66/4.10 inference(rectify,[],[f106])).
% 24.66/4.10 thf(f501,plain,(
% 24.66/4.10 (binunionLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f500])).
% 24.66/4.10 thf(f502,plain,(
% 24.66/4.10 (powersetTE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X1 @ (powerset @ X2)) => ((in @ X3 @ X1) => (in @ X3 @ X2)))))))),
% 24.66/4.10 inference(rectify,[],[f238])).
% 24.66/4.10 thf(f503,plain,(
% 24.66/4.10 (powersetTE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f502])).
% 24.66/4.10 thf(f504,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kpair @ X2 @ X3)) = ((kpair @ X2 @ X3))))) = cartprodmempaircEq)),
% 24.66/4.10 inference(rectify,[],[f180])).
% 24.66/4.10 thf(f505,plain,(
% 24.66/4.10 (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))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f504])).
% 24.66/4.10 thf(f506,plain,(
% 24.66/4.10 (setunionE = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X0 @ X3) => ((in @ X3 @ X1) => X2)) => X2)))),
% 24.66/4.10 inference(rectify,[],[f42])).
% 24.66/4.10 thf(f507,plain,(
% 24.66/4.10 (setunionE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => Y2)))) => Y2))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f506])).
% 24.66/4.10 thf(f508,plain,(
% 24.66/4.10 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = noeltsimpempty)),
% 24.66/4.10 inference(rectify,[],[f25])).
% 24.66/4.10 thf(f509,plain,(
% 24.66/4.10 (noeltsimpempty = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 24.66/4.10 inference(fool_elimination,[],[f508])).
% 24.66/4.10 thf(f512,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (in @ X0 @ (binunion @ X2 @ X1))) = binunionIL)),
% 24.66/4.10 inference(rectify,[],[f101])).
% 24.66/4.10 thf(f513,plain,(
% 24.66/4.10 (binunionIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f512])).
% 24.66/4.10 thf(f514,plain,(
% 24.66/4.10 (doubleComplementI1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))))),
% 24.66/4.10 inference(rectify,[],[f247])).
% 24.66/4.10 thf(f515,plain,(
% 24.66/4.10 (doubleComplementI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f514])).
% 24.66/4.10 thf(f516,plain,(
% 24.66/4.10 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f184])).
% 24.66/4.10 thf(f519,plain,(
% 24.66/4.10 (ubforcartprodlem1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X2 @ X1))))))),
% 24.66/4.10 inference(rectify,[],[f146])).
% 24.66/4.10 thf(f520,plain,(
% 24.66/4.10 (ubforcartprodlem1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f519])).
% 24.66/4.10 thf(f521,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))) = powersetTI1)),
% 24.66/4.10 inference(rectify,[],[f237])).
% 24.66/4.10 thf(f522,plain,(
% 24.66/4.10 (powersetTI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f521])).
% 24.66/4.10 thf(f525,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X1) => (subset @ X1 @ X0)) = binintersectSubset3)),
% 24.66/4.10 inference(rectify,[],[f113])).
% 24.66/4.10 thf(f526,plain,(
% 24.66/4.10 (binintersectSubset3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f525])).
% 24.66/4.10 thf(f531,plain,(
% 24.66/4.10 (setminusLsub = ! [X0 : $i,X1 : $i] : (subset @ (setminus @ X1 @ X0) @ X1))),
% 24.66/4.10 inference(rectify,[],[f128])).
% 24.66/4.10 thf(f532,plain,(
% 24.66/4.10 (setminusLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f531])).
% 24.66/4.10 thf(f533,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X1 @ X0)) = X1)) = binintersectSubset2)),
% 24.66/4.10 inference(rectify,[],[f112])).
% 24.66/4.10 thf(f534,plain,(
% 24.66/4.10 (binintersectSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f533])).
% 24.66/4.10 thf(f539,plain,(
% 24.66/4.10 (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
% 24.66/4.10 inference(rectify,[],[f96])).
% 24.66/4.10 thf(f540,plain,(
% 24.66/4.10 (powersetE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f539])).
% 24.66/4.10 thf(f541,plain,(
% 24.66/4.10 (emptyI = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 24.66/4.10 inference(rectify,[],[f24])).
% 24.66/4.10 thf(f542,plain,(
% 24.66/4.10 (emptyI = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0))))))),
% 24.66/4.10 inference(fool_elimination,[],[f541])).
% 24.66/4.10 thf(f543,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 24.66/4.10 inference(rectify,[],[f46])).
% 24.66/4.10 thf(f544,plain,(
% 24.66/4.10 (uniqinunit = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f543])).
% 24.66/4.10 thf(f547,plain,(
% 24.66/4.10 (emptyinunitempty = ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))),
% 24.66/4.10 inference(fool_elimination,[],[f32])).
% 24.66/4.10 thf(f550,plain,(
% 24.66/4.10 (setminusIRneg = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ~(in @ X0 @ (setminus @ X2 @ X1))))),
% 24.66/4.10 inference(rectify,[],[f127])).
% 24.66/4.10 thf(f551,plain,(
% 24.66/4.10 (setminusIRneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f550])).
% 24.66/4.10 thf(f552,plain,(
% 24.66/4.10 (exuI1 = ! [X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X3 : $i] : ((X0 @ X3))))))),
% 24.66/4.10 inference(rectify,[],[f63])).
% 24.66/4.10 thf(f553,plain,(
% 24.66/4.10 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f552])).
% 24.66/4.10 thf(f554,plain,(
% 24.66/4.10 (funcGraphProp1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0))))),
% 24.66/4.10 inference(rectify,[],[f204])).
% 24.66/4.10 thf(f555,plain,(
% 24.66/4.10 (funcGraphProp1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f554])).
% 24.66/4.10 thf(f556,plain,(
% 24.66/4.10 (! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : ((in @ (setadjoin @ X1 @ emptyset) @ X0)))))) = kfstsingleton)),
% 24.66/4.10 inference(rectify,[],[f162])).
% 24.66/4.10 thf(f557,plain,(
% 24.66/4.10 (kfstsingleton = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f556])).
% 24.66/4.10 thf(f558,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)) = kpairp)),
% 24.66/4.10 inference(rectify,[],[f139])).
% 24.66/4.10 thf(f559,plain,(
% 24.66/4.10 (kpairp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f558])).
% 24.66/4.10 thf(f560,plain,(
% 24.66/4.10 (exuEu = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3)))))),
% 24.66/4.10 inference(rectify,[],[f75])).
% 24.66/4.10 thf(f561,plain,(
% 24.66/4.10 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f560])).
% 24.66/4.10 thf(f562,plain,(
% 24.66/4.10 (singletonsuniq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f160])).
% 24.66/4.10 thf(f563,plain,(
% 24.66/4.10 (subPowSU = ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (powerset @ (setunion @ X1)))))),
% 24.66/4.10 inference(rectify,[],[f43])).
% 24.66/4.10 thf(f564,plain,(
% 24.66/4.10 (subPowSU = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f563])).
% 24.66/4.10 thf(f567,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => (in @ X1 @ (funcSet @ X0 @ X2))) = funcinfuncset)),
% 24.66/4.10 inference(rectify,[],[f197])).
% 24.66/4.10 thf(f568,plain,(
% 24.66/4.10 (funcinfuncset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (in @ Y1 @ (funcSet @ Y2 @ Y0)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f567])).
% 24.66/4.10 thf(f569,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ (setminus @ X1 @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = setminusERneg)),
% 24.66/4.10 inference(rectify,[],[f124])).
% 24.66/4.10 thf(f570,plain,(
% 24.66/4.10 (setminusERneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f569])).
% 24.66/4.10 thf(f573,plain,(
% 24.66/4.10 (! [X0 : $i] : (subset @ X0 @ X0) = subsetRefl)),
% 24.66/4.10 inference(rectify,[],[f88])).
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% 24.66/4.10 (subsetRefl = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))))),
% 24.66/4.10 inference(fool_elimination,[],[f573])).
% 24.66/4.10 thf(f577,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)) = eqimpsubset2)),
% 24.66/4.10 inference(rectify,[],[f79])).
% 24.66/4.10 thf(f578,plain,(
% 24.66/4.10 (eqimpsubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f577])).
% 24.66/4.10 thf(f581,plain,(
% 24.66/4.10 (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)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f169])).
% 24.66/4.10 thf(f586,plain,(
% 24.66/4.10 (setadjoinAx = ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) | (X1 = X2)) <=> (in @ X1 @ (setadjoin @ X2 @ X0))))),
% 24.66/4.10 inference(rectify,[],[f4])).
% 24.66/4.10 thf(f587,plain,(
% 24.66/4.10 (setadjoinAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y1 = Y0) | (in @ Y1 @ Y2)) = (in @ Y1 @ (setadjoin @ Y0 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f586])).
% 24.66/4.10 thf(f592,plain,(
% 24.66/4.10 (ex1E1 = ! [X0 : ($i > $o),X1 : $i] : ((ex1 @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) => ? [X3 : $i] : ((X0 @ X3) & (in @ X3 @ X1))))),
% 24.66/4.10 inference(rectify,[],[f157])).
% 24.66/4.10 thf(f593,plain,(
% 24.66/4.10 (ex1E1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f592])).
% 24.66/4.10 thf(f594,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (emptyset = ((setminus @ X1 @ X0)))) = setminusSubset2)),
% 24.66/4.10 inference(rectify,[],[f123])).
% 24.66/4.10 thf(f595,plain,(
% 24.66/4.10 (setminusSubset2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f594])).
% 24.66/4.10 thf(f596,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))) = binunionT_lem)),
% 24.66/4.10 inference(rectify,[],[f231])).
% 24.66/4.10 thf(f597,plain,(
% 24.66/4.10 (binunionT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (binunion @ Y1 @ Y2) @ (powerset @ Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f596])).
% 24.66/4.10 thf(f598,plain,(
% 24.66/4.10 (demorgan1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (((setminus @ X1 @ (binintersect @ X0 @ X2))) = ((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))))))),
% 24.66/4.10 inference(rectify,[],[f273])).
% 24.66/4.10 thf(f599,plain,(
% 24.66/4.10 (demorgan1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((setminus @ Y0 @ (binintersect @ Y1 @ Y2)) = (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f598])).
% 24.66/4.10 thf(f600,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((((binintersect @ X0 @ X1)) = X0) => (subset @ X0 @ X1)) = binintersectSubset1)),
% 24.66/4.10 inference(rectify,[],[f118])).
% 24.66/4.10 thf(f601,plain,(
% 24.66/4.10 (binintersectSubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f600])).
% 24.66/4.10 thf(f602,plain,(
% 24.66/4.10 (dsetconstrEL = ! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : ((X0 @ X3))))) => (in @ X1 @ X2)))),
% 24.66/4.10 inference(rectify,[],[f15])).
% 24.66/4.10 thf(f603,plain,(
% 24.66/4.10 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y1 @ Y0))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f602])).
% 24.66/4.10 thf(f604,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X0 @ X2)))) = singletoninpowunion)),
% 24.66/4.10 inference(rectify,[],[f142])).
% 24.66/4.10 thf(f605,plain,(
% 24.66/4.10 (singletoninpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f604])).
% 24.66/4.10 thf(f610,plain,(
% 24.66/4.10 (nonemptyE1 = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)))),
% 24.66/4.10 inference(rectify,[],[f28])).
% 24.66/4.10 thf(f611,plain,(
% 24.66/4.10 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f610])).
% 24.66/4.10 thf(f614,plain,(
% 24.66/4.10 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))))),
% 24.66/4.10 inference(rectify,[],[f45])).
% 24.66/4.10 thf(f615,plain,(
% 24.66/4.10 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f614])).
% 24.66/4.10 thf(f616,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (kfst @ X2) @ X0)) = cartprodfstin)),
% 24.66/4.10 inference(rectify,[],[f165])).
% 24.66/4.10 thf(f617,plain,(
% 24.66/4.10 (cartprodfstin = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f616])).
% 24.66/4.10 thf(f618,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X2 @ X0)) => ~(in @ X1 @ X0)) = setminusER)),
% 24.66/4.10 inference(rectify,[],[f122])).
% 24.66/4.10 thf(f619,plain,(
% 24.66/4.10 (setminusER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f618])).
% 24.66/4.10 thf(f620,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) = powersetT_lem)),
% 24.66/4.10 inference(rectify,[],[f232])).
% 24.66/4.10 thf(f621,plain,(
% 24.66/4.10 (powersetT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (powerset @ Y0) @ (powerset @ (powerset @ Y1))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f620])).
% 24.66/4.10 thf(f622,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) <=> (in @ X2 @ X0)) => (X0 = X1)) = setextAx)),
% 24.66/4.10 inference(rectify,[],[f2])).
% 24.66/4.10 thf(f623,plain,(
% 24.66/4.10 (setextAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f622])).
% 24.66/4.10 thf(f628,plain,(
% 24.66/4.10 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((in @ X1 @ X2) => (in @ X1 @ X0))))),
% 24.66/4.10 inference(rectify,[],[f40])).
% 24.66/4.10 thf(f629,plain,(
% 24.66/4.10 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f628])).
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% 24.66/4.10 (quantDeMorgan1 = ! [X0 : ($i > $o),X1 : $i] : (~ ! [X2 : $i] : ((in @ X2 @ X1) => (X0 @ X2)) => ? [X3 : $i] : ((in @ X3 @ X1) & ~(X0 @ X3))))),
% 24.66/4.10 inference(rectify,[],[f55])).
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% 24.66/4.10 (quantDeMorgan1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f634])).
% 24.66/4.10 thf(f638,plain,(
% 24.66/4.10 (setunionsingleton = ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0)))))),
% 24.66/4.10 inference(fool_elimination,[],[f155])).
% 24.66/4.10 thf(f639,plain,(
% 24.66/4.10 (setminusILneg = ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ X1) => ~(in @ X0 @ (setminus @ X1 @ X2))))),
% 24.66/4.10 inference(rectify,[],[f126])).
% 24.66/4.10 thf(f640,plain,(
% 24.66/4.10 (setminusILneg = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f639])).
% 24.66/4.10 thf(f641,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : ($i > $o)] : (~ ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ~(X1 @ X3))) = notdexE)),
% 24.66/4.10 inference(rectify,[],[f61])).
% 24.66/4.10 thf(f642,plain,(
% 24.66/4.10 (notdexE = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f641])).
% 24.66/4.10 thf(f643,plain,(
% 24.66/4.10 (setunion__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f73])).
% 24.66/4.10 thf(f644,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (setunion @ (dsetconstr @ X2 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X1))))) @ X2))) = apProp)),
% 24.66/4.10 inference(rectify,[],[f193])).
% 24.66/4.10 thf(f645,plain,(
% 24.66/4.10 (apProp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))) @ Y0)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f644])).
% 24.66/4.10 thf(f646,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (((binintersect @ X0 @ X1)) = emptyset)) = disjointsetsI1)),
% 24.66/4.10 inference(rectify,[],[f115])).
% 24.66/4.10 thf(f647,plain,(
% 24.66/4.10 (disjointsetsI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f646])).
% 24.66/4.10 thf(f648,plain,(
% 24.66/4.10 (! [X0 : ($i > $o),X1 : $i] : (subset @ (dsetconstr @ X1 @ (^[X2 : $i] : ((X0 @ X2)))) @ X1) = sepSubset)),
% 24.66/4.10 inference(rectify,[],[f100])).
% 24.66/4.10 thf(f649,plain,(
% 24.66/4.10 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ Y0)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f648])).
% 24.66/4.10 thf(f650,plain,(
% 24.66/4.10 (inPowerset = ! [X0 : $i] : (in @ X0 @ (powerset @ X0)))),
% 24.66/4.10 inference(rectify,[],[f97])).
% 24.66/4.10 thf(f651,plain,(
% 24.66/4.10 (inPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0))))))),
% 24.66/4.10 inference(fool_elimination,[],[f650])).
% 24.66/4.10 thf(f654,plain,(
% 24.66/4.10 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))),
% 24.66/4.10 inference(rectify,[],[f230])).
% 24.66/4.10 thf(f655,plain,(
% 24.66/4.10 (binintersectT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f654])).
% 24.66/4.10 thf(f656,plain,(
% 24.66/4.10 (setukpairinjL1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X0 = X1)))),
% 24.66/4.10 inference(rectify,[],[f161])).
% 24.66/4.10 thf(f657,plain,(
% 24.66/4.10 (setukpairinjL1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y2 = Y1))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f656])).
% 24.66/4.10 thf(f658,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
% 24.66/4.10 inference(rectify,[],[f81])).
% 24.66/4.10 thf(f659,plain,(
% 24.66/4.10 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f658])).
% 24.66/4.10 thf(f660,plain,(
% 24.66/4.10 (upairsetIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 24.66/4.10 inference(rectify,[],[f51])).
% 24.66/4.10 thf(f661,plain,(
% 24.66/4.10 (upairsetIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f660])).
% 24.66/4.10 thf(f662,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (symdiff @ X0 @ X1)))) = symdiffI2)),
% 24.66/4.10 inference(rectify,[],[f132])).
% 24.66/4.10 thf(f663,plain,(
% 24.66/4.10 (symdiffI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f662])).
% 24.66/4.10 thf(f664,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) <=> (in @ X0 @ (powerset @ X1))) = powersetAx)),
% 24.66/4.10 inference(rectify,[],[f5])).
% 24.66/4.10 thf(f665,plain,(
% 24.66/4.10 (powersetAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f664])).
% 24.66/4.10 thf(f666,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X2 @ X3))))) => (X2 @ X1)) = dsetconstrER)),
% 24.66/4.10 inference(rectify,[],[f16])).
% 24.66/4.10 thf(f667,plain,(
% 24.66/4.10 (dsetconstrER = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y1))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f666])).
% 24.66/4.10 thf(f668,plain,(
% 24.66/4.10 (nonemptyI = ! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 24.66/4.10 inference(rectify,[],[f29])).
% 24.66/4.10 thf(f669,plain,(
% 24.66/4.10 (nonemptyI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (nonempty @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f668])).
% 24.66/4.10 thf(f670,plain,(
% 24.66/4.10 (emptyE1 = ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((((dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) = emptyset) => $false)))),
% 24.66/4.10 inference(rectify,[],[f53])).
% 24.66/4.10 thf(f671,plain,(
% 24.66/4.10 (emptyE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (((dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) = emptyset) => $false))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f670])).
% 24.66/4.10 thf(f672,plain,(
% 24.66/4.10 (ap2apEq1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X2) => (((ap @ X2 @ X0 @ X1 @ X3)) = ((ap @ X2 @ X0 @ X1 @ X3))))))),
% 24.66/4.10 inference(rectify,[],[f213])).
% 24.66/4.10 thf(f673,plain,(
% 24.66/4.10 (ap2apEq1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y2 @ Y1 @ Y3) = (ap @ Y0 @ Y2 @ Y1 @ Y3))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f672])).
% 24.66/4.10 thf(f674,plain,(
% 24.66/4.10 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 24.66/4.10 inference(fool_elimination,[],[f288])).
% 24.66/4.10 thf(f677,plain,(
% 24.66/4.10 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X1 @ X0)) => (in @ X2 @ X0)))),
% 24.66/4.10 inference(rectify,[],[f114])).
% 24.66/4.10 thf(f678,plain,(
% 24.66/4.10 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y2))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f677])).
% 24.66/4.10 thf(f681,plain,(
% 24.66/4.10 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => (! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (in @ (kpair @ X3 @ X4) @ X2)))) => (subset @ X0 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.66/4.10 inference(rectify,[],[f295])).
% 24.66/4.10 thf(f682,plain,(
% 24.66/4.10 (((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 24.66/4.10 inference(fool_elimination,[],[f681])).
% 24.66/4.10 thf(f683,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => (((setadjoin @ X0 @ X2)) = ((setadjoin @ X1 @ X3))))) = setadjoin__Cong)),
% 24.66/4.10 inference(rectify,[],[f71])).
% 24.66/4.10 thf(f684,plain,(
% 24.66/4.10 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f683])).
% 24.66/4.10 thf(f687,plain,(
% 24.66/4.10 (setunionsingleton1 = ! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))),
% 24.66/4.10 inference(rectify,[],[f153])).
% 24.66/4.10 thf(f688,plain,(
% 24.66/4.10 (setunionsingleton1 = ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0)))))),
% 24.66/4.10 inference(fool_elimination,[],[f687])).
% 24.66/4.10 thf(f691,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X0 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
% 24.66/4.10 inference(rectify,[],[f47])).
% 24.66/4.10 thf(f692,plain,(
% 24.66/4.10 (notinsingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f691])).
% 24.66/4.10 thf(f693,plain,(
% 24.66/4.10 (setoftrueEq = ! [X0 : $i] : (X0 = ((dsetconstr @ X0 @ (^[X1 : $i] : ($true))))))),
% 24.66/4.10 inference(rectify,[],[f36])).
% 24.66/4.10 thf(f694,plain,(
% 24.66/4.10 (setoftrueEq = ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f693])).
% 24.66/4.10 thf(f695,plain,(
% 24.66/4.10 (omega0Ax = ((in @ emptyset @ omega)))),
% 24.66/4.10 inference(fool_elimination,[],[f7])).
% 24.66/4.10 thf(f696,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((subset @ X1 @ X2) => (subset @ X1 @ (binintersect @ X0 @ X2)))) = binintersectSubset5)),
% 24.66/4.10 inference(rectify,[],[f109])).
% 24.66/4.10 thf(f697,plain,(
% 24.66/4.10 (binintersectSubset5 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((subset @ Y1 @ Y0) => (subset @ Y1 @ (binintersect @ Y2 @ Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f696])).
% 24.66/4.10 thf(f700,plain,(
% 24.66/4.10 (funcGraphProp4 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X2) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (((ap @ X2 @ X0 @ X1 @ X3)) = X4))))))),
% 24.66/4.10 inference(rectify,[],[f208])).
% 24.66/4.10 thf(f701,plain,(
% 24.66/4.10 (funcGraphProp4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => ((ap @ Y0 @ Y2 @ Y1 @ Y3) = Y4)))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f700])).
% 24.66/4.10 thf(f702,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = setukpairIR)),
% 24.66/4.10 inference(rectify,[],[f137])).
% 24.66/4.10 thf(f703,plain,(
% 24.66/4.10 (setukpairIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f702])).
% 24.66/4.10 thf(f704,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((kpair @ X3 @ X1)) = ((kpair @ X0 @ X2))) => (X0 = X3)) = setukpairinjL)),
% 24.66/4.10 inference(rectify,[],[f167])).
% 24.66/4.10 thf(f705,plain,(
% 24.66/4.10 (setukpairinjL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y2) = (kpair @ Y3 @ Y1)) => (Y3 = Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f704])).
% 24.66/4.10 thf(f706,plain,(
% 24.66/4.10 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 24.66/4.10 inference(rectify,[],[f20])).
% 24.66/4.10 thf(f707,plain,(
% 24.66/4.10 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false)))))),
% 24.66/4.10 inference(fool_elimination,[],[f706])).
% 24.66/4.10 thf(f712,plain,(
% 24.66/4.10 (notsubsetI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1))))),
% 24.66/4.10 inference(rectify,[],[f85])).
% 24.66/4.10 thf(f713,plain,(
% 24.66/4.10 (notsubsetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f712])).
% 24.66/4.10 thf(f714,plain,(
% 24.66/4.10 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X2 @ X0)) => (in @ X1 @ X2)))),
% 24.66/4.10 inference(rectify,[],[f110])).
% 24.66/4.10 thf(f715,plain,(
% 24.66/4.10 (binintersectEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f714])).
% 24.66/4.10 thf(f718,plain,(
% 24.66/4.10 (setunionsingleton2 = ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))),
% 24.66/4.10 inference(rectify,[],[f154])).
% 24.66/4.10 thf(f719,plain,(
% 24.66/4.10 (setunionsingleton2 = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f718])).
% 24.66/4.10 thf(f720,plain,(
% 24.66/4.10 (cartprodpairsurjEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (((kpair @ (kfst @ X2) @ (ksnd @ X2))) = X2)))),
% 24.66/4.10 inference(rectify,[],[f183])).
% 24.66/4.10 thf(f721,plain,(
% 24.66/4.10 (cartprodpairsurjEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f720])).
% 24.66/4.10 thf(f722,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => (in @ X0 @ (setminus @ X1 @ X2)))) = setminusI)),
% 24.66/4.10 inference(rectify,[],[f120])).
% 24.66/4.10 thf(f723,plain,(
% 24.66/4.10 (setminusI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (in @ Y2 @ (setminus @ Y1 @ Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f722])).
% 24.66/4.10 thf(f726,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))) = woz13rule2)),
% 24.66/4.10 inference(rectify,[],[f280])).
% 24.66/4.10 thf(f727,plain,(
% 24.66/4.10 (woz13rule2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3)))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f726])).
% 24.66/4.10 thf(f732,plain,(
% 24.66/4.10 (ap2apEq2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => (((ap @ X2 @ X1 @ X0 @ X3)) = ((ap @ X2 @ X1 @ X0 @ X3))))))),
% 24.66/4.10 inference(rectify,[],[f214])).
% 24.66/4.10 thf(f733,plain,(
% 24.66/4.10 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ Y2 @ Y3) = (ap @ Y0 @ Y1 @ Y2 @ Y3))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f732])).
% 24.66/4.10 thf(f736,plain,(
% 24.66/4.10 (exuE3e = ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : (X0 @ X2)))),
% 24.66/4.10 inference(rectify,[],[f22])).
% 24.66/4.10 thf(f737,plain,(
% 24.66/4.10 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f736])).
% 24.66/4.10 thf(f738,plain,(
% 24.66/4.10 (bs114d = ! [X0 : $i,X1 : $i,X2 : $i] : (((binintersect @ X0 @ (binunion @ X2 @ X1))) = ((binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1)))))),
% 24.66/4.10 inference(rectify,[],[f119])).
% 24.66/4.10 thf(f739,plain,(
% 24.66/4.10 (bs114d = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y0 @ Y1)) = (binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f738])).
% 24.66/4.10 thf(f742,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (in @ X2 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X1 & (X4 = X2)) | ((X4 = X3) & ~X1)))))))) = iftrueProp1)),
% 24.66/4.10 inference(rectify,[],[f222])).
% 24.66/4.10 thf(f743,plain,(
% 24.66/4.10 (iftrueProp1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (Y1 => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((~ Y1) & (Y3 = Y4)) | ((Y0 = Y4) & Y1))))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f742])).
% 24.66/4.10 thf(f744,plain,(
% 24.66/4.10 (setminusEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X1 @ X2)) => (in @ X0 @ X1)))),
% 24.66/4.10 inference(rectify,[],[f121])).
% 24.66/4.10 thf(f745,plain,(
% 24.66/4.10 (setminusEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f744])).
% 24.66/4.10 thf(f746,plain,(
% 24.66/4.10 (lam2lamEq = ! [X0 : $i,X1 : ($i > $i),X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X1 @ X3) @ X0)) => (((lam @ X2 @ X0 @ (^[X4 : $i] : ((X1 @ X4))))) = ((lam @ X2 @ X0 @ (^[X5 : $i] : ((X1 @ X5))))))))),
% 24.66/4.10 inference(rectify,[],[f217])).
% 24.66/4.10 thf(f747,plain,(
% 24.66/4.10 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => ((lam @ Y0 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))) = (lam @ Y0 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f746])).
% 24.66/4.10 thf(f748,plain,(
% 24.66/4.10 (ex1E2 = ! [X0 : $i,X1 : ($i > $o)] : ((ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((X1 @ X3) => ((X1 @ X4) => (X3 = X4)))))))),
% 24.66/4.10 inference(rectify,[],[f203])).
% 24.66/4.10 thf(f749,plain,(
% 24.66/4.10 (ex1E2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f748])).
% 24.66/4.10 thf(f750,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = ((setminus @ X1 @ (binunion @ X0 @ X2)))))) = demorgan2)),
% 24.66/4.10 inference(rectify,[],[f277])).
% 24.66/4.10 thf(f751,plain,(
% 24.66/4.10 (demorgan2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((binintersect @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2)) = (setminus @ Y0 @ (binunion @ Y1 @ Y2)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f750])).
% 24.66/4.10 thf(f754,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (((setminus @ X1 @ (setminus @ X1 @ X0))) = X0)) = doubleComplementEq)),
% 24.66/4.10 inference(rectify,[],[f251])).
% 24.66/4.10 thf(f755,plain,(
% 24.66/4.10 (doubleComplementEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f754])).
% 24.66/4.10 thf(f756,plain,(
% 24.66/4.10 (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)) = nonemptyI1)),
% 24.66/4.10 inference(rectify,[],[f30])).
% 24.66/4.10 thf(f757,plain,(
% 24.66/4.10 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0))))))),
% 24.66/4.10 inference(fool_elimination,[],[f756])).
% 24.66/4.10 thf(f758,plain,(
% 24.66/4.10 (emptyinPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 24.66/4.10 inference(rectify,[],[f38])).
% 24.66/4.10 thf(f759,plain,(
% 24.66/4.10 (emptyinPowerset = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 24.66/4.10 inference(fool_elimination,[],[f758])).
% 24.66/4.10 thf(f762,plain,(
% 24.66/4.10 (powersetsubset = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (subset @ (powerset @ X1) @ (powerset @ X0))))),
% 24.66/4.10 inference(rectify,[],[f98])).
% 24.66/4.10 thf(f763,plain,(
% 24.66/4.10 (powersetsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f762])).
% 24.66/4.10 thf(f764,plain,(
% 24.66/4.10 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 24.66/4.10 inference(rectify,[],[f80])).
% 24.66/4.10 thf(f765,plain,(
% 24.66/4.10 (eqimpsubset1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f764])).
% 24.66/4.10 thf(f770,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 24.66/4.10 inference(rectify,[],[f234])).
% 24.66/4.10 thf(f771,plain,(
% 24.66/4.10 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f770])).
% 24.66/4.10 thf(f772,plain,(
% 24.66/4.10 (cartprodfstpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kfst @ (kpair @ X2 @ X3))) = X2))))),
% 24.66/4.10 inference(rectify,[],[f181])).
% 24.66/4.10 thf(f773,plain,(
% 24.66/4.10 (cartprodfstpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f772])).
% 24.66/4.10 thf(f774,plain,(
% 24.66/4.10 (ksndpairEq = ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X1 @ X0))) = X0))),
% 24.66/4.10 inference(rectify,[],[f175])).
% 24.66/4.10 thf(f775,plain,(
% 24.66/4.10 (ksndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f774])).
% 24.66/4.10 thf(f776,plain,(
% 24.66/4.10 (dpsetconstrER = ! [X0 : $i,X1 : ($i > $i > $o),X2 : $i,X3 : $i,X4 : $i] : ((in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X2 @ (^[X5 : $i, X6 : $i] : ((X1 @ X5 @ X6))))) => (X1 @ X4 @ X0)))),
% 24.66/4.10 inference(rectify,[],[f191])).
% 24.66/4.10 thf(f777,plain,(
% 24.66/4.10 (dpsetconstrER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (Y3 @ Y0 @ Y4))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f776])).
% 24.66/4.10 thf(f778,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ksnd @ (kpair @ X1 @ X3))) = X3))) = cartprodsndpairEq)),
% 24.66/4.10 inference(rectify,[],[f182])).
% 24.66/4.10 thf(f779,plain,(
% 24.66/4.10 (cartprodsndpairEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f778])).
% 24.66/4.10 thf(f780,plain,(
% 24.66/4.10 (subsetTrans = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((subset @ X2 @ X0) => (subset @ X1 @ X0))))),
% 24.66/4.10 inference(rectify,[],[f89])).
% 24.66/4.10 thf(f781,plain,(
% 24.66/4.10 (subsetTrans = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y2) => (subset @ Y1 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f780])).
% 24.66/4.10 thf(f786,plain,(
% 24.66/4.10 (singletonsswitch = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 24.66/4.10 inference(rectify,[],[f49])).
% 24.66/4.10 thf(f787,plain,(
% 24.66/4.10 (singletonsswitch = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f786])).
% 24.66/4.10 thf(f788,plain,(
% 24.66/4.10 (sepInPowerset = ! [X0 : $i,X1 : ($i > $o)] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))) @ (powerset @ X0)))),
% 24.66/4.10 inference(rectify,[],[f99])).
% 24.66/4.10 thf(f789,plain,(
% 24.66/4.10 (sepInPowerset = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ (powerset @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f788])).
% 24.66/4.10 thf(f794,plain,(
% 24.66/4.10 (subset2powerset = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 24.66/4.10 inference(rectify,[],[f92])).
% 24.66/4.10 thf(f795,plain,(
% 24.66/4.10 (subset2powerset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f794])).
% 24.66/4.10 thf(f796,plain,(
% 24.66/4.10 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 24.66/4.10 inference(rectify,[],[f59])).
% 24.66/4.10 thf(f797,plain,(
% 24.66/4.10 (prop2setI = ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))))))),
% 24.66/4.10 inference(fool_elimination,[],[f796])).
% 24.66/4.10 thf(f800,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))) = setext)),
% 24.66/4.10 inference(rectify,[],[f23])).
% 24.66/4.10 thf(f801,plain,(
% 24.66/4.10 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f800])).
% 24.66/4.10 thf(f802,plain,(
% 24.66/4.10 (binunionIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X1 @ X0))))),
% 24.66/4.10 inference(rectify,[],[f103])).
% 24.66/4.10 thf(f803,plain,(
% 24.66/4.10 (binunionIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f802])).
% 24.66/4.10 thf(f804,plain,(
% 24.66/4.10 (binunionE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binunion @ X1 @ X2)) => ((in @ X0 @ X2) | (in @ X0 @ X1))))),
% 24.66/4.10 inference(rectify,[],[f105])).
% 24.66/4.10 thf(f805,plain,(
% 24.66/4.10 (binunionE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f804])).
% 24.66/4.10 thf(f806,plain,(
% 24.66/4.10 (binintersectSubset4 = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (((binintersect @ X1 @ X0)) = X0)))),
% 24.66/4.10 inference(rectify,[],[f117])).
% 24.66/4.10 thf(f807,plain,(
% 24.66/4.10 (binintersectSubset4 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f806])).
% 24.66/4.10 thf(f808,plain,(
% 24.66/4.10 (subsetemptysetimpeq = ! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)))),
% 24.66/4.10 inference(rectify,[],[f94])).
% 24.66/4.10 thf(f809,plain,(
% 24.66/4.10 (subsetemptysetimpeq = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0))))))),
% 24.66/4.10 inference(fool_elimination,[],[f808])).
% 24.66/4.10 thf(f812,plain,(
% 24.66/4.10 (emptyset__Cong = ((emptyset = emptyset)))),
% 24.66/4.10 inference(fool_elimination,[],[f70])).
% 24.66/4.10 thf(f813,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))))))) = demorgan1a)),
% 24.66/4.10 inference(rectify,[],[f271])).
% 24.66/4.10 thf(f814,plain,(
% 24.66/4.10 (demorgan1a = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))) => (in @ Y3 @ (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2)))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f813])).
% 24.66/4.10 thf(f817,plain,(
% 24.66/4.10 (notequalI1 = ! [X0 : $i,X1 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)))),
% 24.66/4.10 inference(rectify,[],[f86])).
% 24.66/4.10 thf(f818,plain,(
% 24.66/4.10 (notequalI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f817])).
% 24.66/4.10 thf(f821,plain,(
% 24.66/4.10 (dpsetconstrSub = ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i] : (subset @ (dpsetconstr @ X1 @ X2 @ (^[X3 : $i, X4 : $i] : ((X0 @ X3 @ X4)))) @ (cartprod @ X1 @ X2)))),
% 24.66/4.10 inference(rectify,[],[f186])).
% 24.66/4.10 thf(f822,plain,(
% 24.66/4.10 (dpsetconstrSub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y1 @ Y0))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f821])).
% 24.66/4.10 thf(f823,plain,(
% 24.66/4.10 (doubleComplementSub2 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)))),
% 24.66/4.10 inference(rectify,[],[f250])).
% 24.66/4.10 thf(f824,plain,(
% 24.66/4.10 (doubleComplementSub2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ (setminus @ Y0 @ Y1)) @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f823])).
% 24.66/4.10 thf(f831,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))) = woz1_3)),
% 24.66/4.10 inference(rectify,[],[f285])).
% 24.66/4.10 thf(f832,plain,(
% 24.66/4.10 (woz1_3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y0 @ Y3) @ (binunion @ Y2 @ Y3)))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f831])).
% 24.66/4.10 thf(f833,plain,(
% 24.66/4.10 (eta1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => (X2 = ((lam @ X0 @ X1 @ (^[X3 : $i] : ((ap @ X0 @ X1 @ X2 @ X3))))))))),
% 24.66/4.10 inference(rectify,[],[f216])).
% 24.66/4.10 thf(f834,plain,(
% 24.66/4.10 (eta1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (Y0 = (lam @ Y2 @ Y1 @ (^[Y3 : $i]: (ap @ Y2 @ Y1 @ Y0 @ Y3)))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f833])).
% 24.66/4.10 thf(f837,plain,(
% 24.66/4.10 (setadjoinIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (in @ X0 @ (setadjoin @ X1 @ X2))))),
% 24.66/4.10 inference(rectify,[],[f33])).
% 24.66/4.10 thf(f838,plain,(
% 24.66/4.10 (setadjoinIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0)))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f837])).
% 24.66/4.10 thf(f839,plain,(
% 24.66/4.10 (upairsetIR = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 24.66/4.10 inference(rectify,[],[f52])).
% 24.66/4.10 thf(f840,plain,(
% 24.66/4.10 (upairsetIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f839])).
% 24.66/4.10 thf(f843,plain,(
% 24.66/4.10 (! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X0 @ X3) @ X2)) => ! [X4 : $i] : ((in @ X4 @ X1) => (((ap @ X1 @ X2 @ (lam @ X1 @ X2 @ (^[X5 : $i] : ((X0 @ X5)))) @ X4)) = ((X0 @ X4))))) = beta1)),
% 24.66/4.10 inference(rectify,[],[f215])).
% 24.66/4.10 thf(f844,plain,(
% 24.66/4.10 (beta1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3) = (Y2 @ Y3))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f843])).
% 24.66/4.10 thf(f845,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 24.66/4.10 inference(rectify,[],[f135])).
% 24.66/4.10 thf(f846,plain,(
% 24.66/4.10 (secondinupair = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f845])).
% 24.66/4.10 thf(f850,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X0 @ X2) => ((X1 @ X0) => (in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : ((X1 @ X3))))))) = dsetconstrI)),
% 24.66/4.10 inference(rectify,[],[f14])).
% 24.66/4.10 thf(f851,plain,(
% 24.66/4.10 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f850])).
% 24.66/4.10 thf(f852,plain,(
% 24.66/4.10 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 24.66/4.10 inference(fool_elimination,[],[f27])).
% 24.66/4.10 thf(f855,plain,(
% 24.66/4.10 (vacuousDall = ! [X0 : $i,X1 : ($i > $o)] : ((in @ X0 @ emptyset) => (X1 @ X0)))),
% 24.66/4.10 inference(rectify,[],[f54])).
% 24.66/4.10 thf(f856,plain,(
% 24.66/4.10 (vacuousDall = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f855])).
% 24.66/4.10 thf(f857,plain,(
% 24.66/4.10 (setadjoinSub = ! [X0 : $i,X1 : $i] : (subset @ X0 @ (setadjoin @ X1 @ X0)))),
% 24.66/4.10 inference(rectify,[],[f90])).
% 24.66/4.10 thf(f858,plain,(
% 24.66/4.10 (setadjoinSub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f857])).
% 24.66/4.10 thf(f859,plain,(
% 24.66/4.10 (setminusT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X0 @ X2) @ (powerset @ X1)))))),
% 24.66/4.10 inference(rectify,[],[f233])).
% 24.66/4.10 thf(f860,plain,(
% 24.66/4.10 (setminusT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y1 @ Y2) @ (powerset @ Y0))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f859])).
% 24.66/4.10 thf(f861,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))) = subbreln)),
% 24.66/4.10 inference(rectify,[],[f209])).
% 24.66/4.10 thf(f862,plain,(
% 24.66/4.10 (subbreln = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f861])).
% 24.66/4.10 thf(f863,plain,(
% 24.66/4.10 (ubforcartprodlem2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X0)))))))),
% 24.66/4.10 inference(rectify,[],[f147])).
% 24.66/4.10 thf(f864,plain,(
% 24.66/4.10 (ubforcartprodlem2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2))))))))))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f863])).
% 24.66/4.10 thf(f865,plain,(
% 24.66/4.10 (! [X0 : $i,X1 : $i] : ((in @ X1 @ X0) => (subset @ (setadjoin @ X1 @ emptyset) @ X0)) = singletonsubset)),
% 24.66/4.10 inference(rectify,[],[f140])).
% 24.66/4.10 thf(f866,plain,(
% 24.66/4.10 (singletonsubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1))))))))),
% 24.66/4.10 inference(fool_elimination,[],[f865])).
% 24.66/4.10 thf(f871,plain,(
% 24.66/4.10 (powerset__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0)))))))))),
% 24.66/4.10 inference(cnf_transformation,[],[f300])).
% 24.66/4.10 thf(f873,plain,(
% 24.66/4.10 (disjointsetsI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0)))))))))),
% 24.66/4.10 inference(cnf_transformation,[],[f647])).
% 24.66/4.10 thf(f874,plain,(
% 24.66/4.10 (notsubsetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1))))))))))))),
% 24.66/4.10 inference(cnf_transformation,[],[f713])).
% 24.66/4.10 thf(f875,plain,(
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% 24.66/4.11 inference(cnf_transformation,[],[f320])).
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% 24.66/4.11 inference(cnf_transformation,[],[f601])).
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% 24.66/4.11 inference(cnf_transformation,[],[f455])).
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% 24.66/4.11 inference(cnf_transformation,[],[f299])).
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% 24.66/4.11 inference(cnf_transformation,[],[f858])).
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% 24.66/4.11 inference(cnf_transformation,[],[f851])).
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% 24.66/4.11 inference(cnf_transformation,[],[f812])).
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% 24.66/4.11 inference(cnf_transformation,[],[f551])).
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% 24.66/4.11 inference(cnf_transformation,[],[f727])).
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% 24.66/4.11 inference(cnf_transformation,[],[f856])).
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(exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 24.66/4.11 inference(cnf_transformation,[],[f682])).
% 24.66/4.11 thf(f1142,plain,(
% 24.66/4.11 (notinsingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f692])).
% 24.66/4.11 thf(f1143,plain,(
% 24.66/4.11 (subbreln = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f862])).
% 24.66/4.11 thf(f1144,plain,(
% 24.66/4.11 (subsetemptysetimpeq = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f809])).
% 24.66/4.11 thf(f1147,plain,(
% 24.66/4.11 (singletoninpowunion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f605])).
% 24.66/4.11 thf(f1150,plain,(
% 24.66/4.11 (binunionIR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2)))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f803])).
% 24.66/4.11 thf(f1151,plain,(
% 24.66/4.11 (setukpairinjL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y2) = (kpair @ Y3 @ Y1)) => (Y3 = Y0))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f705])).
% 24.66/4.11 thf(f1152,plain,(
% 24.66/4.11 (ex1I = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f310])).
% 24.66/4.11 thf(f1153,plain,(
% 24.66/4.11 (ksndsingleton = ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0)))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f497])).
% 24.66/4.11 thf(f1154,plain,(
% 24.66/4.11 (kpairp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f559])).
% 24.66/4.11 thf(f1156,plain,(
% 24.66/4.11 (complementUnionInPowersetComplement = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ (binunion @ Y0 @ Y2)) @ (powerset @ (setminus @ Y1 @ Y0)))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f469])).
% 24.66/4.11 thf(f1158,plain,(
% 24.66/4.11 (singletonsuniq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f562])).
% 24.66/4.11 thf(f1159,plain,(
% 24.66/4.11 (ifp = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (if @ Y0 @ Y2 @ Y1 @ Y3) @ Y0)))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f366])).
% 24.66/4.11 thf(f1160,plain,(
% 24.66/4.11 (woz13rule0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y1 @ Y2)) => (in @ Y3 @ Y0))))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f423])).
% 24.66/4.11 thf(f1162,plain,(
% 24.66/4.11 (ap2apEq1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y2 @ Y1 @ Y3) = (ap @ Y0 @ Y2 @ Y1 @ Y3))))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f673])).
% 24.66/4.11 thf(f1163,plain,(
% 24.66/4.11 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f388])).
% 24.66/4.11 thf(f1164,plain,(
% 24.66/4.11 (setminusI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (in @ Y2 @ (setminus @ Y1 @ Y0))))))))))))),
% 24.66/4.11 inference(cnf_transformation,[],[f723])).
% 24.66/4.11 thf(f1166,definition,(
% 24.66/4.11 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 24.66/4.11 introduced(theory,[fool_exhaustiveness_axiom])).
% 24.66/4.11 thf(f1167,plain,(
% 24.66/4.11 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 24.66/4.11 inference(definition_unfolding,[],[f1095,f890])).
% 24.66/4.11 thf(f1169,plain,(
% 24.66/4.11 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => ((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f882,f876])).
% 24.66/4.11 thf(f1170,plain,(
% 24.66/4.11 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f905,f1092])).
% 24.66/4.11 thf(f1171,plain,(
% 24.66/4.11 (nonemptyI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((^[Y3 : $i]: (~ (emptyset = Y3))) @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f906,f876])).
% 24.66/4.11 thf(f1172,plain,(
% 24.66/4.11 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f944,f1092])).
% 24.66/4.11 thf(f1176,plain,(
% 24.66/4.11 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f976,f1092])).
% 24.66/4.11 thf(f1177,plain,(
% 24.66/4.11 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f979,f876])).
% 24.66/4.11 thf(f1178,plain,(
% 24.66/4.11 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f980,f1092])).
% 24.66/4.11 thf(f1179,plain,(
% 24.66/4.11 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f985,f1092])).
% 24.66/4.11 thf(f1181,plain,(
% 24.66/4.11 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f1009,f876])).
% 24.66/4.11 thf(f1189,plain,(
% 24.66/4.11 (exuE2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f1104,f1092])).
% 24.66/4.11 thf(f1190,plain,(
% 24.66/4.11 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f1113,f1092])).
% 24.66/4.11 thf(f1191,plain,(
% 24.66/4.11 ($true = ((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (subset @ Y7 @ (cartprod @ Y5 @ Y6))))))) @ Y3 @ Y3 @ Y4)))) @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f1141,f1167,f1167])).
% 24.66/4.11 thf(f1192,plain,(
% 24.66/4.11 (subbreln = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))))))),
% 24.66/4.11 inference(definition_unfolding,[],[f1143,f890,f890])).
% 24.66/4.11 thf(f1194,definition,(
% 24.66/4.11 (sF0 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (subset @ Y7 @ (cartprod @ Y5 @ Y6))))))) @ Y3 @ Y3 @ Y4)))) @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))))))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])).
% 24.66/4.11 thf(f1195,plain,(
% 24.66/4.11 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y2 @ Y2 @ Y3)))) @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (subset @ Y7 @ (cartprod @ Y5 @ Y6))))))) @ Y3 @ Y3 @ Y4)))) @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))))) = sF0)),
% 24.66/4.11 inference(reorient_equations,[],[f1194])).
% 24.66/4.11 thf(f1196,definition,(
% 24.66/4.11 (sF1 = ((breln1all1 => sF0)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 24.66/4.11 thf(f1197,definition,(
% 24.66/4.11 (sF2 = ((setOfPairsIsBReln1 => sF1)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 24.66/4.11 thf(f1198,definition,(
% 24.66/4.11 (sF3 = ((choice2fnsingleton => sF2)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 24.66/4.11 thf(f1199,definition,(
% 24.66/4.11 (sF4 = ((breln1SetBreln1 => sF3)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 24.66/4.11 thf(f1200,plain,(
% 24.66/4.11 (((breln1SetBreln1 => sF3)) = sF4)),
% 24.66/4.11 inference(reorient_equations,[],[f1199])).
% 24.66/4.11 thf(f1201,definition,(
% 24.66/4.11 (sF5 = ((breln1all2 => sF4)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 24.66/4.11 thf(f1202,plain,(
% 24.66/4.11 (((breln1all2 => sF4)) = sF5)),
% 24.66/4.11 inference(reorient_equations,[],[f1201])).
% 24.66/4.11 thf(f1203,definition,(
% 24.66/4.11 (sF6 = ((woz1_5 => sF5)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 24.66/4.11 thf(f1204,definition,(
% 24.66/4.11 (sF7 = ((woz1_4 => sF6)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 24.66/4.11 thf(f1205,plain,(
% 24.66/4.11 (((woz1_4 => sF6)) = sF7)),
% 24.66/4.11 inference(reorient_equations,[],[f1204])).
% 24.66/4.11 thf(f1206,definition,(
% 24.66/4.11 (sF8 = ((woz1_3 => sF7)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
% 24.66/4.11 thf(f1207,plain,(
% 24.66/4.11 (((woz1_3 => sF7)) = sF8)),
% 24.66/4.11 inference(reorient_equations,[],[f1206])).
% 24.66/4.11 thf(f1208,definition,(
% 24.66/4.11 (sF9 = ((woz1_2 => sF8)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
% 24.66/4.11 thf(f1209,plain,(
% 24.66/4.11 (((woz1_2 => sF8)) = sF9)),
% 24.66/4.11 inference(reorient_equations,[],[f1208])).
% 24.66/4.11 thf(f1210,definition,(
% 24.66/4.11 (sF10 = ((woz1_1 => sF9)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
% 24.66/4.11 thf(f1211,plain,(
% 24.66/4.11 (((woz1_1 => sF9)) = sF10)),
% 24.66/4.11 inference(reorient_equations,[],[f1210])).
% 24.66/4.11 thf(f1212,definition,(
% 24.66/4.11 (sF11 = ((woz13rule4 => sF10)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
% 24.66/4.11 thf(f1213,definition,(
% 24.66/4.11 (sF12 = ((woz13rule3 => sF11)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 24.66/4.11 thf(f1214,definition,(
% 24.66/4.11 (sF13 = ((woz13rule2 => sF12)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
% 24.66/4.11 thf(f1215,plain,(
% 24.66/4.11 (((woz13rule2 => sF12)) = sF13)),
% 24.66/4.11 inference(reorient_equations,[],[f1214])).
% 24.66/4.11 thf(f1216,definition,(
% 24.66/4.11 (sF14 = ((woz13rule1 => sF13)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
% 24.66/4.11 thf(f1217,definition,(
% 24.66/4.11 (sF15 = ((woz13rule0 => sF14)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
% 24.66/4.11 thf(f1218,plain,(
% 24.66/4.11 (((woz13rule0 => sF14)) = sF15)),
% 24.66/4.11 inference(reorient_equations,[],[f1217])).
% 24.66/4.11 thf(f1219,definition,(
% 24.66/4.11 (sF16 = ((demorgan2 => sF15)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF16])],[function_definition])).
% 24.66/4.11 thf(f1220,plain,(
% 24.66/4.11 (((demorgan2 => sF15)) = sF16)),
% 24.66/4.11 inference(reorient_equations,[],[f1219])).
% 24.66/4.11 thf(f1221,definition,(
% 24.66/4.11 (sF17 = ((demorgan2b => sF16)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF17])],[function_definition])).
% 24.66/4.11 thf(f1222,plain,(
% 24.66/4.11 (((demorgan2b => sF16)) = sF17)),
% 24.66/4.11 inference(reorient_equations,[],[f1221])).
% 24.66/4.11 thf(f1223,definition,(
% 24.66/4.11 (sF18 = ((demorgan2b2 => sF17)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF18])],[function_definition])).
% 24.66/4.11 thf(f1224,plain,(
% 24.66/4.11 (((demorgan2b2 => sF17)) = sF18)),
% 24.66/4.11 inference(reorient_equations,[],[f1223])).
% 24.66/4.11 thf(f1225,definition,(
% 24.66/4.11 (sF19 = ((demorgan2a => sF18)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF19])],[function_definition])).
% 24.66/4.11 thf(f1226,definition,(
% 24.66/4.11 (sF20 = ((demorgan1 => sF19)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF20])],[function_definition])).
% 24.66/4.11 thf(f1227,definition,(
% 24.66/4.11 (sF21 = ((demorgan1b => sF20)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF21])],[function_definition])).
% 24.66/4.11 thf(f1228,plain,(
% 24.66/4.11 (((demorgan1b => sF20)) = sF21)),
% 24.66/4.11 inference(reorient_equations,[],[f1227])).
% 24.66/4.11 thf(f1229,definition,(
% 24.66/4.11 (sF22 = ((demorgan1a => sF21)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF22])],[function_definition])).
% 24.66/4.11 thf(f1230,definition,(
% 24.66/4.11 (sF23 = ((demorgan2a2 => sF22)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF23])],[function_definition])).
% 24.66/4.11 thf(f1231,plain,(
% 24.66/4.11 (((demorgan2a2 => sF22)) = sF23)),
% 24.66/4.11 inference(reorient_equations,[],[f1230])).
% 24.66/4.11 thf(f1232,definition,(
% 24.66/4.11 (sF24 = ((complementUnionInPowersetComplement => sF23)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF24])],[function_definition])).
% 24.66/4.11 thf(f1233,definition,(
% 24.66/4.11 (sF25 = ((demorgan2a1 => sF24)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF25])],[function_definition])).
% 24.66/4.11 thf(f1234,plain,(
% 24.66/4.11 (((demorgan2a1 => sF24)) = sF25)),
% 24.66/4.11 inference(reorient_equations,[],[f1233])).
% 24.66/4.11 thf(f1235,definition,(
% 24.66/4.11 (sF26 = ((binunionTEcontra => sF25)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF26])],[function_definition])).
% 24.66/4.11 thf(f1236,definition,(
% 24.66/4.11 (sF27 = ((binunionTE => sF26)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF27])],[function_definition])).
% 24.66/4.11 thf(f1237,definition,(
% 24.66/4.11 (sF28 = ((inComplementUnionImpInComplement1 => sF27)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF28])],[function_definition])).
% 24.66/4.11 thf(f1238,definition,(
% 24.66/4.11 (sF29 = ((inComplementUnionImpNotIn1 => sF28)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF29])],[function_definition])).
% 24.66/4.11 thf(f1239,plain,(
% 24.66/4.11 (((inComplementUnionImpNotIn1 => sF28)) = sF29)),
% 24.66/4.11 inference(reorient_equations,[],[f1238])).
% 24.66/4.11 thf(f1240,definition,(
% 24.66/4.11 (sF30 = ((intersectInPowersetIntersectUnions => sF29)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF30])],[function_definition])).
% 24.66/4.11 thf(f1241,plain,(
% 24.66/4.11 (((intersectInPowersetIntersectUnions => sF29)) = sF30)),
% 24.66/4.11 inference(reorient_equations,[],[f1240])).
% 24.66/4.11 thf(f1242,definition,(
% 24.66/4.11 (sF31 = ((inIntersectImpInIntersectUnions => sF30)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF31])],[function_definition])).
% 24.66/4.11 thf(f1243,plain,(
% 24.66/4.11 (((inIntersectImpInIntersectUnions => sF30)) = sF31)),
% 24.66/4.11 inference(reorient_equations,[],[f1242])).
% 24.66/4.11 thf(f1244,definition,(
% 24.66/4.11 (sF32 = ((inIntersectImpInUnion2 => sF31)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF32])],[function_definition])).
% 24.66/4.11 thf(f1245,definition,(
% 24.66/4.11 (sF33 = ((inIntersectImpInUnion => sF32)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF33])],[function_definition])).
% 24.66/4.11 thf(f1246,definition,(
% 24.66/4.11 (sF34 = ((binunionTIRcontra => sF33)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF34])],[function_definition])).
% 24.66/4.11 thf(f1247,definition,(
% 24.66/4.11 (sF35 = ((binunionTILcontra => sF34)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF35])],[function_definition])).
% 24.66/4.11 thf(f1248,plain,(
% 24.66/4.11 (((binunionTILcontra => sF34)) = sF35)),
% 24.66/4.11 inference(reorient_equations,[],[f1247])).
% 24.66/4.11 thf(f1249,definition,(
% 24.66/4.11 (sF36 = ((complementTcontraSubset => sF35)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF36])],[function_definition])).
% 24.66/4.11 thf(f1250,definition,(
% 24.66/4.11 (sF37 = ((contraSubsetComplement => sF36)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF37])],[function_definition])).
% 24.66/4.11 thf(f1251,plain,(
% 24.66/4.11 (((contraSubsetComplement => sF36)) = sF37)),
% 24.66/4.11 inference(reorient_equations,[],[f1250])).
% 24.66/4.11 thf(f1252,definition,(
% 24.66/4.11 (sF38 = ((complementInPowersetComplementIntersect => sF37)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF38])],[function_definition])).
% 24.66/4.11 thf(f1253,definition,(
% 24.66/4.11 (sF39 = ((complementSubsetComplementIntersect => sF38)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF39])],[function_definition])).
% 24.66/4.11 thf(f1254,definition,(
% 24.66/4.11 (sF40 = ((complementImpComplementIntersect => sF39)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF40])],[function_definition])).
% 24.66/4.11 thf(f1255,plain,(
% 24.66/4.11 (((complementImpComplementIntersect => sF39)) = sF40)),
% 24.66/4.11 inference(reorient_equations,[],[f1254])).
% 24.66/4.11 thf(f1256,definition,(
% 24.66/4.11 (sF41 = ((complementTnotintersectT => sF40)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF41])],[function_definition])).
% 24.66/4.11 thf(f1257,plain,(
% 24.66/4.11 (((complementTnotintersectT => sF40)) = sF41)),
% 24.66/4.11 inference(reorient_equations,[],[f1256])).
% 24.66/4.11 thf(f1258,definition,(
% 24.66/4.11 (sF42 = ((doubleComplementEq => sF41)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF42])],[function_definition])).
% 24.66/4.11 thf(f1259,plain,(
% 24.66/4.11 (((doubleComplementEq => sF41)) = sF42)),
% 24.66/4.11 inference(reorient_equations,[],[f1258])).
% 24.66/4.11 thf(f1260,definition,(
% 24.66/4.11 (sF43 = ((doubleComplementSub2 => sF42)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF43])],[function_definition])).
% 24.66/4.11 thf(f1261,definition,(
% 24.66/4.11 (sF44 = ((doubleComplementSub1 => sF43)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF44])],[function_definition])).
% 24.66/4.11 thf(f1262,definition,(
% 24.66/4.11 (sF45 = ((doubleComplementE1 => sF44)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF45])],[function_definition])).
% 24.66/4.11 thf(f1263,plain,(
% 24.66/4.11 (((doubleComplementE1 => sF44)) = sF45)),
% 24.66/4.11 inference(reorient_equations,[],[f1262])).
% 24.66/4.11 thf(f1264,definition,(
% 24.66/4.11 (sF46 = ((doubleComplementI1 => sF45)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF46])],[function_definition])).
% 24.66/4.11 thf(f1265,definition,(
% 24.66/4.11 (sF47 = ((contrasubsetT3 => sF46)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF47])],[function_definition])).
% 24.66/4.11 thf(f1266,plain,(
% 24.66/4.11 (((contrasubsetT3 => sF46)) = sF47)),
% 24.66/4.11 inference(reorient_equations,[],[f1265])).
% 24.66/4.11 thf(f1267,definition,(
% 24.66/4.11 (sF48 = ((contrasubsetT2 => sF47)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF48])],[function_definition])).
% 24.66/4.11 thf(f1268,plain,(
% 24.66/4.11 (((contrasubsetT2 => sF47)) = sF48)),
% 24.66/4.11 inference(reorient_equations,[],[f1267])).
% 24.66/4.11 thf(f1269,definition,(
% 24.66/4.11 (sF49 = ((contrasubsetT1 => sF48)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF49])],[function_definition])).
% 24.66/4.11 thf(f1270,plain,(
% 24.66/4.11 (((contrasubsetT1 => sF48)) = sF49)),
% 24.66/4.11 inference(reorient_equations,[],[f1269])).
% 24.66/4.11 thf(f1271,definition,(
% 24.66/4.11 (sF50 = ((contrasubsetT => sF49)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF50])],[function_definition])).
% 24.66/4.11 thf(f1272,plain,(
% 24.66/4.11 (((contrasubsetT => sF49)) = sF50)),
% 24.66/4.11 inference(reorient_equations,[],[f1271])).
% 24.66/4.11 thf(f1273,definition,(
% 24.66/4.11 (sF51 = ((binintersectTERcontra => sF50)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF51])],[function_definition])).
% 24.66/4.11 thf(f1274,plain,(
% 24.66/4.11 (((binintersectTERcontra => sF50)) = sF51)),
% 24.66/4.11 inference(reorient_equations,[],[f1273])).
% 24.66/4.11 thf(f1275,definition,(
% 24.66/4.11 (sF52 = ((binintersectTELcontra => sF51)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF52])],[function_definition])).
% 24.66/4.11 thf(f1276,plain,(
% 24.66/4.11 (((binintersectTELcontra => sF51)) = sF52)),
% 24.66/4.11 inference(reorient_equations,[],[f1275])).
% 24.66/4.11 thf(f1277,definition,(
% 24.66/4.11 (sF53 = ((complementTE1 => sF52)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF53])],[function_definition])).
% 24.66/4.11 thf(f1278,definition,(
% 24.66/4.11 (sF54 = ((complementTI1 => sF53)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF54])],[function_definition])).
% 24.66/4.11 thf(f1279,definition,(
% 24.66/4.11 (sF55 = ((powersetTE1 => sF54)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF55])],[function_definition])).
% 24.66/4.11 thf(f1280,plain,(
% 24.66/4.11 (((powersetTE1 => sF54)) = sF55)),
% 24.66/4.11 inference(reorient_equations,[],[f1279])).
% 24.66/4.11 thf(f1281,definition,(
% 24.66/4.11 (sF56 = ((powersetTI1 => sF55)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF56])],[function_definition])).
% 24.66/4.11 thf(f1282,definition,(
% 24.66/4.11 (sF57 = ((subsetTI => sF56)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF57])],[function_definition])).
% 24.66/4.11 thf(f1283,plain,(
% 24.66/4.11 (((subsetTI => sF56)) = sF57)),
% 24.66/4.11 inference(reorient_equations,[],[f1282])).
% 24.66/4.11 thf(f1284,definition,(
% 24.66/4.11 (sF58 = ((setextT => sF57)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF58])],[function_definition])).
% 24.66/4.11 thf(f1285,plain,(
% 24.66/4.11 (((setextT => sF57)) = sF58)),
% 24.66/4.11 inference(reorient_equations,[],[f1284])).
% 24.66/4.11 thf(f1286,definition,(
% 24.66/4.11 (sF59 = ((complementT_lem => sF58)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF59])],[function_definition])).
% 24.66/4.11 thf(f1287,definition,(
% 24.66/4.11 (sF60 = ((setminusT_lem => sF59)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF60])],[function_definition])).
% 24.66/4.11 thf(f1288,plain,(
% 24.66/4.11 (((setminusT_lem => sF59)) = sF60)),
% 24.66/4.11 inference(reorient_equations,[],[f1287])).
% 24.66/4.11 thf(f1289,definition,(
% 24.66/4.11 (sF61 = ((powersetT_lem => sF60)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF61])],[function_definition])).
% 24.66/4.11 thf(f1290,plain,(
% 24.66/4.11 (((powersetT_lem => sF60)) = sF61)),
% 24.66/4.11 inference(reorient_equations,[],[f1289])).
% 24.66/4.11 thf(f1291,definition,(
% 24.66/4.11 (sF62 = ((binunionT_lem => sF61)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF62])],[function_definition])).
% 24.66/4.11 thf(f1292,plain,(
% 24.66/4.11 (((binunionT_lem => sF61)) = sF62)),
% 24.66/4.11 inference(reorient_equations,[],[f1291])).
% 24.66/4.11 thf(f1293,definition,(
% 24.66/4.11 (sF63 = ((binintersectT_lem => sF62)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF63])],[function_definition])).
% 24.66/4.11 thf(f1294,plain,(
% 24.66/4.11 (((binintersectT_lem => sF62)) = sF63)),
% 24.66/4.11 inference(reorient_equations,[],[f1293])).
% 24.66/4.11 thf(f1295,definition,(
% 24.66/4.11 (sF64 = ((iftrueorfalse => sF63)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF64])],[function_definition])).
% 24.66/4.11 thf(f1296,plain,(
% 24.66/4.11 (((iftrueorfalse => sF63)) = sF64)),
% 24.66/4.11 inference(reorient_equations,[],[f1295])).
% 24.66/4.11 thf(f1297,definition,(
% 24.66/4.11 (sF65 = ((iffalse => sF64)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF65])],[function_definition])).
% 24.66/4.11 thf(f1298,definition,(
% 24.66/4.11 (sF66 = ((iftrue => sF65)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF66])],[function_definition])).
% 24.66/4.11 thf(f1299,definition,(
% 24.66/4.11 (sF67 = ((theeq => sF66)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF67])],[function_definition])).
% 24.66/4.11 thf(f1300,definition,(
% 24.66/4.11 (sF68 = ((ifp => sF67)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF68])],[function_definition])).
% 24.66/4.11 thf(f1301,plain,(
% 24.66/4.11 (((ifp => sF67)) = sF68)),
% 24.66/4.11 inference(reorient_equations,[],[f1300])).
% 24.66/4.11 thf(f1302,definition,(
% 24.66/4.11 (sF69 = ((ifSingleton => sF68)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF69])],[function_definition])).
% 24.66/4.11 thf(f1303,plain,(
% 24.66/4.11 (((ifSingleton => sF68)) = sF69)),
% 24.66/4.11 inference(reorient_equations,[],[f1302])).
% 24.66/4.11 thf(f1304,definition,(
% 24.66/4.11 (sF70 = ((iftrueProp2 => sF69)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF70])],[function_definition])).
% 24.66/4.11 thf(f1305,plain,(
% 24.66/4.11 (((iftrueProp2 => sF69)) = sF70)),
% 24.66/4.11 inference(reorient_equations,[],[f1304])).
% 24.66/4.11 thf(f1306,definition,(
% 24.66/4.11 (sF71 = ((iftrueProp1 => sF70)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF71])],[function_definition])).
% 24.66/4.11 thf(f1307,plain,(
% 24.66/4.11 (((iftrueProp1 => sF70)) = sF71)),
% 24.66/4.11 inference(reorient_equations,[],[f1306])).
% 24.66/4.11 thf(f1308,definition,(
% 24.66/4.11 (sF72 = ((iffalseProp2 => sF71)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF72])],[function_definition])).
% 24.66/4.11 thf(f1309,definition,(
% 24.66/4.11 (sF73 = ((iffalseProp1 => sF72)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF73])],[function_definition])).
% 24.66/4.11 thf(f1310,definition,(
% 24.66/4.11 (sF74 = ((eta2 => sF73)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF74])],[function_definition])).
% 24.66/4.11 thf(f1311,plain,(
% 24.66/4.11 (((eta2 => sF73)) = sF74)),
% 24.66/4.11 inference(reorient_equations,[],[f1310])).
% 24.66/4.11 thf(f1312,definition,(
% 24.66/4.11 (sF75 = ((beta2 => sF74)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF75])],[function_definition])).
% 24.66/4.11 thf(f1313,definition,(
% 24.66/4.11 (sF76 = ((lam2lamEq => sF75)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF76])],[function_definition])).
% 24.66/4.11 thf(f1314,plain,(
% 24.66/4.11 (((lam2lamEq => sF75)) = sF76)),
% 24.66/4.11 inference(reorient_equations,[],[f1313])).
% 24.66/4.11 thf(f1315,definition,(
% 24.66/4.11 (sF77 = ((eta1 => sF76)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF77])],[function_definition])).
% 24.66/4.11 thf(f1316,definition,(
% 24.66/4.11 (sF78 = ((beta1 => sF77)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF78])],[function_definition])).
% 24.66/4.11 thf(f1317,plain,(
% 24.66/4.11 (((beta1 => sF77)) = sF78)),
% 24.66/4.11 inference(reorient_equations,[],[f1316])).
% 24.66/4.11 thf(f1318,definition,(
% 24.66/4.11 (sF79 = ((ap2apEq2 => sF78)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF79])],[function_definition])).
% 24.66/4.11 thf(f1319,plain,(
% 24.66/4.11 (((ap2apEq2 => sF78)) = sF79)),
% 24.66/4.11 inference(reorient_equations,[],[f1318])).
% 24.66/4.11 thf(f1320,definition,(
% 24.66/4.11 (sF80 = ((ap2apEq1 => sF79)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF80])],[function_definition])).
% 24.66/4.11 thf(f1321,plain,(
% 24.66/4.11 (((ap2apEq1 => sF79)) = sF80)),
% 24.66/4.11 inference(reorient_equations,[],[f1320])).
% 24.66/4.11 thf(f1322,definition,(
% 24.66/4.11 (sF81 = ((funcext2 => sF80)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF81])],[function_definition])).
% 24.66/4.11 thf(f1323,plain,(
% 24.66/4.11 (((funcext2 => sF80)) = sF81)),
% 24.66/4.11 inference(reorient_equations,[],[f1322])).
% 24.66/4.11 thf(f1324,definition,(
% 24.66/4.11 (sF82 = ((funcext => sF81)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF82])],[function_definition])).
% 24.66/4.11 thf(f1325,plain,(
% 24.66/4.11 (((funcext => sF81)) = sF82)),
% 24.66/4.11 inference(reorient_equations,[],[f1324])).
% 24.66/4.11 thf(f1326,definition,(
% 24.66/4.11 (sF83 = ((eqbreln => sF82)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF83])],[function_definition])).
% 24.66/4.11 thf(f1327,plain,(
% 24.66/4.11 (((eqbreln => sF82)) = sF83)),
% 24.66/4.11 inference(reorient_equations,[],[f1326])).
% 24.66/4.11 thf(f1328,definition,(
% 24.66/4.11 (sF84 = ((subbreln => sF83)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF84])],[function_definition])).
% 24.66/4.11 thf(f1329,definition,(
% 24.66/4.11 (sF85 = ((funcGraphProp4 => sF84)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF85])],[function_definition])).
% 24.66/4.11 thf(f1330,definition,(
% 24.66/4.11 (sF86 = ((funcextLem => sF85)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF86])],[function_definition])).
% 24.66/4.11 thf(f1331,definition,(
% 24.66/4.11 (sF87 = ((funcGraphProp2 => sF86)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF87])],[function_definition])).
% 24.66/4.11 thf(f1332,definition,(
% 24.66/4.11 (sF88 = ((funcGraphProp3 => sF87)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF88])],[function_definition])).
% 24.66/4.11 thf(f1333,definition,(
% 24.66/4.11 (sF89 = ((funcGraphProp1 => sF88)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF89])],[function_definition])).
% 24.66/4.11 thf(f1334,plain,(
% 24.66/4.11 (((funcGraphProp1 => sF88)) = sF89)),
% 24.66/4.11 inference(reorient_equations,[],[f1333])).
% 24.66/4.11 thf(f1335,definition,(
% 24.66/4.11 (sF90 = ((ex1E2 => sF89)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF90])],[function_definition])).
% 24.66/4.11 thf(f1336,definition,(
% 24.66/4.11 (sF91 = ((brelnall2 => sF90)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF91])],[function_definition])).
% 24.66/4.11 thf(f1337,plain,(
% 24.66/4.11 (((brelnall2 => sF90)) = sF91)),
% 24.66/4.11 inference(reorient_equations,[],[f1336])).
% 24.66/4.11 thf(f1338,definition,(
% 24.66/4.11 (sF92 = ((brelnall1 => sF91)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF92])],[function_definition])).
% 24.66/4.11 thf(f1339,definition,(
% 24.66/4.11 (sF93 = ((lam2p => sF92)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF93])],[function_definition])).
% 24.66/4.11 thf(f1340,plain,(
% 24.66/4.11 (((lam2p => sF92)) = sF93)),
% 24.66/4.11 inference(reorient_equations,[],[f1339])).
% 24.66/4.11 thf(f1341,definition,(
% 24.66/4.11 (sF94 = ((lamp => sF93)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF94])],[function_definition])).
% 24.66/4.11 thf(f1342,plain,(
% 24.66/4.11 (((lamp => sF93)) = sF94)),
% 24.66/4.11 inference(reorient_equations,[],[f1341])).
% 24.66/4.11 thf(f1343,definition,(
% 24.66/4.11 (sF95 = ((lamProp => sF94)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF95])],[function_definition])).
% 24.66/4.11 thf(f1344,definition,(
% 24.66/4.11 (sF96 = ((funcinfuncset => sF95)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF96])],[function_definition])).
% 24.66/4.11 thf(f1345,definition,(
% 24.66/4.11 (sF97 = ((ap2p => sF96)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF97])],[function_definition])).
% 24.66/4.11 thf(f1346,plain,(
% 24.66/4.11 (((ap2p => sF96)) = sF97)),
% 24.66/4.11 inference(reorient_equations,[],[f1345])).
% 24.66/4.11 thf(f1347,definition,(
% 24.66/4.11 (sF98 = ((infuncsetfunc => sF97)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF98])],[function_definition])).
% 24.66/4.11 thf(f1348,definition,(
% 24.66/4.11 (sF99 = ((app => sF98)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF99])],[function_definition])).
% 24.66/4.11 thf(f1349,definition,(
% 24.66/4.11 (sF100 = ((apProp => sF99)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF100])],[function_definition])).
% 24.66/4.11 thf(f1350,plain,(
% 24.66/4.11 (((apProp => sF99)) = sF100)),
% 24.66/4.11 inference(reorient_equations,[],[f1349])).
% 24.66/4.11 thf(f1351,definition,(
% 24.66/4.11 (sF101 = ((funcImageSingleton => sF100)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF101])],[function_definition])).
% 24.66/4.11 thf(f1352,plain,(
% 24.66/4.11 (((funcImageSingleton => sF100)) = sF101)),
% 24.66/4.11 inference(reorient_equations,[],[f1351])).
% 24.66/4.11 thf(f1353,definition,(
% 24.66/4.11 (sF102 = ((dpsetconstrER => sF101)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF102])],[function_definition])).
% 24.66/4.11 thf(f1354,plain,(
% 24.66/4.11 (((dpsetconstrER => sF101)) = sF102)),
% 24.66/4.11 inference(reorient_equations,[],[f1353])).
% 24.66/4.11 thf(f1355,definition,(
% 24.66/4.11 (sF103 = ((dpsetconstrEL2 => sF102)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF103])],[function_definition])).
% 24.66/4.11 thf(f1356,plain,(
% 24.66/4.11 (((dpsetconstrEL2 => sF102)) = sF103)),
% 24.66/4.11 inference(reorient_equations,[],[f1355])).
% 24.66/4.11 thf(f1357,definition,(
% 24.66/4.11 (sF104 = ((dpsetconstrEL1 => sF103)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF104])],[function_definition])).
% 24.66/4.11 thf(f1358,definition,(
% 24.66/4.11 (sF105 = ((dpsetconstrERa => sF104)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF105])],[function_definition])).
% 24.66/4.11 thf(f1359,definition,(
% 24.66/4.11 (sF106 = ((setOfPairsIsBReln => sF105)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF106])],[function_definition])).
% 24.66/4.11 thf(f1360,plain,(
% 24.66/4.11 (((setOfPairsIsBReln => sF105)) = sF106)),
% 24.66/4.11 inference(reorient_equations,[],[f1359])).
% 24.66/4.11 thf(f1361,definition,(
% 24.66/4.11 (sF107 = ((dpsetconstrSub => sF106)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF107])],[function_definition])).
% 24.66/4.11 thf(f1362,definition,(
% 24.66/4.11 (sF108 = ((dpsetconstrI => sF107)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF108])],[function_definition])).
% 24.66/4.11 thf(f1363,definition,(
% 24.66/4.11 (sF109 = ((cartprodpairsurjEq => sF108)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF109])],[function_definition])).
% 24.66/4.11 thf(f1364,definition,(
% 24.66/4.11 (sF110 = ((cartprodsndpairEq => sF109)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF110])],[function_definition])).
% 24.66/4.11 thf(f1365,definition,(
% 24.66/4.11 (sF111 = ((cartprodfstpairEq => sF110)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF111])],[function_definition])).
% 24.66/4.11 thf(f1366,plain,(
% 24.66/4.11 (((cartprodfstpairEq => sF110)) = sF111)),
% 24.66/4.11 inference(reorient_equations,[],[f1365])).
% 24.66/4.11 thf(f1367,definition,(
% 24.66/4.11 (sF112 = ((cartprodmempaircEq => sF111)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF112])],[function_definition])).
% 24.66/4.11 thf(f1368,plain,(
% 24.66/4.11 (((cartprodmempaircEq => sF111)) = sF112)),
% 24.66/4.11 inference(reorient_equations,[],[f1367])).
% 24.66/4.11 thf(f1369,definition,(
% 24.66/4.11 (sF113 = ((cartprodpairmemER => sF112)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF113])],[function_definition])).
% 24.66/4.11 thf(f1370,plain,(
% 24.66/4.11 (((cartprodpairmemER => sF112)) = sF113)),
% 24.66/4.11 inference(reorient_equations,[],[f1369])).
% 24.66/4.11 thf(f1371,definition,(
% 24.66/4.11 (sF114 = ((cartprodpairmemEL => sF113)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF114])],[function_definition])).
% 24.66/4.11 thf(f1372,plain,(
% 24.66/4.11 (((cartprodpairmemEL => sF113)) = sF114)),
% 24.66/4.11 inference(reorient_equations,[],[f1371])).
% 24.66/4.11 thf(f1373,definition,(
% 24.66/4.11 (sF115 = ((cartprodsndin => sF114)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF115])],[function_definition])).
% 24.66/4.11 thf(f1374,definition,(
% 24.66/4.11 (sF116 = ((kpairsurjEq => sF115)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF116])],[function_definition])).
% 24.66/4.11 thf(f1375,definition,(
% 24.66/4.11 (sF117 = ((ksndpairEq => sF116)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF117])],[function_definition])).
% 24.66/4.11 thf(f1376,definition,(
% 24.66/4.11 (sF118 = ((ksndsingleton => sF117)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF118])],[function_definition])).
% 24.66/4.11 thf(f1377,definition,(
% 24.66/4.11 (sF119 = ((setukpairinjR => sF118)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF119])],[function_definition])).
% 24.66/4.11 thf(f1378,plain,(
% 24.66/4.11 (((setukpairinjR => sF118)) = sF119)),
% 24.66/4.11 inference(reorient_equations,[],[f1377])).
% 24.66/4.11 thf(f1379,definition,(
% 24.66/4.11 (sF120 = ((setukpairinjR2 => sF119)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF120])],[function_definition])).
% 24.66/4.11 thf(f1380,plain,(
% 24.66/4.11 (((setukpairinjR2 => sF119)) = sF120)),
% 24.66/4.11 inference(reorient_equations,[],[f1379])).
% 24.66/4.11 thf(f1381,definition,(
% 24.66/4.11 (sF121 = ((upairequniteq => sF120)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF121])],[function_definition])).
% 24.66/4.11 thf(f1382,definition,(
% 24.66/4.11 (sF122 = ((setukpairinjR1 => sF121)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF122])],[function_definition])).
% 24.66/4.11 thf(f1383,plain,(
% 24.66/4.11 (((setukpairinjR1 => sF121)) = sF122)),
% 24.66/4.11 inference(reorient_equations,[],[f1382])).
% 24.66/4.11 thf(f1384,definition,(
% 24.66/4.11 (sF123 = ((setukpairinjR12 => sF122)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF123])],[function_definition])).
% 24.66/4.11 thf(f1385,plain,(
% 24.66/4.11 (((setukpairinjR12 => sF122)) = sF123)),
% 24.66/4.11 inference(reorient_equations,[],[f1384])).
% 24.66/4.11 thf(f1386,definition,(
% 24.66/4.11 (sF124 = ((setukpairinjR11 => sF123)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF124])],[function_definition])).
% 24.66/4.11 thf(f1387,plain,(
% 24.66/4.11 (((setukpairinjR11 => sF123)) = sF124)),
% 24.66/4.11 inference(reorient_equations,[],[f1386])).
% 24.66/4.11 thf(f1388,definition,(
% 24.66/4.11 (sF125 = ((setukpairinjL => sF124)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF125])],[function_definition])).
% 24.66/4.11 thf(f1389,definition,(
% 24.66/4.11 (sF126 = ((setukpairinjL2 => sF125)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF126])],[function_definition])).
% 24.66/4.11 thf(f1390,plain,(
% 24.66/4.11 (((setukpairinjL2 => sF125)) = sF126)),
% 24.66/4.11 inference(reorient_equations,[],[f1389])).
% 24.66/4.11 thf(f1391,definition,(
% 24.66/4.11 (sF127 = ((cartprodfstin => sF126)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF127])],[function_definition])).
% 24.66/4.11 thf(f1392,definition,(
% 24.66/4.11 (sF128 = ((kfstpairEq => sF127)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF128])],[function_definition])).
% 24.66/4.11 thf(f1393,definition,(
% 24.66/4.11 (sF129 = ((theprop => sF128)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF129])],[function_definition])).
% 24.66/4.11 thf(f1394,definition,(
% 24.66/4.11 (sF130 = ((kfstsingleton => sF129)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF130])],[function_definition])).
% 24.66/4.11 thf(f1395,plain,(
% 24.66/4.11 (((kfstsingleton => sF129)) = sF130)),
% 24.66/4.11 inference(reorient_equations,[],[f1394])).
% 24.66/4.11 thf(f1396,definition,(
% 24.66/4.11 (sF131 = ((setukpairinjL1 => sF130)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF131])],[function_definition])).
% 24.66/4.11 thf(f1397,definition,(
% 24.66/4.11 (sF132 = ((singletonsuniq => sF131)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF132])],[function_definition])).
% 24.66/4.11 thf(f1398,definition,(
% 24.66/4.11 (sF133 = ((ex1I2 => sF132)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF133])],[function_definition])).
% 24.66/4.11 thf(f1399,definition,(
% 24.66/4.11 (sF134 = ((ex1I => sF133)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF134])],[function_definition])).
% 24.66/4.11 thf(f1400,plain,(
% 24.66/4.11 (((ex1I => sF133)) = sF134)),
% 24.66/4.11 inference(reorient_equations,[],[f1399])).
% 24.66/4.11 thf(f1401,definition,(
% 24.66/4.11 (sF135 = ((ex1E1 => sF134)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF135])],[function_definition])).
% 24.66/4.11 thf(f1402,definition,(
% 24.66/4.11 (sF136 = ((singletonprop => sF135)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF136])],[function_definition])).
% 24.66/4.11 thf(f1403,plain,(
% 24.66/4.11 (((singletonprop => sF135)) = sF136)),
% 24.66/4.11 inference(reorient_equations,[],[f1402])).
% 24.66/4.11 thf(f1404,definition,(
% 24.66/4.11 (sF137 = ((setunionsingleton => sF136)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF137])],[function_definition])).
% 24.66/4.11 thf(f1405,definition,(
% 24.66/4.11 (sF138 = ((setunionsingleton2 => sF137)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF138])],[function_definition])).
% 24.66/4.11 thf(f1406,plain,(
% 24.66/4.11 (((setunionsingleton2 => sF137)) = sF138)),
% 24.66/4.11 inference(reorient_equations,[],[f1405])).
% 24.66/4.11 thf(f1407,definition,(
% 24.66/4.11 (sF139 = ((setunionsingleton1 => sF138)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF139])],[function_definition])).
% 24.66/4.11 thf(f1408,definition,(
% 24.66/4.11 (sF140 = ((setunionE2 => sF139)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF140])],[function_definition])).
% 24.66/4.11 thf(f1409,plain,(
% 24.66/4.11 (((setunionE2 => sF139)) = sF140)),
% 24.66/4.11 inference(reorient_equations,[],[f1408])).
% 24.66/4.11 thf(f1410,definition,(
% 24.66/4.11 (sF141 = ((cartprodmempair => sF140)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF141])],[function_definition])).
% 24.66/4.11 thf(f1411,plain,(
% 24.66/4.11 (((cartprodmempair => sF140)) = sF141)),
% 24.66/4.11 inference(reorient_equations,[],[f1410])).
% 24.66/4.11 thf(f1412,definition,(
% 24.66/4.11 (sF142 = ((cartprodmempair1 => sF141)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF142])],[function_definition])).
% 24.66/4.11 thf(f1413,plain,(
% 24.66/4.11 (((cartprodmempair1 => sF141)) = sF142)),
% 24.66/4.11 inference(reorient_equations,[],[f1412])).
% 24.66/4.11 thf(f1414,definition,(
% 24.66/4.11 (sF143 = ((cartprodpairin => sF142)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF143])],[function_definition])).
% 24.66/4.11 thf(f1415,definition,(
% 24.66/4.11 (sF144 = ((ubforcartprodlem3 => sF143)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF144])],[function_definition])).
% 24.66/4.11 thf(f1416,plain,(
% 24.66/4.11 (((ubforcartprodlem3 => sF143)) = sF144)),
% 24.66/4.11 inference(reorient_equations,[],[f1415])).
% 24.66/4.11 thf(f1417,definition,(
% 24.66/4.11 (sF145 = ((ubforcartprodlem2 => sF144)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF145])],[function_definition])).
% 24.66/4.11 thf(f1418,plain,(
% 24.66/4.11 (((ubforcartprodlem2 => sF144)) = sF145)),
% 24.66/4.11 inference(reorient_equations,[],[f1417])).
% 24.66/4.11 thf(f1419,definition,(
% 24.66/4.11 (sF146 = ((ubforcartprodlem1 => sF145)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF146])],[function_definition])).
% 24.66/4.11 thf(f1420,definition,(
% 24.66/4.11 (sF147 = ((upairinpowunion => sF146)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF147])],[function_definition])).
% 24.66/4.11 thf(f1421,plain,(
% 24.66/4.11 (((upairinpowunion => sF146)) = sF147)),
% 24.66/4.11 inference(reorient_equations,[],[f1420])).
% 24.66/4.11 thf(f1422,definition,(
% 24.66/4.11 (sF148 = ((upairsubunion => sF147)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF148])],[function_definition])).
% 24.66/4.11 thf(f1423,definition,(
% 24.66/4.11 (sF149 = ((upairset2E => sF148)))),
% 24.66/4.11 introduced(definition,[new_symbols(definition,[sF149])],[function_definition])).
% 24.66/4.11 thf(f1424,plain,(
% 24.66/4.11 (((upairset2E => sF148)) = sF149)),
% 24.66/4.11 inference(reorient_equations,[],[f1423])).
% 24.66/4.11 thf(f1425,definition,(
% 24.66/4.11 (sF150 = ((singletoninpowunion => sF149)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF150])],[function_definition])).
% 24.66/4.12 thf(f1426,plain,(
% 24.66/4.12 (((singletoninpowunion => sF149)) = sF150)),
% 24.66/4.12 inference(reorient_equations,[],[f1425])).
% 24.66/4.12 thf(f1427,definition,(
% 24.66/4.12 (sF151 = ((singletoninpowerset => sF150)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF151])],[function_definition])).
% 24.66/4.12 thf(f1428,definition,(
% 24.66/4.12 (sF152 = ((singletonsubset => sF151)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF152])],[function_definition])).
% 24.66/4.12 thf(f1429,plain,(
% 24.66/4.12 (((singletonsubset => sF151)) = sF152)),
% 24.66/4.12 inference(reorient_equations,[],[f1428])).
% 24.66/4.12 thf(f1430,definition,(
% 24.66/4.12 (sF153 = ((kpairp => sF152)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF153])],[function_definition])).
% 24.66/4.12 thf(f1431,definition,(
% 24.66/4.12 (sF154 = ((kpairiskpair => sF153)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF154])],[function_definition])).
% 24.66/4.12 thf(f1432,plain,(
% 24.66/4.12 (((kpairiskpair => sF153)) = sF154)),
% 24.66/4.12 inference(reorient_equations,[],[f1431])).
% 24.66/4.12 thf(f1433,definition,(
% 24.66/4.12 (sF155 = ((setukpairIR => sF154)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF155])],[function_definition])).
% 24.66/4.12 thf(f1434,plain,(
% 24.66/4.12 (((setukpairIR => sF154)) = sF155)),
% 24.66/4.12 inference(reorient_equations,[],[f1433])).
% 24.66/4.12 thf(f1435,definition,(
% 24.66/4.12 (sF156 = ((setukpairIL => sF155)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF156])],[function_definition])).
% 24.66/4.12 thf(f1436,plain,(
% 24.66/4.12 (((setukpairIL => sF155)) = sF156)),
% 24.66/4.12 inference(reorient_equations,[],[f1435])).
% 24.66/4.12 thf(f1437,definition,(
% 24.66/4.12 (sF157 = ((secondinupair => sF156)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF157])],[function_definition])).
% 24.66/4.12 thf(f1438,plain,(
% 24.66/4.12 (((secondinupair => sF156)) = sF157)),
% 24.66/4.12 inference(reorient_equations,[],[f1437])).
% 24.66/4.12 thf(f1439,definition,(
% 24.66/4.12 (sF158 = ((symdiffIneg2 => sF157)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF158])],[function_definition])).
% 24.66/4.12 thf(f1440,plain,(
% 24.66/4.12 (((symdiffIneg2 => sF157)) = sF158)),
% 24.66/4.12 inference(reorient_equations,[],[f1439])).
% 24.66/4.12 thf(f1441,definition,(
% 24.66/4.12 (sF159 = ((symdiffIneg1 => sF158)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF159])],[function_definition])).
% 24.66/4.12 thf(f1442,plain,(
% 24.66/4.12 (((symdiffIneg1 => sF158)) = sF159)),
% 24.66/4.12 inference(reorient_equations,[],[f1441])).
% 24.66/4.12 thf(f1443,definition,(
% 24.66/4.12 (sF160 = ((symdiffI2 => sF159)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF160])],[function_definition])).
% 24.66/4.12 thf(f1444,definition,(
% 24.66/4.12 (sF161 = ((symdiffI1 => sF160)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF161])],[function_definition])).
% 24.66/4.12 thf(f1445,definition,(
% 24.66/4.12 (sF162 = ((symdiffE => sF161)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF162])],[function_definition])).
% 24.66/4.12 thf(f1446,plain,(
% 24.66/4.12 (((symdiffE => sF161)) = sF162)),
% 24.66/4.12 inference(reorient_equations,[],[f1445])).
% 24.66/4.12 thf(f1447,definition,(
% 24.66/4.12 (sF163 = ((setminusSubset1 => sF162)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF163])],[function_definition])).
% 24.66/4.12 thf(f1448,plain,(
% 24.66/4.12 (((setminusSubset1 => sF162)) = sF163)),
% 24.66/4.12 inference(reorient_equations,[],[f1447])).
% 24.66/4.12 thf(f1449,definition,(
% 24.66/4.12 (sF164 = ((setminusLsub => sF163)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF164])],[function_definition])).
% 24.66/4.12 thf(f1450,plain,(
% 24.66/4.12 (((setminusLsub => sF163)) = sF164)),
% 24.66/4.12 inference(reorient_equations,[],[f1449])).
% 24.66/4.12 thf(f1451,definition,(
% 24.66/4.12 (sF165 = ((setminusIRneg => sF164)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF165])],[function_definition])).
% 24.66/4.12 thf(f1452,plain,(
% 24.66/4.12 (((setminusIRneg => sF164)) = sF165)),
% 24.66/4.12 inference(reorient_equations,[],[f1451])).
% 24.66/4.12 thf(f1453,definition,(
% 24.66/4.12 (sF166 = ((setminusILneg => sF165)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF166])],[function_definition])).
% 24.66/4.12 thf(f1454,definition,(
% 24.66/4.12 (sF167 = ((setminusELneg => sF166)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF167])],[function_definition])).
% 24.66/4.12 thf(f1455,definition,(
% 24.66/4.12 (sF168 = ((setminusERneg => sF167)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF168])],[function_definition])).
% 24.66/4.12 thf(f1456,plain,(
% 24.66/4.12 (((setminusERneg => sF167)) = sF168)),
% 24.66/4.12 inference(reorient_equations,[],[f1455])).
% 24.66/4.12 thf(f1457,definition,(
% 24.66/4.12 (sF169 = ((setminusSubset2 => sF168)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF169])],[function_definition])).
% 24.66/4.12 thf(f1458,plain,(
% 24.66/4.12 (((setminusSubset2 => sF168)) = sF169)),
% 24.66/4.12 inference(reorient_equations,[],[f1457])).
% 24.66/4.12 thf(f1459,definition,(
% 24.66/4.12 (sF170 = ((setminusER => sF169)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF170])],[function_definition])).
% 24.66/4.12 thf(f1460,definition,(
% 24.66/4.12 (sF171 = ((setminusEL => sF170)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF171])],[function_definition])).
% 24.66/4.12 thf(f1461,definition,(
% 24.66/4.12 (sF172 = ((setminusI => sF171)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF172])],[function_definition])).
% 24.66/4.12 thf(f1462,definition,(
% 24.66/4.12 (sF173 = ((bs114d => sF172)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF173])],[function_definition])).
% 24.66/4.12 thf(f1463,plain,(
% 24.66/4.12 (((bs114d => sF172)) = sF173)),
% 24.66/4.12 inference(reorient_equations,[],[f1462])).
% 24.66/4.12 thf(f1464,definition,(
% 24.66/4.12 (sF174 = ((binintersectSubset1 => sF173)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF174])],[function_definition])).
% 24.66/4.12 thf(f1465,plain,(
% 24.66/4.12 (((binintersectSubset1 => sF173)) = sF174)),
% 24.66/4.12 inference(reorient_equations,[],[f1464])).
% 24.66/4.12 thf(f1466,definition,(
% 24.66/4.12 (sF175 = ((binintersectSubset4 => sF174)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF175])],[function_definition])).
% 24.66/4.12 thf(f1467,definition,(
% 24.66/4.12 (sF176 = ((binintersectRsub => sF175)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF176])],[function_definition])).
% 24.66/4.12 thf(f1468,plain,(
% 24.66/4.12 (((binintersectRsub => sF175)) = sF176)),
% 24.66/4.12 inference(reorient_equations,[],[f1467])).
% 24.66/4.12 thf(f1469,definition,(
% 24.66/4.12 (sF177 = ((disjointsetsI1 => sF176)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF177])],[function_definition])).
% 24.66/4.12 thf(f1470,plain,(
% 24.66/4.12 (((disjointsetsI1 => sF176)) = sF177)),
% 24.66/4.12 inference(reorient_equations,[],[f1469])).
% 24.66/4.12 thf(f1471,definition,(
% 24.66/4.12 (sF178 = ((binintersectER => sF177)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF178])],[function_definition])).
% 24.66/4.12 thf(f1472,definition,(
% 24.66/4.12 (sF179 = ((binintersectSubset3 => sF178)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF179])],[function_definition])).
% 24.66/4.12 thf(f1473,definition,(
% 24.66/4.12 (sF180 = ((binintersectSubset2 => sF179)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF180])],[function_definition])).
% 24.66/4.12 thf(f1474,plain,(
% 24.66/4.12 (((binintersectSubset2 => sF179)) = sF180)),
% 24.66/4.12 inference(reorient_equations,[],[f1473])).
% 24.66/4.12 thf(f1475,definition,(
% 24.66/4.12 (sF181 = ((binintersectLsub => sF180)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF181])],[function_definition])).
% 24.66/4.12 thf(f1476,plain,(
% 24.66/4.12 (((binintersectLsub => sF180)) = sF181)),
% 24.66/4.12 inference(reorient_equations,[],[f1475])).
% 24.66/4.12 thf(f1477,definition,(
% 24.66/4.12 (sF182 = ((binintersectEL => sF181)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF182])],[function_definition])).
% 24.66/4.12 thf(f1478,definition,(
% 24.66/4.12 (sF183 = ((binintersectSubset5 => sF182)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF183])],[function_definition])).
% 24.66/4.12 thf(f1479,definition,(
% 24.66/4.12 (sF184 = ((binintersectI => sF183)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF184])],[function_definition])).
% 24.66/4.12 thf(f1480,definition,(
% 24.66/4.12 (sF185 = ((binunionRsub => sF184)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF185])],[function_definition])).
% 24.66/4.12 thf(f1481,definition,(
% 24.66/4.12 (sF186 = ((binunionLsub => sF185)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF186])],[function_definition])).
% 24.66/4.12 thf(f1482,plain,(
% 24.66/4.12 (((binunionLsub => sF185)) = sF186)),
% 24.66/4.12 inference(reorient_equations,[],[f1481])).
% 24.66/4.12 thf(f1483,definition,(
% 24.66/4.12 (sF187 = ((binunionE => sF186)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF187])],[function_definition])).
% 24.66/4.12 thf(f1484,definition,(
% 24.66/4.12 (sF188 = ((binunionEcases => sF187)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF188])],[function_definition])).
% 24.66/4.12 thf(f1485,plain,(
% 24.66/4.12 (((binunionEcases => sF187)) = sF188)),
% 24.66/4.12 inference(reorient_equations,[],[f1484])).
% 24.66/4.12 thf(f1486,definition,(
% 24.66/4.12 (sF189 = ((binunionIR => sF188)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF189])],[function_definition])).
% 24.66/4.12 thf(f1487,plain,(
% 24.66/4.12 (((binunionIR => sF188)) = sF189)),
% 24.66/4.12 inference(reorient_equations,[],[f1486])).
% 24.66/4.12 thf(f1488,definition,(
% 24.66/4.12 (sF190 = ((upairset2IR => sF189)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF190])],[function_definition])).
% 24.66/4.12 thf(f1489,plain,(
% 24.66/4.12 (((upairset2IR => sF189)) = sF190)),
% 24.66/4.12 inference(reorient_equations,[],[f1488])).
% 24.66/4.12 thf(f1490,definition,(
% 24.66/4.12 (sF191 = ((binunionIL => sF190)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF191])],[function_definition])).
% 24.66/4.12 thf(f1491,definition,(
% 24.66/4.12 (sF192 = ((sepSubset => sF191)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF192])],[function_definition])).
% 24.66/4.12 thf(f1492,plain,(
% 24.66/4.12 (((sepSubset => sF191)) = sF192)),
% 24.66/4.12 inference(reorient_equations,[],[f1491])).
% 24.66/4.12 thf(f1493,definition,(
% 24.66/4.12 (sF193 = ((sepInPowerset => sF192)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF193])],[function_definition])).
% 24.66/4.12 thf(f1494,plain,(
% 24.66/4.12 (((sepInPowerset => sF192)) = sF193)),
% 24.66/4.12 inference(reorient_equations,[],[f1493])).
% 24.66/4.12 thf(f1495,definition,(
% 24.66/4.12 (sF194 = ((powersetsubset => sF193)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF194])],[function_definition])).
% 24.66/4.12 thf(f1496,plain,(
% 24.66/4.12 (((powersetsubset => sF193)) = sF194)),
% 24.66/4.12 inference(reorient_equations,[],[f1495])).
% 24.66/4.12 thf(f1497,definition,(
% 24.66/4.12 (sF195 = ((inPowerset => sF194)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF195])],[function_definition])).
% 24.66/4.12 thf(f1498,definition,(
% 24.66/4.12 (sF196 = ((powersetE1 => sF195)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF196])],[function_definition])).
% 24.66/4.12 thf(f1499,plain,(
% 24.66/4.12 (((powersetE1 => sF195)) = sF196)),
% 24.66/4.12 inference(reorient_equations,[],[f1498])).
% 24.66/4.12 thf(f1500,definition,(
% 24.66/4.12 (sF197 = ((powersetI1 => sF196)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF197])],[function_definition])).
% 24.66/4.12 thf(f1501,plain,(
% 24.66/4.12 (((powersetI1 => sF196)) = sF197)),
% 24.66/4.12 inference(reorient_equations,[],[f1500])).
% 24.66/4.12 thf(f1502,definition,(
% 24.66/4.12 (sF198 = ((subsetemptysetimpeq => sF197)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF198])],[function_definition])).
% 24.66/4.12 thf(f1503,definition,(
% 24.66/4.12 (sF199 = ((setextsub => sF198)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF199])],[function_definition])).
% 24.66/4.12 thf(f1504,plain,(
% 24.66/4.12 (((setextsub => sF198)) = sF199)),
% 24.66/4.12 inference(reorient_equations,[],[f1503])).
% 24.66/4.12 thf(f1505,definition,(
% 24.66/4.12 (sF200 = ((subset2powerset => sF199)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF200])],[function_definition])).
% 24.66/4.12 thf(f1506,plain,(
% 24.66/4.12 (((subset2powerset => sF199)) = sF200)),
% 24.66/4.12 inference(reorient_equations,[],[f1505])).
% 24.66/4.12 thf(f1507,definition,(
% 24.66/4.12 (sF201 = ((setadjoinSub2 => sF200)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF201])],[function_definition])).
% 24.66/4.12 thf(f1508,plain,(
% 24.66/4.12 (((setadjoinSub2 => sF200)) = sF201)),
% 24.66/4.12 inference(reorient_equations,[],[f1507])).
% 24.66/4.12 thf(f1509,definition,(
% 24.66/4.12 (sF202 = ((setadjoinSub => sF201)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF202])],[function_definition])).
% 24.66/4.12 thf(f1510,definition,(
% 24.66/4.12 (sF203 = ((subsetTrans => sF202)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF203])],[function_definition])).
% 24.66/4.12 thf(f1511,definition,(
% 24.66/4.12 (sF204 = ((subsetRefl => sF203)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF204])],[function_definition])).
% 24.66/4.12 thf(f1512,definition,(
% 24.66/4.12 (sF205 = ((notequalI2 => sF204)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF205])],[function_definition])).
% 24.66/4.12 thf(f1513,definition,(
% 24.66/4.12 (sF206 = ((notequalI1 => sF205)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF206])],[function_definition])).
% 24.66/4.12 thf(f1514,plain,(
% 24.66/4.12 (((notequalI1 => sF205)) = sF206)),
% 24.66/4.12 inference(reorient_equations,[],[f1513])).
% 24.66/4.12 thf(f1515,definition,(
% 24.66/4.12 (sF207 = ((notsubsetI => sF206)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF207])],[function_definition])).
% 24.66/4.12 thf(f1516,definition,(
% 24.66/4.12 (sF208 = ((subsetE2 => sF207)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF208])],[function_definition])).
% 24.66/4.12 thf(f1517,plain,(
% 24.66/4.12 (((subsetE2 => sF207)) = sF208)),
% 24.66/4.12 inference(reorient_equations,[],[f1516])).
% 24.66/4.12 thf(f1518,definition,(
% 24.66/4.12 (sF209 = ((subsetE => sF208)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF209])],[function_definition])).
% 24.66/4.12 thf(f1519,definition,(
% 24.66/4.12 (sF210 = ((emptysetsubset => sF209)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF210])],[function_definition])).
% 24.66/4.12 thf(f1520,plain,(
% 24.66/4.12 (((emptysetsubset => sF209)) = sF210)),
% 24.66/4.12 inference(reorient_equations,[],[f1519])).
% 24.66/4.12 thf(f1521,definition,(
% 24.66/4.12 (sF211 = ((subsetI2 => sF210)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF211])],[function_definition])).
% 24.66/4.12 thf(f1522,plain,(
% 24.66/4.12 (((subsetI2 => sF210)) = sF211)),
% 24.66/4.12 inference(reorient_equations,[],[f1521])).
% 24.66/4.12 thf(f1523,definition,(
% 24.66/4.12 (sF212 = ((eqimpsubset1 => sF211)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF212])],[function_definition])).
% 24.66/4.12 thf(f1524,definition,(
% 24.66/4.12 (sF213 = ((eqimpsubset2 => sF212)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF213])],[function_definition])).
% 24.66/4.12 thf(f1525,plain,(
% 24.66/4.12 (((eqimpsubset2 => sF212)) = sF213)),
% 24.66/4.12 inference(reorient_equations,[],[f1524])).
% 24.66/4.12 thf(f1526,definition,(
% 24.66/4.12 (sF214 = ((subsetI1 => sF213)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF214])],[function_definition])).
% 24.66/4.12 thf(f1527,plain,(
% 24.66/4.12 (((subsetI1 => sF213)) = sF214)),
% 24.66/4.12 inference(reorient_equations,[],[f1526])).
% 24.66/4.12 thf(f1528,definition,(
% 24.66/4.12 (sF215 = ((dsetconstr__Cong => sF214)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF215])],[function_definition])).
% 24.66/4.12 thf(f1529,definition,(
% 24.66/4.12 (sF216 = ((descr__Cong => sF215)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF216])],[function_definition])).
% 24.66/4.12 thf(f1530,plain,(
% 24.66/4.12 (((descr__Cong => sF215)) = sF216)),
% 24.66/4.12 inference(reorient_equations,[],[f1529])).
% 24.66/4.12 thf(f1531,definition,(
% 24.66/4.12 (sF217 = ((exuEu => sF216)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF217])],[function_definition])).
% 24.66/4.12 thf(f1532,definition,(
% 24.66/4.12 (sF218 = ((omega__Cong => sF217)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF218])],[function_definition])).
% 24.66/4.12 thf(f1533,definition,(
% 24.66/4.12 (sF219 = ((setunion__Cong => sF218)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF219])],[function_definition])).
% 24.66/4.12 thf(f1534,plain,(
% 24.66/4.12 (((setunion__Cong => sF218)) = sF219)),
% 24.66/4.12 inference(reorient_equations,[],[f1533])).
% 24.66/4.12 thf(f1535,definition,(
% 24.66/4.12 (sF220 = ((powerset__Cong => sF219)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF220])],[function_definition])).
% 24.66/4.12 thf(f1536,definition,(
% 24.66/4.12 (sF221 = ((setadjoin__Cong => sF220)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF221])],[function_definition])).
% 24.66/4.12 thf(f1537,plain,(
% 24.66/4.12 (((setadjoin__Cong => sF220)) = sF221)),
% 24.66/4.12 inference(reorient_equations,[],[f1536])).
% 24.66/4.12 thf(f1538,definition,(
% 24.66/4.12 (sF222 = ((emptyset__Cong => sF221)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF222])],[function_definition])).
% 24.66/4.12 thf(f1539,definition,(
% 24.66/4.12 (sF223 = ((exu__Cong => sF222)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF223])],[function_definition])).
% 24.66/4.12 thf(f1540,definition,(
% 24.66/4.12 (sF224 = ((exuE3u => sF223)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF224])],[function_definition])).
% 24.66/4.12 thf(f1541,definition,(
% 24.66/4.12 (sF225 = ((in__Cong => sF224)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF225])],[function_definition])).
% 24.66/4.12 thf(f1542,definition,(
% 24.66/4.12 (sF226 = ((inCongP => sF225)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF226])],[function_definition])).
% 24.66/4.12 thf(f1543,plain,(
% 24.66/4.12 (((inCongP => sF225)) = sF226)),
% 24.66/4.12 inference(reorient_equations,[],[f1542])).
% 24.66/4.12 thf(f1544,definition,(
% 24.66/4.12 (sF227 = ((exuI2 => sF226)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF227])],[function_definition])).
% 24.66/4.12 thf(f1545,definition,(
% 24.66/4.12 (sF228 = ((exuI3 => sF227)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF228])],[function_definition])).
% 24.66/4.12 thf(f1546,definition,(
% 24.66/4.12 (sF229 = ((exuI1 => sF228)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF229])],[function_definition])).
% 24.66/4.12 thf(f1547,definition,(
% 24.66/4.12 (sF230 = ((notdallE => sF229)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF230])],[function_definition])).
% 24.66/4.12 thf(f1548,plain,(
% 24.66/4.12 (((notdallE => sF229)) = sF230)),
% 24.66/4.12 inference(reorient_equations,[],[f1547])).
% 24.66/4.12 thf(f1549,definition,(
% 24.66/4.12 (sF231 = ((notdexE => sF230)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF231])],[function_definition])).
% 24.66/4.12 thf(f1550,definition,(
% 24.66/4.12 (sF232 = ((prop2set2propI => sF231)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF232])],[function_definition])).
% 24.66/4.12 thf(f1551,plain,(
% 24.66/4.12 (((prop2set2propI => sF231)) = sF232)),
% 24.66/4.12 inference(reorient_equations,[],[f1550])).
% 24.66/4.12 thf(f1552,definition,(
% 24.66/4.12 (sF233 = ((prop2setI => sF232)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF233])],[function_definition])).
% 24.66/4.12 thf(f1553,definition,(
% 24.66/4.12 (sF234 = ((quantDeMorgan4 => sF233)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF234])],[function_definition])).
% 24.66/4.12 thf(f1554,definition,(
% 24.66/4.12 (sF235 = ((quantDeMorgan3 => sF234)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF235])],[function_definition])).
% 24.66/4.12 thf(f1555,plain,(
% 24.66/4.12 (((quantDeMorgan3 => sF234)) = sF235)),
% 24.66/4.12 inference(reorient_equations,[],[f1554])).
% 24.66/4.12 thf(f1556,definition,(
% 24.66/4.12 (sF236 = ((quantDeMorgan2 => sF235)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF236])],[function_definition])).
% 24.66/4.12 thf(f1557,definition,(
% 24.66/4.12 (sF237 = ((quantDeMorgan1 => sF236)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF237])],[function_definition])).
% 24.66/4.12 thf(f1558,plain,(
% 24.66/4.12 (((quantDeMorgan1 => sF236)) = sF237)),
% 24.66/4.12 inference(reorient_equations,[],[f1557])).
% 24.66/4.12 thf(f1559,definition,(
% 24.66/4.12 (sF238 = ((vacuousDall => sF237)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF238])],[function_definition])).
% 24.66/4.12 thf(f1560,definition,(
% 24.66/4.12 (sF239 = ((emptyE1 => sF238)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF239])],[function_definition])).
% 24.66/4.12 thf(f1561,plain,(
% 24.66/4.12 (((emptyE1 => sF238)) = sF239)),
% 24.66/4.12 inference(reorient_equations,[],[f1560])).
% 24.66/4.12 thf(f1562,definition,(
% 24.66/4.12 (sF240 = ((upairsetIR => sF239)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF240])],[function_definition])).
% 24.66/4.12 thf(f1563,definition,(
% 24.66/4.12 (sF241 = ((upairsetIL => sF240)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF241])],[function_definition])).
% 24.66/4.12 thf(f1564,plain,(
% 24.66/4.12 (((upairsetIL => sF240)) = sF241)),
% 24.66/4.12 inference(reorient_equations,[],[f1563])).
% 24.66/4.12 thf(f1565,definition,(
% 24.66/4.12 (sF242 = ((upairsetE => sF241)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF242])],[function_definition])).
% 24.66/4.12 thf(f1566,definition,(
% 24.66/4.12 (sF243 = ((singletonsswitch => sF242)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF243])],[function_definition])).
% 24.66/4.12 thf(f1567,plain,(
% 24.66/4.12 (((singletonsswitch => sF242)) = sF243)),
% 24.66/4.12 inference(reorient_equations,[],[f1566])).
% 24.66/4.12 thf(f1568,definition,(
% 24.66/4.12 (sF244 = ((eqinunit => sF243)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF244])],[function_definition])).
% 24.66/4.12 thf(f1569,plain,(
% 24.66/4.12 (((eqinunit => sF243)) = sF244)),
% 24.66/4.12 inference(reorient_equations,[],[f1568])).
% 24.66/4.12 thf(f1570,definition,(
% 24.66/4.12 (sF245 = ((notinsingleton => sF244)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF245])],[function_definition])).
% 24.66/4.12 thf(f1571,definition,(
% 24.66/4.12 (sF246 = ((uniqinunit => sF245)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF246])],[function_definition])).
% 24.66/4.12 thf(f1572,definition,(
% 24.66/4.12 (sF247 = ((nonemptyImpWitness => sF246)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF247])],[function_definition])).
% 24.66/4.12 thf(f1573,definition,(
% 24.66/4.12 (sF248 = ((exuE2 => sF247)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF248])],[function_definition])).
% 24.66/4.12 thf(f1574,definition,(
% 24.66/4.12 (sF249 = ((subPowSU => sF248)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF249])],[function_definition])).
% 24.66/4.12 thf(f1575,plain,(
% 24.66/4.12 (((subPowSU => sF248)) = sF249)),
% 24.66/4.12 inference(reorient_equations,[],[f1574])).
% 24.66/4.12 thf(f1576,definition,(
% 24.66/4.12 (sF250 = ((setunionE => sF249)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF250])],[function_definition])).
% 24.66/4.12 thf(f1577,plain,(
% 24.66/4.12 (((setunionE => sF249)) = sF250)),
% 24.66/4.12 inference(reorient_equations,[],[f1576])).
% 24.66/4.12 thf(f1578,definition,(
% 24.66/4.12 (sF251 = ((setunionI => sF250)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF251])],[function_definition])).
% 24.66/4.12 thf(f1579,plain,(
% 24.66/4.12 (((setunionI => sF250)) = sF251)),
% 24.66/4.12 inference(reorient_equations,[],[f1578])).
% 24.66/4.12 thf(f1580,definition,(
% 24.66/4.12 (sF252 = ((powersetE => sF251)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF252])],[function_definition])).
% 24.66/4.12 thf(f1581,plain,(
% 24.66/4.12 (((powersetE => sF251)) = sF252)),
% 24.66/4.12 inference(reorient_equations,[],[f1580])).
% 24.66/4.12 thf(f1582,definition,(
% 24.66/4.12 (sF253 = ((emptyInPowerset => sF252)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF253])],[function_definition])).
% 24.66/4.12 thf(f1583,plain,(
% 24.66/4.12 (((emptyInPowerset => sF252)) = sF253)),
% 24.66/4.12 inference(reorient_equations,[],[f1582])).
% 24.66/4.12 thf(f1584,definition,(
% 24.66/4.12 (sF254 = ((emptyinPowerset => sF253)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF254])],[function_definition])).
% 24.66/4.12 thf(f1585,definition,(
% 24.66/4.12 (sF255 = ((powersetI => sF254)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF255])],[function_definition])).
% 24.66/4.12 thf(f1586,plain,(
% 24.66/4.12 (((powersetI => sF254)) = sF255)),
% 24.66/4.12 inference(reorient_equations,[],[f1585])).
% 24.66/4.12 thf(f1587,definition,(
% 24.66/4.12 (sF256 = ((setoftrueEq => sF255)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF256])],[function_definition])).
% 24.66/4.12 thf(f1588,definition,(
% 24.66/4.12 (sF257 = ((setadjoinOr => sF256)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF257])],[function_definition])).
% 24.66/4.12 thf(f1589,plain,(
% 24.66/4.12 (((setadjoinOr => sF256)) = sF257)),
% 24.66/4.12 inference(reorient_equations,[],[f1588])).
% 24.66/4.12 thf(f1590,definition,(
% 24.66/4.12 (sF258 = ((setadjoinE => sF257)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF258])],[function_definition])).
% 24.66/4.12 thf(f1591,plain,(
% 24.66/4.12 (((setadjoinE => sF257)) = sF258)),
% 24.66/4.12 inference(reorient_equations,[],[f1590])).
% 24.66/4.12 thf(f1592,definition,(
% 24.66/4.12 (sF259 = ((setadjoinIR => sF258)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF259])],[function_definition])).
% 24.66/4.12 thf(f1593,plain,(
% 24.66/4.12 (((setadjoinIR => sF258)) = sF259)),
% 24.66/4.12 inference(reorient_equations,[],[f1592])).
% 24.66/4.12 thf(f1594,definition,(
% 24.66/4.12 (sF260 = ((emptyinunitempty => sF259)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF260])],[function_definition])).
% 24.66/4.12 thf(f1595,definition,(
% 24.66/4.12 (sF261 = ((setadjoinIL => sF260)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF261])],[function_definition])).
% 24.66/4.12 thf(f1596,definition,(
% 24.66/4.12 (sF262 = ((nonemptyI1 => sF261)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF262])],[function_definition])).
% 24.66/4.12 thf(f1597,plain,(
% 24.66/4.12 (((nonemptyI1 => sF261)) = sF262)),
% 24.66/4.12 inference(reorient_equations,[],[f1596])).
% 24.66/4.12 thf(f1598,definition,(
% 24.66/4.12 (sF263 = ((nonemptyI => sF262)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF263])],[function_definition])).
% 24.66/4.12 thf(f1599,plain,(
% 24.66/4.12 (((nonemptyI => sF262)) = sF263)),
% 24.66/4.12 inference(reorient_equations,[],[f1598])).
% 24.66/4.12 thf(f1600,definition,(
% 24.66/4.12 (sF264 = ((nonemptyE1 => sF263)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF264])],[function_definition])).
% 24.66/4.12 thf(f1601,definition,(
% 24.66/4.12 (sF265 = ((setbeta => sF264)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF265])],[function_definition])).
% 24.66/4.12 thf(f1602,definition,(
% 24.66/4.12 (sF266 = ((noeltsimpempty => sF265)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF266])],[function_definition])).
% 24.66/4.12 thf(f1603,plain,(
% 24.66/4.12 (((noeltsimpempty => sF265)) = sF266)),
% 24.66/4.12 inference(reorient_equations,[],[f1602])).
% 24.66/4.12 thf(f1604,definition,(
% 24.66/4.12 (sF267 = ((emptyI => sF266)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF267])],[function_definition])).
% 24.66/4.12 thf(f1605,plain,(
% 24.66/4.12 (((emptyI => sF266)) = sF267)),
% 24.66/4.12 inference(reorient_equations,[],[f1604])).
% 24.66/4.12 thf(f1606,definition,(
% 24.66/4.12 (sF268 = ((setext => sF267)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF268])],[function_definition])).
% 24.66/4.12 thf(f1607,definition,(
% 24.66/4.12 (sF269 = ((exuE3e => sF268)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF269])],[function_definition])).
% 24.66/4.12 thf(f1608,plain,(
% 24.66/4.12 (((exuE3e => sF268)) = sF269)),
% 24.66/4.12 inference(reorient_equations,[],[f1607])).
% 24.66/4.12 thf(f1609,definition,(
% 24.66/4.12 (sF270 = ((notinemptyset => sF269)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF270])],[function_definition])).
% 24.66/4.12 thf(f1610,plain,(
% 24.66/4.12 (((notinemptyset => sF269)) = sF270)),
% 24.66/4.12 inference(reorient_equations,[],[f1609])).
% 24.66/4.12 thf(f1611,definition,(
% 24.66/4.12 (sF271 = ((emptysetimpfalse => sF270)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF271])],[function_definition])).
% 24.66/4.12 thf(f1612,definition,(
% 24.66/4.12 (sF272 = ((emptysetE => sF271)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF272])],[function_definition])).
% 24.66/4.12 thf(f1613,plain,(
% 24.66/4.12 (((emptysetE => sF271)) = sF272)),
% 24.66/4.12 inference(reorient_equations,[],[f1612])).
% 24.66/4.12 thf(f1614,definition,(
% 24.66/4.12 (sF273 = ((prop2setE => sF272)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF273])],[function_definition])).
% 24.66/4.12 thf(f1615,plain,(
% 24.66/4.12 (((prop2setE => sF272)) = sF273)),
% 24.66/4.12 inference(reorient_equations,[],[f1614])).
% 24.66/4.12 thf(f1616,definition,(
% 24.66/4.12 (sF274 = ((exuE1 => sF273)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF274])],[function_definition])).
% 24.66/4.12 thf(f1617,definition,(
% 24.66/4.12 (sF275 = ((dsetconstrER => sF274)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF275])],[function_definition])).
% 24.66/4.12 thf(f1618,plain,(
% 24.66/4.12 (((dsetconstrER => sF274)) = sF275)),
% 24.66/4.12 inference(reorient_equations,[],[f1617])).
% 24.66/4.12 thf(f1619,definition,(
% 24.66/4.12 (sF276 = ((dsetconstrEL => sF275)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF276])],[function_definition])).
% 24.66/4.12 thf(f1620,definition,(
% 24.66/4.12 (sF277 = ((dsetconstrI => sF276)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF277])],[function_definition])).
% 24.66/4.12 thf(f1621,plain,(
% 24.66/4.12 (((dsetconstrI => sF276)) = sF277)),
% 24.66/4.12 inference(reorient_equations,[],[f1620])).
% 24.66/4.12 thf(f1622,definition,(
% 24.66/4.12 (sF278 = ((descrp => sF277)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF278])],[function_definition])).
% 24.66/4.12 thf(f1623,plain,(
% 24.66/4.12 (((descrp => sF277)) = sF278)),
% 24.66/4.12 inference(reorient_equations,[],[f1622])).
% 24.66/4.12 thf(f1624,definition,(
% 24.66/4.12 (sF279 = ((wellorderingAx => sF278)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF279])],[function_definition])).
% 24.66/4.12 thf(f1625,plain,(
% 24.66/4.12 (((wellorderingAx => sF278)) = sF279)),
% 24.66/4.12 inference(reorient_equations,[],[f1624])).
% 24.66/4.12 thf(f1626,definition,(
% 24.66/4.12 (sF280 = ((foundationAx => sF279)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF280])],[function_definition])).
% 24.66/4.12 thf(f1627,definition,(
% 24.66/4.12 (sF281 = ((replAx => sF280)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF281])],[function_definition])).
% 24.66/4.12 thf(f1628,plain,(
% 24.66/4.12 (((replAx => sF280)) = sF281)),
% 24.66/4.12 inference(reorient_equations,[],[f1627])).
% 24.66/4.12 thf(f1629,definition,(
% 24.66/4.12 (sF282 = ((omegaIndAx => sF281)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF282])],[function_definition])).
% 24.66/4.12 thf(f1630,plain,(
% 24.66/4.12 (((omegaIndAx => sF281)) = sF282)),
% 24.66/4.12 inference(reorient_equations,[],[f1629])).
% 24.66/4.12 thf(f1631,definition,(
% 24.66/4.12 (sF283 = ((omegaSAx => sF282)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF283])],[function_definition])).
% 24.66/4.12 thf(f1632,plain,(
% 24.66/4.12 (((omegaSAx => sF282)) = sF283)),
% 24.66/4.12 inference(reorient_equations,[],[f1631])).
% 24.66/4.12 thf(f1633,definition,(
% 24.66/4.12 (sF284 = ((omega0Ax => sF283)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF284])],[function_definition])).
% 24.66/4.12 thf(f1634,plain,(
% 24.66/4.12 (((omega0Ax => sF283)) = sF284)),
% 24.66/4.12 inference(reorient_equations,[],[f1633])).
% 24.66/4.12 thf(f1635,definition,(
% 24.66/4.12 (sF285 = ((setunionAx => sF284)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF285])],[function_definition])).
% 24.66/4.12 thf(f1636,plain,(
% 24.66/4.12 (((setunionAx => sF284)) = sF285)),
% 24.66/4.12 inference(reorient_equations,[],[f1635])).
% 24.66/4.12 thf(f1637,definition,(
% 24.66/4.12 (sF286 = ((powersetAx => sF285)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF286])],[function_definition])).
% 24.66/4.12 thf(f1638,definition,(
% 24.66/4.12 (sF287 = ((setadjoinAx => sF286)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF287])],[function_definition])).
% 24.66/4.12 thf(f1639,plain,(
% 24.66/4.12 (((setadjoinAx => sF286)) = sF287)),
% 24.66/4.12 inference(reorient_equations,[],[f1638])).
% 24.66/4.12 thf(f1640,definition,(
% 24.66/4.12 (sF288 = ((emptysetAx => sF287)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF288])],[function_definition])).
% 24.66/4.12 thf(f1641,definition,(
% 24.66/4.12 (sF289 = ((setextAx => sF288)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF289])],[function_definition])).
% 24.66/4.12 thf(f1642,definition,(
% 24.66/4.12 (sF290 = ((~ sF289)))),
% 24.66/4.12 introduced(definition,[new_symbols(definition,[sF290])],[function_definition])).
% 24.66/4.12 thf(f1643,plain,(
% 24.66/4.12 ($true = sF290)),
% 24.66/4.12 inference(definition_folding,[],[f1191,f1642,f1641,f1640,f1639,f1637,f1636,f1634,f1632,f1630,f1628,f1626,f1625,f1623,f1621,f1619,f1618,f1616,f1615,f1613,f1611,f1610,f1608,f1606,f1605,f1603,f1601,f1600,f1599,f1597,f1595,f1594,f1593,f1591,f1589,f1587,f1586,f1584,f1583,f1581,f1579,f1577,f1575,f1573,f1572,f1571,f1570,f1569,f1567,f1565,f1564,f1562,f1561,f1559,f1558,f1556,f1555,f1553,f1552,f1551,f1549,f1548,f1546,f1545,f1544,f1543,f1541,f1540,f1539,f1538,f1537,f1535,f1534,f1532,f1531,f1530,f1528,f1527,f1525,f1523,f1522,f1520,f1518,f1517,f1515,f1514,f1512,f1511,f1510,f1509,f1508,f1506,f1504,f1502,f1501,f1499,f1497,f1496,f1494,f1492,f1490,f1489,f1487,f1485,f1483,f1482,f1480,f1479,f1478,f1477,f1476,f1474,f1472,f1471,f1470,f1468,f1466,f1465,f1463,f1461,f1460,f1459,f1458,f1456,f1454,f1453,f1452,f1450,f1448,f1446,f1444,f1443,f1442,f1440,f1438,f1436,f1434,f1432,f1430,f1429,f1427,f1426,f1424,f1422,f1421,f1419,f1418,f1416,f1414,f1413,f1411,f1409,f1407,f1406,f1404,f1403,f1401,f1400,f1398,f1397,f1396,f1395,f1393,f1392,f1391,f1390,f1388,f1387,f1385,f1383,f1381,f1380,f1378,f1376,f1375,f1374,f1373,f1372,f1370,f1368,f1366,f1364,f1363,f1362,f1361,f1360,f1358,f1357,f1356,f1354,f1352,f1350,f1348,f1347,f1346,f1344,f1343,f1342,f1340,f1338,f1337,f1335,f1334,f1332,f1331,f1330,f1329,f1328,f1327,f1325,f1323,f1321,f1319,f1317,f1315,f1314,f1312,f1311,f1309,f1308,f1307,f1305,f1303,f1301,f1299,f1298,f1297,f1296,f1294,f1292,f1290,f1288,f1286,f1285,f1283,f1281,f1280,f1278,f1277,f1276,f1274,f1272,f1270,f1268,f1266,f1264,f1263,f1261,f1260,f1259,f1257,f1255,f1253,f1252,f1251,f1249,f1248,f1246,f1245,f1244,f1243,f1241,f1239,f1237,f1236,f1235,f1234,f1232,f1231,f1229,f1228,f1226,f1225,f1224,f1222,f1220,f1218,f1216,f1215,f1213,f1212,f1211,f1209,f1207,f1205,f1203,f1202,f1200,f1198,f1197,f1196,f1195])).
% 24.66/4.12 thf(f1645,plain,(
% 24.66/4.12 (subbreln = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y2 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1192])).
% 24.66/4.12 thf(f1646,plain,(
% 24.66/4.12 (sepInPowerset = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f983])).
% 24.66/4.12 thf(f1649,plain,(
% 24.66/4.12 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1181])).
% 24.66/4.12 thf(f1650,plain,(
% 24.66/4.12 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1649])).
% 24.66/4.12 thf(f1654,plain,(
% 24.66/4.12 (nonemptyI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (~ (emptyset = (dsetconstr @ Y2 @ Y1)))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1171])).
% 24.66/4.12 thf(f1655,plain,(
% 24.66/4.12 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1172])).
% 24.66/4.12 thf(f1656,plain,(
% 24.66/4.12 (exuI1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true)))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1655])).
% 24.66/4.12 thf(f1657,plain,(
% 24.66/4.12 (dpsetconstrER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3)) => (Y3 @ Y0 @ Y4))))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f910])).
% 24.66/4.12 thf(f1659,plain,(
% 24.66/4.12 (eta1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f999])).
% 24.66/4.12 thf(f1660,plain,(
% 24.66/4.12 (beta1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ Y2) @ Y3) = (Y2 @ Y3))))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f899])).
% 24.66/4.12 thf(f1661,plain,(
% 24.66/4.12 (exuI2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1190])).
% 24.66/4.12 thf(f1664,plain,(
% 24.66/4.12 (emptysetimpfalse = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1011])).
% 24.66/4.12 thf(f1670,plain,(
% 24.66/4.12 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))))) = sF0)),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1195])).
% 24.66/4.12 thf(f1671,plain,(
% 24.66/4.12 (dpsetconstrSub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1002])).
% 24.66/4.12 thf(f1672,plain,(
% 24.66/4.12 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => ((lam @ Y0 @ Y2 @ Y1) = (lam @ Y0 @ Y2 @ Y1)))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1014])).
% 24.66/4.12 thf(f1673,plain,(
% 24.66/4.12 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => $true)))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1672])).
% 24.66/4.12 thf(f1674,plain,(
% 24.66/4.12 (lam2lamEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ($true)))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1673])).
% 24.66/4.12 thf(f1675,plain,(
% 24.66/4.12 (nonemptyI1 = ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0)))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1169])).
% 24.66/4.12 thf(f1677,plain,(
% 24.66/4.12 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => $true))))))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1018])).
% 24.66/4.12 thf(f1678,plain,(
% 24.66/4.12 (ap2apEq2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1677])).
% 24.66/4.12 thf(f1679,plain,(
% 24.66/4.12 (emptysetsubset = ((!! @ $i @ (subset @ emptyset))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1105])).
% 24.66/4.12 thf(f1680,plain,(
% 24.66/4.12 (exuE3u = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1178])).
% 24.66/4.12 thf(f1682,plain,(
% 24.66/4.12 (dsetconstrER = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f971])).
% 24.66/4.12 thf(f1683,plain,(
% 24.66/4.12 (exuE3e = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1176])).
% 24.66/4.12 thf(f1684,plain,(
% 24.66/4.12 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => $true))))))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f896])).
% 24.66/4.12 thf(f1685,plain,(
% 24.66/4.12 (cartprodmempaircEq = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1684])).
% 24.66/4.12 thf(f1686,plain,(
% 24.66/4.12 (dsetconstrEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1031])).
% 24.66/4.12 thf(f1687,plain,(
% 24.66/4.12 (emptyset__Cong = $true)),
% 24.66/4.12 inference(boolean_simplification,[],[f1078])).
% 24.66/4.12 thf(f1689,plain,(
% 24.66/4.12 (exuI3 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1179])).
% 24.66/4.12 thf(f1691,plain,(
% 24.66/4.12 (exuEu = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1170])).
% 24.66/4.12 thf(f1692,plain,(
% 24.66/4.12 (ap2apEq1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => $true))))))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1162])).
% 24.66/4.12 thf(f1693,plain,(
% 24.66/4.12 (ap2apEq1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ($true))))))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1692])).
% 24.66/4.12 thf(f1694,plain,(
% 24.66/4.12 (exuE2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1189])).
% 24.66/4.12 thf(f1697,plain,(
% 24.66/4.12 (sepSubset = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0)))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f940])).
% 24.66/4.12 thf(f1698,plain,(
% 24.66/4.12 (ex1E1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1003])).
% 24.66/4.12 thf(f1699,plain,(
% 24.66/4.12 (omega__Cong = $true)),
% 24.66/4.12 inference(boolean_simplification,[],[f1108])).
% 24.66/4.12 thf(f1700,plain,(
% 24.66/4.12 (emptyE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1070])).
% 24.66/4.12 thf(f1701,plain,(
% 24.66/4.12 (emptyE1 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset)))))))))),
% 24.66/4.12 inference(boolean_simplification,[],[f1700])).
% 24.66/4.12 thf(f1702,plain,(
% 24.66/4.12 (ex1E2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1098])).
% 24.66/4.12 thf(f1704,plain,(
% 24.66/4.12 (ex1I = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y2 @ Y1))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1152])).
% 24.66/4.12 thf(f1705,plain,(
% 24.66/4.12 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1077])).
% 24.66/4.12 thf(f1708,plain,(
% 24.66/4.12 (nonemptyE1 = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f1177])).
% 24.66/4.12 thf(f1710,plain,(
% 24.66/4.12 (ex1I2 = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ Y0)))))))))),
% 24.66/4.12 inference(beta-eta_normalization,[],[f992])).
% 24.66/4.12 thf(f1712,plain,(
% 24.66/4.12 ($true = ((~ sF289)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1642,f1643])).
% 24.66/4.12 thf(f1714,plain,(
% 24.66/4.12 (((~ $true)) = $true) | (sF289 = $false)),
% 24.66/4.12 inference(superposition,[],[f1712,f1166])).
% 24.66/4.12 thf(f1715,plain,(
% 24.66/4.12 ($true = $false) | (sF289 = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f1714])).
% 24.66/4.12 thf(f1716,plain,(
% 24.66/4.12 (sF289 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f1715])).
% 24.66/4.12 thf(f1718,plain,(
% 24.66/4.12 ($false = ((setextAx => sF288)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1641,f1716])).
% 24.66/4.12 thf(f1720,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => sF288)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f1718,f1020])).
% 24.66/4.12 thf(f1721,plain,(
% 24.66/4.12 (sF288 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f1720])).
% 24.66/4.12 thf(f1731,plain,(
% 24.66/4.12 ($false = ((emptysetAx => sF287)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1640,f1721])).
% 24.66/4.12 thf(f1736,plain,(
% 24.66/4.12 ($false = (((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => sF287)))),
% 24.66/4.12 inference(forward_demodulation,[],[f1731,f1087])).
% 24.66/4.12 thf(f1742,plain,(
% 24.66/4.12 ($true = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset))))))),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f1736])).
% 24.66/4.12 thf(f1743,plain,(
% 24.66/4.12 ($false = (((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true))) | (sF287 = $false)),
% 24.66/4.12 inference(superposition,[],[f1736,f1166])).
% 24.66/4.12 thf(f1748,plain,(
% 24.66/4.12 ($true = $false) | (sF287 = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f1743])).
% 24.66/4.12 thf(f1749,plain,(
% 24.66/4.12 (sF287 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f1748])).
% 24.66/4.12 thf(f1751,plain,(
% 24.66/4.12 (notinemptyset = $true)),
% 24.66/4.12 inference(backward_demodulation,[],[f962,f1742])).
% 24.66/4.12 thf(f1752,plain,(
% 24.66/4.12 (emptysetimpfalse = $true)),
% 24.66/4.12 inference(backward_demodulation,[],[f1664,f1742])).
% 24.66/4.12 thf(f1759,plain,(
% 24.66/4.12 (((setadjoinAx => sF286)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1639,f1749])).
% 24.66/4.12 thf(f1760,plain,(
% 24.66/4.12 ((($true => sF270)) = sF271)),
% 24.66/4.12 inference(backward_demodulation,[],[f1611,f1752])).
% 24.66/4.12 thf(f1761,plain,(
% 24.66/4.12 (sF270 = sF271)),
% 24.66/4.12 inference(boolean_simplification,[],[f1760])).
% 24.66/4.12 thf(f1762,plain,(
% 24.66/4.12 (sF270 = (($true => sF269)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1610,f1751])).
% 24.66/4.12 thf(f1763,plain,(
% 24.66/4.12 (sF270 = sF269)),
% 24.66/4.12 inference(boolean_simplification,[],[f1762])).
% 24.66/4.12 thf(f1764,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y1 = Y0) | (in @ Y1 @ Y2)) = (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => sF286)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f1759,f963])).
% 24.66/4.12 thf(f1765,plain,(
% 24.66/4.12 (((emptysetE => sF270)) = sF272)),
% 24.66/4.12 inference(backward_demodulation,[],[f1613,f1761])).
% 24.66/4.12 thf(f1767,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => sF270)) = sF272)),
% 24.66/4.12 inference(forward_demodulation,[],[f1765,f895])).
% 24.66/4.12 thf(f1768,plain,(
% 24.66/4.12 (sF272 = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => sF269)))),
% 24.66/4.12 inference(forward_demodulation,[],[f1767,f1763])).
% 24.66/4.12 thf(f1769,plain,(
% 24.66/4.12 (sF273 = ((prop2setE => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => sF269))))),
% 24.66/4.12 inference(backward_demodulation,[],[f1615,f1768])).
% 24.66/4.12 thf(f1770,plain,(
% 24.66/4.12 (sF273 = (((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => sF269))))),
% 24.66/4.12 inference(forward_demodulation,[],[f1769,f1119])).
% 24.66/4.12 thf(f1793,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y1 = Y0) | (in @ Y1 @ Y2)) = (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => $true)) = $false) | (sF286 = $false)),
% 24.66/4.12 inference(superposition,[],[f1764,f1166])).
% 24.66/4.12 thf(f1797,plain,(
% 24.66/4.12 ($true = $false) | (sF286 = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f1793])).
% 24.66/4.12 thf(f1798,plain,(
% 24.66/4.12 (sF286 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f1797])).
% 24.66/4.12 thf(f1805,plain,(
% 24.66/4.12 (((powersetAx => sF285)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1637,f1798])).
% 24.66/4.12 thf(f1808,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => sF285)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f1805,f902])).
% 24.66/4.12 thf(f1811,plain,(
% 24.66/4.12 ($false = sF285) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => $true)))),
% 24.66/4.12 inference(superposition,[],[f1808,f1166])).
% 24.66/4.12 thf(f1816,plain,(
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% 24.66/4.12 inference(boolean_simplification,[],[f1811])).
% 24.66/4.12 thf(f1817,plain,(
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% 24.66/4.12 inference(trivial_inequality_removal,[],[f1816])).
% 24.66/4.12 thf(f1819,plain,(
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% 24.66/4.12 inference(backward_demodulation,[],[f1636,f1817])).
% 24.66/4.12 thf(f1824,plain,(
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% 24.66/4.12 thf(f1834,plain,(
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% 24.66/4.12 inference(backward_demodulation,[],[f1634,f1824])).
% 24.66/4.12 thf(f1837,plain,(
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% 24.66/4.12 inference(forward_demodulation,[],[f1834,f1139])).
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% 24.66/4.12 inference(superposition,[],[f1837,f1166])).
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% 24.66/4.12 inference(trivial_inequality_removal,[],[f1845])).
% 24.66/4.12 thf(f1850,plain,(
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% 24.66/4.12 inference(backward_demodulation,[],[f1632,f1846])).
% 24.66/4.12 thf(f1855,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => sF282)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f1850,f913])).
% 24.66/4.12 thf(f1860,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => (omegaIndAx => sF281))) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f1855,f1630])).
% 24.66/4.12 thf(f1865,plain,(
% 24.66/4.12 (sF281 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => (omegaIndAx => $true))))),
% 24.66/4.12 inference(superposition,[],[f1860,f1166])).
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% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => $true)) = $false) | (sF281 = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f1865])).
% 24.66/4.12 thf(f1873,plain,(
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% 24.66/4.12 inference(boolean_simplification,[],[f1872])).
% 24.66/4.12 thf(f1874,plain,(
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% 24.66/4.12 inference(trivial_inequality_removal,[],[f1873])).
% 24.66/4.12 thf(f1887,plain,(
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% 24.66/4.12 inference(backward_demodulation,[],[f1628,f1874])).
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% 24.66/4.12 inference(backward_demodulation,[],[f1626,f1907])).
% 24.66/4.12 thf(f1918,plain,(
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% 24.66/4.12 inference(backward_demodulation,[],[f1625,f1923])).
% 24.66/4.12 thf(f1929,plain,(
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% 24.66/4.12 inference(forward_demodulation,[],[f1928,f1623])).
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% 24.66/4.12 thf(f1943,plain,(
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% 24.66/4.12 thf(f1944,plain,(
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% 24.66/4.12 inference(trivial_inequality_removal,[],[f1943])).
% 24.66/4.12 thf(f1952,plain,(
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% 24.66/4.12 inference(forward_demodulation,[],[f1952,f1705])).
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% 24.66/4.12 inference(superposition,[],[f1770,f1166])).
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% 24.66/4.12 inference(boolean_simplification,[],[f1974])).
% 24.66/4.12 thf(f1982,plain,(
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% 24.66/4.12 thf(f1997,plain,(
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% 24.66/4.12 inference(backward_demodulation,[],[f1619,f1987])).
% 24.66/4.12 thf(f2004,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => sF275)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f1997,f1686])).
% 24.66/4.12 thf(f2005,plain,(
% 24.66/4.12 ($false = sF275)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2004])).
% 24.66/4.12 thf(f2015,plain,(
% 24.66/4.12 ($false = ((dsetconstrER => sF274)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1618,f2005])).
% 24.66/4.12 thf(f2020,plain,(
% 24.66/4.12 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => sF274)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2015,f1682])).
% 24.66/4.12 thf(f2023,plain,(
% 24.66/4.12 (sF274 = $false) | ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => $true)) = $false)),
% 24.66/4.12 inference(superposition,[],[f2020,f1166])).
% 24.66/4.12 thf(f2027,plain,(
% 24.66/4.12 (sF274 = $false) | ($true = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2023])).
% 24.66/4.12 thf(f2028,plain,(
% 24.66/4.12 (sF274 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2027])).
% 24.66/4.12 thf(f2035,plain,(
% 24.66/4.12 ($false = ((exuE1 => sF273)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1616,f2028])).
% 24.66/4.12 thf(f2040,plain,(
% 24.66/4.12 (((exuE1 => $true)) = $false) | (sF273 = $false)),
% 24.66/4.12 inference(superposition,[],[f2035,f1166])).
% 24.66/4.12 thf(f2043,plain,(
% 24.66/4.12 (sF273 = $false) | ($true = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2040])).
% 24.66/4.12 thf(f2044,plain,(
% 24.66/4.12 (sF273 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2043])).
% 24.66/4.12 thf(f2049,plain,(
% 24.66/4.12 ($true = $false) | ($false = sF269)),
% 24.66/4.12 inference(backward_demodulation,[],[f1982,f2044])).
% 24.66/4.12 thf(f2054,plain,(
% 24.66/4.12 ($false = sF269)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2049])).
% 24.66/4.12 thf(f2061,plain,(
% 24.66/4.12 (((exuE3e => sF268)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1608,f2054])).
% 24.66/4.12 thf(f2074,plain,(
% 24.66/4.12 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => sF268)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2061,f1683])).
% 24.66/4.12 thf(f2101,plain,(
% 24.66/4.12 (sF268 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2074])).
% 24.66/4.12 thf(f2111,plain,(
% 24.66/4.12 (((setext => sF267)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1606,f2101])).
% 24.66/4.12 thf(f2118,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => sF267)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2111,f959])).
% 24.66/4.12 thf(f2126,plain,(
% 24.66/4.12 ($false = sF267)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2118])).
% 24.66/4.12 thf(f2136,plain,(
% 24.66/4.12 (((emptyI => sF266)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1605,f2126])).
% 24.66/4.12 thf(f2141,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => sF266)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2136,f995])).
% 24.66/4.12 thf(f2146,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => (noeltsimpempty => sF265))) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2141,f1603])).
% 24.66/4.12 thf(f2147,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => sF265))) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2146,f919])).
% 24.66/4.12 thf(f2150,plain,(
% 24.66/4.12 (sF265 = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true))) = $false)),
% 24.66/4.12 inference(superposition,[],[f2147,f1166])).
% 24.66/4.12 thf(f2159,plain,(
% 24.66/4.12 (sF265 = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true)) = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2150])).
% 24.66/4.12 thf(f2160,plain,(
% 24.66/4.12 ($true = $false) | (sF265 = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2159])).
% 24.66/4.12 thf(f2161,plain,(
% 24.66/4.12 (sF265 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2160])).
% 24.66/4.12 thf(f2168,plain,(
% 24.66/4.12 (((setbeta => sF264)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1601,f2161])).
% 24.66/4.12 thf(f2183,plain,(
% 24.66/4.12 (sF264 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2168])).
% 24.66/4.12 thf(f2193,plain,(
% 24.66/4.12 (((nonemptyE1 => sF263)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1600,f2183])).
% 24.66/4.12 thf(f2201,plain,(
% 24.66/4.12 (nonemptyE1 = $true)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2193])).
% 24.66/4.12 thf(f2202,plain,(
% 24.66/4.12 (((nonemptyE1 => $true)) = $false) | ($false = sF263)),
% 24.66/4.12 inference(superposition,[],[f2193,f1166])).
% 24.66/4.12 thf(f2205,plain,(
% 24.66/4.12 ($false = sF263) | ($true = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2202])).
% 24.66/4.12 thf(f2206,plain,(
% 24.66/4.12 ($false = sF263)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2205])).
% 24.66/4.12 thf(f2210,plain,(
% 24.66/4.12 (((nonemptyI => sF262)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1599,f2206])).
% 24.66/4.12 thf(f2214,plain,(
% 24.66/4.12 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))),
% 24.66/4.12 inference(backward_demodulation,[],[f1708,f2201])).
% 24.66/4.12 thf(f2215,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (~ (emptyset = (dsetconstr @ Y2 @ Y1))))))))))) => sF262)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2210,f1654])).
% 24.66/4.12 thf(f2220,plain,(
% 24.66/4.12 (nonemptyImpWitness = $true)),
% 24.66/4.12 inference(backward_demodulation,[],[f1650,f2214])).
% 24.66/4.12 thf(f2221,plain,(
% 24.66/4.12 (sF247 = (($true => sF246)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1572,f2220])).
% 24.66/4.12 thf(f2222,plain,(
% 24.66/4.12 (sF246 = sF247)),
% 24.66/4.12 inference(boolean_simplification,[],[f2221])).
% 24.66/4.12 thf(f2223,plain,(
% 24.66/4.12 (sF247 = ((uniqinunit => sF245)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1571,f2222])).
% 24.66/4.12 thf(f2224,plain,(
% 24.66/4.12 (sF247 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => sF245)))),
% 24.66/4.12 inference(forward_demodulation,[],[f2223,f926])).
% 24.66/4.12 thf(f2225,plain,(
% 24.66/4.12 (sF247 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => (notinsingleton => sF244))))),
% 24.66/4.12 inference(forward_demodulation,[],[f2224,f1570])).
% 24.66/4.12 thf(f2226,plain,(
% 24.66/4.12 (sF247 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => sF244))))),
% 24.66/4.12 inference(forward_demodulation,[],[f2225,f1142])).
% 24.66/4.12 thf(f2264,plain,(
% 24.66/4.12 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (~ (emptyset = (dsetconstr @ Y2 @ Y1))))))))))) => $true))) | ($false = sF262)),
% 24.66/4.12 inference(superposition,[],[f2215,f1166])).
% 24.66/4.12 thf(f2267,plain,(
% 24.66/4.12 ($true = $false) | ($false = sF262)),
% 24.66/4.12 inference(boolean_simplification,[],[f2264])).
% 24.66/4.12 thf(f2268,plain,(
% 24.66/4.12 ($false = sF262)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2267])).
% 24.66/4.12 thf(f2272,plain,(
% 24.66/4.12 (((nonemptyI1 => sF261)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1597,f2268])).
% 24.66/4.12 thf(f2279,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => sF261)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2272,f1675])).
% 24.66/4.12 thf(f2284,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => $true)) = $false) | (sF261 = $false)),
% 24.66/4.12 inference(superposition,[],[f2279,f1166])).
% 24.66/4.12 thf(f2288,plain,(
% 24.66/4.12 (sF261 = $false) | ($true = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2284])).
% 24.66/4.12 thf(f2289,plain,(
% 24.66/4.12 (sF261 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2288])).
% 24.66/4.12 thf(f2292,plain,(
% 24.66/4.12 (((setadjoinIL => sF260)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1595,f2289])).
% 24.66/4.12 thf(f2297,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => sF260)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2292,f1000])).
% 24.66/4.12 thf(f2304,plain,(
% 24.66/4.12 (sF260 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2297])).
% 24.66/4.12 thf(f2318,plain,(
% 24.66/4.12 (((emptyinunitempty => sF259)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1594,f2304])).
% 24.66/4.12 thf(f2319,plain,(
% 24.66/4.12 ((((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => sF259)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2318,f1012])).
% 24.66/4.12 thf(f2320,plain,(
% 24.66/4.12 (sF259 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2319])).
% 24.66/4.12 thf(f2336,plain,(
% 24.66/4.12 (((setadjoinIR => sF258)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1593,f2320])).
% 24.66/4.12 thf(f2337,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => sF258)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2336,f1132])).
% 24.66/4.12 thf(f2338,plain,(
% 24.66/4.12 (sF258 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2337])).
% 24.66/4.12 thf(f2352,plain,(
% 24.66/4.12 (((setadjoinE => sF257)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1591,f2338])).
% 24.66/4.12 thf(f2353,plain,(
% 24.66/4.12 (sF257 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2352])).
% 24.66/4.12 thf(f2369,plain,(
% 24.66/4.12 (((setadjoinOr => sF256)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1589,f2353])).
% 24.66/4.12 thf(f2370,plain,(
% 24.66/4.12 (((setadjoinOr => (setoftrueEq => sF255))) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2369,f1587])).
% 24.66/4.12 thf(f2371,plain,(
% 24.66/4.12 ($false = ((setadjoinOr => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => sF255))))),
% 24.66/4.12 inference(forward_demodulation,[],[f2370,f1090])).
% 24.66/4.12 thf(f2374,plain,(
% 24.66/4.12 ($false = ((setadjoinOr => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => $true)))) | ($false = sF255)),
% 24.66/4.12 inference(superposition,[],[f2371,f1166])).
% 24.66/4.12 thf(f2382,plain,(
% 24.66/4.12 ($false = sF255) | (((setadjoinOr => $true)) = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2374])).
% 24.66/4.12 thf(f2383,plain,(
% 24.66/4.12 ($true = $false) | ($false = sF255)),
% 24.66/4.12 inference(boolean_simplification,[],[f2382])).
% 24.66/4.12 thf(f2384,plain,(
% 24.66/4.12 ($false = sF255)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2383])).
% 24.66/4.12 thf(f2396,plain,(
% 24.66/4.12 ($false = ((powersetI => sF254)))),
% 24.66/4.12 inference(backward_demodulation,[],[f1586,f2384])).
% 24.66/4.12 thf(f2409,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => sF254)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2396,f991])).
% 24.66/4.12 thf(f2433,plain,(
% 24.66/4.12 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => $true))) | (sF254 = $false)),
% 24.66/4.12 inference(superposition,[],[f2409,f1166])).
% 24.66/4.12 thf(f2438,plain,(
% 24.66/4.12 ($true = $false) | (sF254 = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2433])).
% 24.66/4.12 thf(f2439,plain,(
% 24.66/4.12 (sF254 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2438])).
% 24.66/4.12 thf(f2441,plain,(
% 24.66/4.12 (((emptyinPowerset => sF253)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1584,f2439])).
% 24.66/4.12 thf(f2446,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => sF253)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2441,f951])).
% 24.66/4.12 thf(f2447,plain,(
% 24.66/4.12 (sF253 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2446])).
% 24.66/4.12 thf(f2448,plain,(
% 24.66/4.12 ($true = ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))))))),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2446])).
% 24.66/4.12 thf(f2457,plain,(
% 24.66/4.12 (((emptyInPowerset => sF252)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1583,f2447])).
% 24.66/4.12 thf(f2459,plain,(
% 24.66/4.12 (emptyInPowerset = $true)),
% 24.66/4.12 inference(backward_demodulation,[],[f1025,f2448])).
% 24.66/4.12 thf(f2465,plain,(
% 24.66/4.12 ((($true => sF252)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f2457,f2459])).
% 24.66/4.12 thf(f2466,plain,(
% 24.66/4.12 (sF252 = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2465])).
% 24.66/4.12 thf(f2467,plain,(
% 24.66/4.12 (((powersetE => sF251)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1581,f2466])).
% 24.66/4.12 thf(f2468,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => sF251)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2467,f1120])).
% 24.66/4.12 thf(f2473,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => $true)) = $false) | (sF251 = $false)),
% 24.66/4.12 inference(superposition,[],[f2468,f1166])).
% 24.66/4.12 thf(f2476,plain,(
% 24.66/4.12 ($true = $false) | (sF251 = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2473])).
% 24.66/4.12 thf(f2477,plain,(
% 24.66/4.12 (sF251 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2476])).
% 24.66/4.12 thf(f2481,plain,(
% 24.66/4.12 (((setunionI => sF250)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1579,f2477])).
% 24.66/4.12 thf(f2488,plain,(
% 24.66/4.12 (sF250 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2481])).
% 24.66/4.12 thf(f2500,plain,(
% 24.66/4.12 (((setunionE => sF249)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1577,f2488])).
% 24.66/4.12 thf(f2503,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => Y2)))) => Y2)))))))) => sF249)) = $false)),
% 24.66/4.12 inference(forward_demodulation,[],[f2500,f936])).
% 24.66/4.12 thf(f2522,plain,(
% 24.66/4.12 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => Y2)))) => Y2)))))))) => $true)) = $false) | (sF249 = $false)),
% 24.66/4.12 inference(superposition,[],[f2503,f1166])).
% 24.66/4.12 thf(f2526,plain,(
% 24.66/4.12 (sF249 = $false) | ($true = $false)),
% 24.66/4.12 inference(boolean_simplification,[],[f2522])).
% 24.66/4.12 thf(f2527,plain,(
% 24.66/4.12 (sF249 = $false)),
% 24.66/4.12 inference(trivial_inequality_removal,[],[f2526])).
% 24.66/4.12 thf(f2530,plain,(
% 24.66/4.12 (((subPowSU => sF248)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1575,f2527])).
% 24.66/4.12 thf(f2537,plain,(
% 24.66/4.12 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => sF248)))),
% 24.66/4.12 inference(forward_demodulation,[],[f2530,f1006])).
% 24.66/4.12 thf(f2538,plain,(
% 24.66/4.12 (sF248 = $false)),
% 24.66/4.12 inference(imp_proxy_clausification,[],[f2537])).
% 24.66/4.12 thf(f2554,plain,(
% 24.66/4.12 (((exuE2 => sF247)) = $false)),
% 24.66/4.12 inference(backward_demodulation,[],[f1573,f2538])).
% 24.66/4.12 thf(f2555,plain,(
% 24.66/4.12 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => sF247)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2554,f1694])).
% 24.66/4.13 thf(f2571,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => $true)) = $false) | (sF247 = $false)),
% 24.66/4.13 inference(superposition,[],[f2555,f1166])).
% 24.66/4.13 thf(f2575,plain,(
% 24.66/4.13 ($true = $false) | (sF247 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2571])).
% 24.66/4.13 thf(f2576,plain,(
% 24.66/4.13 (sF247 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f2575])).
% 24.66/4.13 thf(f2579,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => sF244))) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f2226,f2576])).
% 24.66/4.13 thf(f2591,plain,(
% 24.66/4.13 (sF244 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => $true))) = $false)),
% 24.66/4.13 inference(superposition,[],[f2579,f1166])).
% 24.66/4.13 thf(f2598,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => $true))) | (sF244 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2591])).
% 24.66/4.13 thf(f2599,plain,(
% 24.66/4.13 (sF244 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2598])).
% 24.66/4.13 thf(f2600,plain,(
% 24.66/4.13 (sF244 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f2599])).
% 24.66/4.13 thf(f2612,plain,(
% 24.66/4.13 (((eqinunit => sF243)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1569,f2600])).
% 24.66/4.13 thf(f2630,plain,(
% 24.66/4.13 ($false = sF243)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2612])).
% 24.66/4.13 thf(f2646,plain,(
% 24.66/4.13 (((singletonsswitch => sF242)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1567,f2630])).
% 24.66/4.13 thf(f2647,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => sF242)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2646,f1042])).
% 24.66/4.13 thf(f2648,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (upairsetE => sF241))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2647,f1565])).
% 24.66/4.13 thf(f2662,plain,(
% 24.66/4.13 (sF241 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => (upairsetE => $true))) = $false)),
% 24.66/4.13 inference(superposition,[],[f2648,f1166])).
% 24.66/4.13 thf(f2671,plain,(
% 24.66/4.13 (sF241 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true)) = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2662])).
% 24.66/4.13 thf(f2672,plain,(
% 24.66/4.13 (sF241 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2671])).
% 24.66/4.13 thf(f2673,plain,(
% 24.66/4.13 (sF241 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f2672])).
% 24.66/4.13 thf(f2680,plain,(
% 24.66/4.13 (((upairsetIL => sF240)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1564,f2673])).
% 24.66/4.13 thf(f2692,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => sF240)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2680,f1035])).
% 24.66/4.13 thf(f2699,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)) = $false) | (sF240 = $false)),
% 24.66/4.13 inference(superposition,[],[f2692,f1166])).
% 24.66/4.13 thf(f2702,plain,(
% 24.66/4.13 ($true = $false) | (sF240 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2699])).
% 24.66/4.13 thf(f2703,plain,(
% 24.66/4.13 (sF240 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f2702])).
% 24.66/4.13 thf(f2707,plain,(
% 24.66/4.13 (((upairsetIR => sF239)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1562,f2703])).
% 24.66/4.13 thf(f2714,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => sF239)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2707,f984])).
% 24.66/4.13 thf(f2715,plain,(
% 24.66/4.13 (sF239 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2714])).
% 24.66/4.13 thf(f2716,plain,(
% 24.66/4.13 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) = $true)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2714])).
% 24.66/4.13 thf(f2725,plain,(
% 24.66/4.13 (((emptyE1 => sF238)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1561,f2715])).
% 24.66/4.13 thf(f2728,plain,(
% 24.66/4.13 (upairset2IR = $true)),
% 24.66/4.13 inference(backward_demodulation,[],[f1163,f2716])).
% 24.66/4.13 thf(f2733,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset))))))) => sF238)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2725,f1701])).
% 24.66/4.13 thf(f2734,plain,(
% 24.66/4.13 ((($true => sF189)) = sF190)),
% 24.66/4.13 inference(backward_demodulation,[],[f1489,f2728])).
% 24.66/4.13 thf(f2735,plain,(
% 24.66/4.13 (sF189 = sF190)),
% 24.66/4.13 inference(boolean_simplification,[],[f2734])).
% 24.66/4.13 thf(f2736,plain,(
% 24.66/4.13 (sF191 = ((binunionIL => sF189)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1490,f2735])).
% 24.66/4.13 thf(f2737,plain,(
% 24.66/4.13 (sF191 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => sF189)))),
% 24.66/4.13 inference(forward_demodulation,[],[f2736,f916])).
% 24.66/4.13 thf(f2738,plain,(
% 24.66/4.13 (((sepSubset => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => sF189))) = sF192)),
% 24.66/4.13 inference(backward_demodulation,[],[f1492,f2737])).
% 24.66/4.13 thf(f2739,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => sF189))) = sF192)),
% 24.66/4.13 inference(forward_demodulation,[],[f2738,f1697])).
% 24.66/4.13 thf(f2754,plain,(
% 24.66/4.13 (sF238 = $false) | ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (~ ((dsetconstr @ Y1 @ Y0) = emptyset))))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f2733,f1166])).
% 24.66/4.13 thf(f2757,plain,(
% 24.66/4.13 ($true = $false) | (sF238 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2754])).
% 24.66/4.13 thf(f2758,plain,(
% 24.66/4.13 (sF238 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f2757])).
% 24.66/4.13 thf(f2762,plain,(
% 24.66/4.13 (((vacuousDall => sF237)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1559,f2758])).
% 24.66/4.13 thf(f2769,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => sF237)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2762,f1093])).
% 24.66/4.13 thf(f2770,plain,(
% 24.66/4.13 ($false = sF237)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2769])).
% 24.66/4.13 thf(f2780,plain,(
% 24.66/4.13 (((quantDeMorgan1 => sF236)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1558,f2770])).
% 24.66/4.13 thf(f2785,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0))))))))) => sF236)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2780,f973])).
% 24.66/4.13 thf(f2790,plain,(
% 24.66/4.13 (sF236 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2785])).
% 24.66/4.13 thf(f2800,plain,(
% 24.66/4.13 (((quantDeMorgan2 => sF235)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1556,f2790])).
% 24.66/4.13 thf(f2807,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => sF235)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2800,f1046])).
% 24.66/4.13 thf(f2808,plain,(
% 24.66/4.13 ($false = sF235)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2807])).
% 24.66/4.13 thf(f2818,plain,(
% 24.66/4.13 (((quantDeMorgan3 => sF234)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1555,f2808])).
% 24.66/4.13 thf(f2825,plain,(
% 24.66/4.13 (sF234 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2818])).
% 24.66/4.13 thf(f2835,plain,(
% 24.66/4.13 (((quantDeMorgan4 => sF233)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1553,f2825])).
% 24.66/4.13 thf(f2846,plain,(
% 24.66/4.13 (((quantDeMorgan4 => $true)) = $false) | (sF233 = $false)),
% 24.66/4.13 inference(superposition,[],[f2835,f1166])).
% 24.66/4.13 thf(f2849,plain,(
% 24.66/4.13 ($true = $false) | (sF233 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2846])).
% 24.66/4.13 thf(f2850,plain,(
% 24.66/4.13 (sF233 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f2849])).
% 24.66/4.13 thf(f2856,plain,(
% 24.66/4.13 ($false = ((prop2setI => sF232)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1552,f2850])).
% 24.66/4.13 thf(f2859,plain,(
% 24.66/4.13 ((((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => sF232)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2856,f960])).
% 24.66/4.13 thf(f2860,plain,(
% 24.66/4.13 (sF232 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2859])).
% 24.66/4.13 thf(f2870,plain,(
% 24.66/4.13 (((prop2set2propI => sF231)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1551,f2860])).
% 24.66/4.13 thf(f2881,plain,(
% 24.66/4.13 (((prop2set2propI => $true)) = $false) | (sF231 = $false)),
% 24.66/4.13 inference(superposition,[],[f2870,f1166])).
% 24.66/4.13 thf(f2886,plain,(
% 24.66/4.13 ($true = $false) | (sF231 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2881])).
% 24.66/4.13 thf(f2887,plain,(
% 24.66/4.13 (sF231 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f2886])).
% 24.66/4.13 thf(f2893,plain,(
% 24.66/4.13 (((notdexE => sF230)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1549,f2887])).
% 24.66/4.13 thf(f2894,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => sF230)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2893,f947])).
% 24.66/4.13 thf(f2924,plain,(
% 24.66/4.13 (sF230 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2894])).
% 24.66/4.13 thf(f2938,plain,(
% 24.66/4.13 (((notdallE => sF229)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1548,f2924])).
% 24.66/4.13 thf(f2939,plain,(
% 24.66/4.13 (sF229 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2938])).
% 24.66/4.13 thf(f2949,plain,(
% 24.66/4.13 (((exuI1 => sF228)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1546,f2939])).
% 24.66/4.13 thf(f2956,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))) => sF228)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2949,f1656])).
% 24.66/4.13 thf(f2959,plain,(
% 24.66/4.13 (sF228 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2956])).
% 24.66/4.13 thf(f2969,plain,(
% 24.66/4.13 (((exuI3 => sF227)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1545,f2959])).
% 24.66/4.13 thf(f2976,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => sF227)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f2969,f1689])).
% 24.66/4.13 thf(f2993,plain,(
% 24.66/4.13 (sF189 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => $true))) = sF192)),
% 24.66/4.13 inference(superposition,[],[f2739,f1166])).
% 24.66/4.13 thf(f3001,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => $true)) = sF192) | (sF189 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f2993])).
% 24.66/4.13 thf(f3002,plain,(
% 24.66/4.13 ($true = sF192) | (sF189 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3001])).
% 24.66/4.13 thf(f3015,plain,(
% 24.66/4.13 (sF227 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f2976])).
% 24.66/4.13 thf(f3029,plain,(
% 24.66/4.13 (((exuI2 => sF226)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1544,f3015])).
% 24.66/4.13 thf(f3030,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => sF226)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3029,f1661])).
% 24.66/4.13 thf(f3031,plain,(
% 24.66/4.13 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => (inCongP => sF225))))),
% 24.66/4.13 inference(forward_demodulation,[],[f3030,f1543])).
% 24.66/4.13 thf(f3034,plain,(
% 24.66/4.13 (sF225 = $false) | ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => (inCongP => $true))) = $false)),
% 24.66/4.13 inference(superposition,[],[f3031,f1166])).
% 24.66/4.13 thf(f3042,plain,(
% 24.66/4.13 (sF225 = $false) | ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => $true)) = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3034])).
% 24.66/4.13 thf(f3043,plain,(
% 24.66/4.13 (sF225 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3042])).
% 24.66/4.13 thf(f3044,plain,(
% 24.66/4.13 (sF225 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3043])).
% 24.66/4.13 thf(f3052,plain,(
% 24.66/4.13 (((in__Cong => sF224)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1541,f3044])).
% 24.66/4.13 thf(f3066,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => sF224)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3052,f966])).
% 24.66/4.13 thf(f3075,plain,(
% 24.66/4.13 (sF224 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => $true)))),
% 24.66/4.13 inference(superposition,[],[f3066,f1166])).
% 24.66/4.13 thf(f3079,plain,(
% 24.66/4.13 (sF224 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3075])).
% 24.66/4.13 thf(f3080,plain,(
% 24.66/4.13 (sF224 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3079])).
% 24.66/4.13 thf(f3087,plain,(
% 24.66/4.13 ($false = ((exuE3u => sF223)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1540,f3080])).
% 24.66/4.13 thf(f3088,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => sF223)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3087,f1680])).
% 24.66/4.13 thf(f3091,plain,(
% 24.66/4.13 (sF223 = $false) | ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f3088,f1166])).
% 24.66/4.13 thf(f3094,plain,(
% 24.66/4.13 ($true = $false) | (sF223 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3091])).
% 24.66/4.13 thf(f3095,plain,(
% 24.66/4.13 (sF223 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3094])).
% 24.66/4.13 thf(f3099,plain,(
% 24.66/4.13 ($false = ((exu__Cong => sF222)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1539,f3095])).
% 24.66/4.13 thf(f3106,plain,(
% 24.66/4.13 (sF222 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3099])).
% 24.66/4.13 thf(f3120,plain,(
% 24.66/4.13 ($false = ((emptyset__Cong => sF221)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1538,f3106])).
% 24.66/4.13 thf(f3121,plain,(
% 24.66/4.13 ((($true => sF221)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3120,f1687])).
% 24.66/4.13 thf(f3122,plain,(
% 24.66/4.13 (sF221 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3121])).
% 24.66/4.13 thf(f3123,plain,(
% 24.66/4.13 (((setadjoin__Cong => sF220)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1537,f3122])).
% 24.66/4.13 thf(f3124,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2)))))))))))) => sF220)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3123,f956])).
% 24.66/4.13 thf(f3127,plain,(
% 24.66/4.13 (sF220 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3124])).
% 24.66/4.13 thf(f3139,plain,(
% 24.66/4.13 (((powerset__Cong => sF219)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1535,f3127])).
% 24.66/4.13 thf(f3140,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => sF219)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3139,f871])).
% 24.66/4.13 thf(f3141,plain,(
% 24.66/4.13 ($false = sF219)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3140])).
% 24.66/4.13 thf(f3151,plain,(
% 24.66/4.13 ($false = ((setunion__Cong => sF218)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1534,f3141])).
% 24.66/4.13 thf(f3156,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => sF218)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3151,f1074])).
% 24.66/4.13 thf(f3159,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => (omega__Cong => sF217))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3156,f1532])).
% 24.66/4.13 thf(f3160,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ($true => sF217))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3159,f1699])).
% 24.66/4.13 thf(f3161,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => sF217)) = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3160])).
% 24.66/4.13 thf(f3166,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => $true)) = $false) | (sF217 = $false)),
% 24.66/4.13 inference(superposition,[],[f3161,f1166])).
% 24.66/4.13 thf(f3170,plain,(
% 24.66/4.13 (sF217 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3166])).
% 24.66/4.13 thf(f3171,plain,(
% 24.66/4.13 (sF217 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3170])).
% 24.66/4.13 thf(f3178,plain,(
% 24.66/4.13 (((exuEu => sF216)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1531,f3171])).
% 24.66/4.13 thf(f3183,plain,(
% 24.66/4.13 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => sF216)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3178,f1691])).
% 24.66/4.13 thf(f3188,plain,(
% 24.66/4.13 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => $true))) | (sF216 = $false)),
% 24.66/4.13 inference(superposition,[],[f3183,f1166])).
% 24.66/4.13 thf(f3191,plain,(
% 24.66/4.13 (sF216 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3188])).
% 24.66/4.13 thf(f3192,plain,(
% 24.66/4.13 (sF216 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3191])).
% 24.66/4.13 thf(f3198,plain,(
% 24.66/4.13 (((descr__Cong => sF215)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1530,f3192])).
% 24.66/4.13 thf(f3201,plain,(
% 24.66/4.13 (sF215 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3198])).
% 24.66/4.13 thf(f3215,plain,(
% 24.66/4.13 ($false = ((dsetconstr__Cong => sF214)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1528,f3201])).
% 24.66/4.13 thf(f3218,plain,(
% 24.66/4.13 (((dsetconstr__Cong => $true)) = $false) | ($false = sF214)),
% 24.66/4.13 inference(superposition,[],[f3215,f1166])).
% 24.66/4.13 thf(f3221,plain,(
% 24.66/4.13 ($false = sF214) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3218])).
% 24.66/4.13 thf(f3222,plain,(
% 24.66/4.13 ($false = sF214)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3221])).
% 24.66/4.13 thf(f3226,plain,(
% 24.66/4.13 ($false = ((subsetI1 => sF213)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1527,f3222])).
% 24.66/4.13 thf(f3231,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => sF213)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3226,f884])).
% 24.66/4.13 thf(f3234,plain,(
% 24.66/4.13 (((subsetI2 => sF213)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3231,f1117])).
% 24.66/4.13 thf(f3235,plain,(
% 24.66/4.13 (((subsetI2 => (eqimpsubset2 => sF212))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3234,f1525])).
% 24.66/4.13 thf(f3236,plain,(
% 24.66/4.13 (((subsetI2 => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => sF212))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3235,f1101])).
% 24.66/4.13 thf(f3238,plain,(
% 24.66/4.13 (subsetI2 = $true)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3236])).
% 24.66/4.13 thf(f3239,plain,(
% 24.66/4.13 (((subsetI2 => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => $true))) = $false) | (sF212 = $false)),
% 24.66/4.13 inference(superposition,[],[f3236,f1166])).
% 24.66/4.13 thf(f3245,plain,(
% 24.66/4.13 (((subsetI2 => $true)) = $false) | (sF212 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3239])).
% 24.66/4.13 thf(f3246,plain,(
% 24.66/4.13 (sF212 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3245])).
% 24.66/4.13 thf(f3247,plain,(
% 24.66/4.13 (sF212 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3246])).
% 24.66/4.13 thf(f3255,plain,(
% 24.66/4.13 ($false = ((eqimpsubset1 => sF211)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1523,f3247])).
% 24.66/4.13 thf(f3268,plain,(
% 24.66/4.13 ((($true => sF210)) = sF211)),
% 24.66/4.13 inference(backward_demodulation,[],[f1522,f3238])).
% 24.66/4.13 thf(f3269,plain,(
% 24.66/4.13 (sF211 = sF210)),
% 24.66/4.13 inference(boolean_simplification,[],[f3268])).
% 24.66/4.13 thf(f3273,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => sF211)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3255,f1004])).
% 24.66/4.13 thf(f3282,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => sF210)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3273,f3269])).
% 24.66/4.13 thf(f3291,plain,(
% 24.66/4.13 ($false = sF210)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3282])).
% 24.66/4.13 thf(f3302,plain,(
% 24.66/4.13 (((emptysetsubset => sF209)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1520,f3291])).
% 24.66/4.13 thf(f3310,plain,(
% 24.66/4.13 ((((!! @ $i @ (subset @ emptyset)) => sF209)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3302,f1679])).
% 24.66/4.13 thf(f3311,plain,(
% 24.66/4.13 ((((!! @ $i @ (subset @ emptyset)) => (subsetE => sF208))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3310,f1518])).
% 24.66/4.13 thf(f3316,plain,(
% 24.66/4.13 (sF208 = $false) | ((((!! @ $i @ (subset @ emptyset)) => (subsetE => $true))) = $false)),
% 24.66/4.13 inference(superposition,[],[f3311,f1166])).
% 24.66/4.13 thf(f3324,plain,(
% 24.66/4.13 (sF208 = $false) | ($false = (((!! @ $i @ (subset @ emptyset)) => $true)))),
% 24.66/4.13 inference(boolean_simplification,[],[f3316])).
% 24.66/4.13 thf(f3325,plain,(
% 24.66/4.13 ($true = $false) | (sF208 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3324])).
% 24.66/4.13 thf(f3326,plain,(
% 24.66/4.13 (sF208 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3325])).
% 24.66/4.13 thf(f3334,plain,(
% 24.66/4.13 (((subsetE2 => sF207)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1517,f3326])).
% 24.66/4.13 thf(f3348,plain,(
% 24.66/4.13 (((subsetE2 => $true)) = $false) | (sF207 = $false)),
% 24.66/4.13 inference(superposition,[],[f3334,f1166])).
% 24.66/4.13 thf(f3352,plain,(
% 24.66/4.13 ($true = $false) | (sF207 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3348])).
% 24.66/4.13 thf(f3353,plain,(
% 24.66/4.13 (sF207 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3352])).
% 24.66/4.13 thf(f3360,plain,(
% 24.66/4.13 (((notsubsetI => sF206)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1515,f3353])).
% 24.66/4.13 thf(f3363,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => sF206)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3360,f874])).
% 24.66/4.13 thf(f3399,plain,(
% 24.66/4.13 ($false = sF206) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f3363,f1166])).
% 24.66/4.13 thf(f3404,plain,(
% 24.66/4.13 ($false = sF206) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3399])).
% 24.66/4.13 thf(f3405,plain,(
% 24.66/4.13 ($false = sF206)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3404])).
% 24.66/4.13 thf(f3413,plain,(
% 24.66/4.13 ($false = ((notequalI1 => sF205)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1514,f3405])).
% 24.66/4.13 thf(f3414,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => sF205)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3413,f1099])).
% 24.66/4.13 thf(f3415,plain,(
% 24.66/4.13 (sF205 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3414])).
% 24.66/4.13 thf(f3425,plain,(
% 24.66/4.13 (((notequalI2 => sF204)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1512,f3415])).
% 24.66/4.13 thf(f3430,plain,(
% 24.66/4.13 (sF204 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3425])).
% 24.66/4.13 thf(f3440,plain,(
% 24.66/4.13 (((subsetRefl => sF203)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1511,f3430])).
% 24.66/4.13 thf(f3445,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => sF203)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3440,f1091])).
% 24.66/4.13 thf(f3450,plain,(
% 24.66/4.13 (sF203 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f3445,f1166])).
% 24.66/4.13 thf(f3453,plain,(
% 24.66/4.13 ($true = $false) | (sF203 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3450])).
% 24.66/4.13 thf(f3454,plain,(
% 24.66/4.13 (sF203 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3453])).
% 24.66/4.13 thf(f3458,plain,(
% 24.66/4.13 ($false = ((subsetTrans => sF202)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1510,f3454])).
% 24.66/4.13 thf(f3463,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y2) => (subset @ Y1 @ Y2))))))))) => sF202)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3458,f1063])).
% 24.66/4.13 thf(f3492,plain,(
% 24.66/4.13 (sF202 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3463])).
% 24.66/4.13 thf(f3502,plain,(
% 24.66/4.13 (((setadjoinSub => sF201)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1509,f3492])).
% 24.66/4.13 thf(f3507,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => sF201)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3502,f1076])).
% 24.66/4.13 thf(f3512,plain,(
% 24.66/4.13 (sF201 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3507])).
% 24.66/4.13 thf(f3522,plain,(
% 24.66/4.13 (((setadjoinSub2 => sF200)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1508,f3512])).
% 24.66/4.13 thf(f3527,plain,(
% 24.66/4.13 (((setadjoinSub2 => (subset2powerset => sF199))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3522,f1506])).
% 24.66/4.13 thf(f3528,plain,(
% 24.66/4.13 (((setadjoinSub2 => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => sF199))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3527,f1124])).
% 24.66/4.13 thf(f3531,plain,(
% 24.66/4.13 ($false = sF199) | (((setadjoinSub2 => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => $true))) = $false)),
% 24.66/4.13 inference(superposition,[],[f3528,f1166])).
% 24.66/4.13 thf(f3541,plain,(
% 24.66/4.13 ($false = ((setadjoinSub2 => $true))) | ($false = sF199)),
% 24.66/4.13 inference(boolean_simplification,[],[f3531])).
% 24.66/4.13 thf(f3542,plain,(
% 24.66/4.13 ($true = $false) | ($false = sF199)),
% 24.66/4.13 inference(boolean_simplification,[],[f3541])).
% 24.66/4.13 thf(f3543,plain,(
% 24.66/4.13 ($false = sF199)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3542])).
% 24.66/4.13 thf(f3548,plain,(
% 24.66/4.13 (((setextsub => sF198)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1504,f3543])).
% 24.66/4.13 thf(f3562,plain,(
% 24.66/4.13 (sF198 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3548])).
% 24.66/4.13 thf(f3572,plain,(
% 24.66/4.13 (((subsetemptysetimpeq => sF197)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1502,f3562])).
% 24.66/4.13 thf(f3579,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => sF197)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3572,f1144])).
% 24.66/4.13 thf(f3582,plain,(
% 24.66/4.13 ($false = sF197) | ((((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f3579,f1166])).
% 24.66/4.13 thf(f3585,plain,(
% 24.66/4.13 ($true = $false) | ($false = sF197)),
% 24.66/4.13 inference(boolean_simplification,[],[f3582])).
% 24.66/4.13 thf(f3586,plain,(
% 24.66/4.13 ($false = sF197)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3585])).
% 24.66/4.13 thf(f3590,plain,(
% 24.66/4.13 (((powersetI1 => sF196)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1501,f3586])).
% 24.66/4.13 thf(f3595,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => sF196)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3590,f952])).
% 24.66/4.13 thf(f3600,plain,(
% 24.66/4.13 ($false = sF196)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3595])).
% 24.66/4.13 thf(f3610,plain,(
% 24.66/4.13 ($false = ((powersetE1 => sF195)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1499,f3600])).
% 24.66/4.13 thf(f3616,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => sF195)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3610,f923])).
% 24.66/4.13 thf(f3619,plain,(
% 24.66/4.13 (sF195 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3616])).
% 24.66/4.13 thf(f3629,plain,(
% 24.66/4.13 ($false = ((inPowerset => sF194)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1497,f3619])).
% 24.66/4.13 thf(f3636,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => sF194)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3629,f904])).
% 24.66/4.13 thf(f3639,plain,(
% 24.66/4.13 ($false = sF194)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3636])).
% 24.66/4.13 thf(f3649,plain,(
% 24.66/4.13 (((powersetsubset => sF193)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1496,f3639])).
% 24.66/4.13 thf(f3656,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => sF193)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3649,f1096])).
% 24.66/4.13 thf(f3659,plain,(
% 24.66/4.13 ($false = sF193)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3656])).
% 24.66/4.13 thf(f3669,plain,(
% 24.66/4.13 (((sepInPowerset => sF192)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1494,f3659])).
% 24.66/4.13 thf(f3674,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => sF192)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3669,f1646])).
% 24.66/4.13 thf(f3681,plain,(
% 24.66/4.13 ($false = sF192) | ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f3674,f1166])).
% 24.66/4.13 thf(f3685,plain,(
% 24.66/4.13 ($false = sF192) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3681])).
% 24.66/4.13 thf(f3686,plain,(
% 24.66/4.13 ($false = sF192)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3685])).
% 24.66/4.13 thf(f3689,plain,(
% 24.66/4.13 (sF189 = $false) | ($true = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f3002,f3686])).
% 24.66/4.13 thf(f3694,plain,(
% 24.66/4.13 (sF189 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3689])).
% 24.66/4.13 thf(f3698,plain,(
% 24.66/4.13 (((binunionIR => sF188)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1487,f3694])).
% 24.66/4.13 thf(f3712,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => sF188)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3698,f1150])).
% 24.66/4.13 thf(f3781,plain,(
% 24.66/4.13 ($false = sF188)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3712])).
% 24.66/4.13 thf(f3791,plain,(
% 24.66/4.13 (((binunionEcases => sF187)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1485,f3781])).
% 24.66/4.13 thf(f3800,plain,(
% 24.66/4.13 (sF187 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3791])).
% 24.66/4.13 thf(f3810,plain,(
% 24.66/4.13 (((binunionE => sF186)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1483,f3800])).
% 24.66/4.13 thf(f3815,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => sF186)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3810,f1129])).
% 24.66/4.13 thf(f3820,plain,(
% 24.66/4.13 ($false = sF186)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3815])).
% 24.66/4.13 thf(f3830,plain,(
% 24.66/4.13 ($false = ((binunionLsub => sF185)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1482,f3820])).
% 24.66/4.13 thf(f3837,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => sF185)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3830,f1084])).
% 24.66/4.13 thf(f3840,plain,(
% 24.66/4.13 (sF185 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f3837,f1166])).
% 24.66/4.13 thf(f3843,plain,(
% 24.66/4.13 ($true = $false) | (sF185 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3840])).
% 24.66/4.13 thf(f3844,plain,(
% 24.66/4.13 (sF185 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3843])).
% 24.66/4.13 thf(f3848,plain,(
% 24.66/4.13 (((binunionRsub => sF184)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1480,f3844])).
% 24.66/4.13 thf(f3853,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => sF184)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3848,f1115])).
% 24.66/4.13 thf(f3858,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => $true)) = $false) | (sF184 = $false)),
% 24.66/4.13 inference(superposition,[],[f3853,f1166])).
% 24.66/4.13 thf(f3862,plain,(
% 24.66/4.13 (sF184 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3858])).
% 24.66/4.13 thf(f3863,plain,(
% 24.66/4.13 (sF184 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3862])).
% 24.66/4.13 thf(f3868,plain,(
% 24.66/4.13 (((binintersectI => sF183)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1479,f3863])).
% 24.66/4.13 thf(f3869,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => sF183)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3868,f1102])).
% 24.66/4.13 thf(f3872,plain,(
% 24.66/4.13 (sF183 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f3869,f1166])).
% 24.66/4.13 thf(f3875,plain,(
% 24.66/4.13 (sF183 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3872])).
% 24.66/4.13 thf(f3876,plain,(
% 24.66/4.13 (sF183 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3875])).
% 24.66/4.13 thf(f3882,plain,(
% 24.66/4.13 (((binintersectSubset5 => sF182)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1478,f3876])).
% 24.66/4.13 thf(f3885,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((subset @ Y1 @ Y0) => (subset @ Y1 @ (binintersect @ Y2 @ Y0)))))))))) => sF182)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3882,f994])).
% 24.66/4.13 thf(f3888,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((subset @ Y1 @ Y0) => (subset @ Y1 @ (binintersect @ Y2 @ Y0)))))))))) => $true)) = $false) | (sF182 = $false)),
% 24.66/4.13 inference(superposition,[],[f3885,f1166])).
% 24.66/4.13 thf(f3891,plain,(
% 24.66/4.13 (sF182 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3888])).
% 24.66/4.13 thf(f3892,plain,(
% 24.66/4.13 (sF182 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3891])).
% 24.66/4.13 thf(f3896,plain,(
% 24.66/4.13 ($false = ((binintersectEL => sF181)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1477,f3892])).
% 24.66/4.13 thf(f3901,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => sF181)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3896,f1138])).
% 24.66/4.13 thf(f3906,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => $true)) = $false) | ($false = sF181)),
% 24.66/4.13 inference(superposition,[],[f3901,f1166])).
% 24.66/4.13 thf(f3909,plain,(
% 24.66/4.13 ($false = sF181) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3906])).
% 24.66/4.13 thf(f3910,plain,(
% 24.66/4.13 ($false = sF181)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3909])).
% 24.66/4.13 thf(f3916,plain,(
% 24.66/4.13 ($false = ((binintersectLsub => sF180)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1476,f3910])).
% 24.66/4.13 thf(f3919,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => sF180)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3916,f939])).
% 24.66/4.13 thf(f3920,plain,(
% 24.66/4.13 (sF180 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f3919])).
% 24.66/4.13 thf(f3932,plain,(
% 24.66/4.13 (((binintersectSubset2 => sF179)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1474,f3920])).
% 24.66/4.13 thf(f3935,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => sF179)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3932,f993])).
% 24.66/4.13 thf(f3938,plain,(
% 24.66/4.13 (sF179 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f3935,f1166])).
% 24.66/4.13 thf(f3941,plain,(
% 24.66/4.13 (sF179 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f3938])).
% 24.66/4.13 thf(f3942,plain,(
% 24.66/4.13 (sF179 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f3941])).
% 24.66/4.13 thf(f3946,plain,(
% 24.66/4.13 (((binintersectSubset3 => sF178)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1472,f3942])).
% 24.66/4.13 thf(f3953,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => sF178)))),
% 24.66/4.13 inference(forward_demodulation,[],[f3946,f931])).
% 24.66/4.13 thf(f3956,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => (binintersectER => sF177))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3953,f1471])).
% 24.66/4.13 thf(f3957,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))) => sF177))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f3956,f969])).
% 24.66/4.13 thf(f4021,plain,(
% 24.66/4.13 (sF177 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y2)))))))) => $true))) = $false)),
% 24.66/4.13 inference(superposition,[],[f3957,f1166])).
% 24.66/4.13 thf(f4027,plain,(
% 24.66/4.13 (sF177 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => $true)))),
% 24.66/4.13 inference(boolean_simplification,[],[f4021])).
% 24.66/4.13 thf(f4028,plain,(
% 24.66/4.13 ($true = $false) | (sF177 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4027])).
% 24.66/4.13 thf(f4029,plain,(
% 24.66/4.13 (sF177 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4028])).
% 24.66/4.13 thf(f4037,plain,(
% 24.66/4.13 (((disjointsetsI1 => sF176)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1470,f4029])).
% 24.66/4.13 thf(f4052,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => sF176)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4037,f873])).
% 24.66/4.13 thf(f4063,plain,(
% 24.66/4.13 (sF176 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f4052,f1166])).
% 24.66/4.13 thf(f4066,plain,(
% 24.66/4.13 (sF176 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4063])).
% 24.66/4.13 thf(f4067,plain,(
% 24.66/4.13 (sF176 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4066])).
% 24.66/4.13 thf(f4071,plain,(
% 24.66/4.13 (((binintersectRsub => sF175)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1468,f4067])).
% 24.66/4.13 thf(f4078,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => sF175)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4071,f917])).
% 24.66/4.13 thf(f4085,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => $true))) | (sF175 = $false)),
% 24.66/4.13 inference(superposition,[],[f4078,f1166])).
% 24.66/4.13 thf(f4090,plain,(
% 24.66/4.13 (sF175 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4085])).
% 24.66/4.13 thf(f4091,plain,(
% 24.66/4.13 (sF175 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4090])).
% 24.66/4.13 thf(f4093,plain,(
% 24.66/4.13 (((binintersectSubset4 => sF174)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1466,f4091])).
% 24.66/4.13 thf(f4098,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => sF174)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4093,f972])).
% 24.66/4.13 thf(f4099,plain,(
% 24.66/4.13 ($false = sF174)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4098])).
% 24.66/4.13 thf(f4113,plain,(
% 24.66/4.13 ($false = ((binintersectSubset1 => sF173)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1465,f4099])).
% 24.66/4.13 thf(f4114,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => sF173)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4113,f1066])).
% 24.66/4.13 thf(f4115,plain,(
% 24.66/4.13 ($false = sF173)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4114])).
% 24.66/4.13 thf(f4129,plain,(
% 24.66/4.13 (((bs114d => sF172)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1463,f4115])).
% 24.66/4.13 thf(f4132,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y0 @ Y1)) = (binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1))))))))) => sF172)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4129,f885])).
% 24.66/4.13 thf(f4135,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y0 @ Y1)) = (binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1))))))))) => $true)) = $false) | ($false = sF172)),
% 24.66/4.13 inference(superposition,[],[f4132,f1166])).
% 24.66/4.13 thf(f4138,plain,(
% 24.66/4.13 ($false = sF172) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4135])).
% 24.66/4.13 thf(f4139,plain,(
% 24.66/4.13 ($false = sF172)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4138])).
% 24.66/4.13 thf(f4143,plain,(
% 24.66/4.13 ($false = ((setminusI => sF171)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1461,f4139])).
% 24.66/4.13 thf(f4150,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => sF171)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4143,f1164])).
% 24.66/4.13 thf(f4155,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => $true))) | (sF171 = $false)),
% 24.66/4.13 inference(superposition,[],[f4150,f1166])).
% 24.66/4.13 thf(f4159,plain,(
% 24.66/4.13 (sF171 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4155])).
% 24.66/4.13 thf(f4160,plain,(
% 24.66/4.13 (sF171 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4159])).
% 24.66/4.13 thf(f4167,plain,(
% 24.66/4.13 (((setminusEL => sF170)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1460,f4160])).
% 24.66/4.13 thf(f4170,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => sF170)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4167,f1118])).
% 24.66/4.13 thf(f4173,plain,(
% 24.66/4.13 (sF170 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f4170,f1166])).
% 24.66/4.13 thf(f4177,plain,(
% 24.66/4.13 ($true = $false) | (sF170 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4173])).
% 24.66/4.13 thf(f4178,plain,(
% 24.66/4.13 (sF170 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4177])).
% 24.66/4.13 thf(f4181,plain,(
% 24.66/4.13 (((setminusER => sF169)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1459,f4178])).
% 24.66/4.13 thf(f4186,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => sF169)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4181,f889])).
% 24.66/4.13 thf(f4191,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => $true)) = $false) | (sF169 = $false)),
% 24.66/4.13 inference(superposition,[],[f4186,f1166])).
% 24.66/4.13 thf(f4194,plain,(
% 24.66/4.13 (sF169 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4191])).
% 24.66/4.13 thf(f4195,plain,(
% 24.66/4.13 (sF169 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4194])).
% 24.66/4.13 thf(f4199,plain,(
% 24.66/4.13 (((setminusSubset2 => sF168)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1458,f4195])).
% 24.66/4.13 thf(f4204,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => sF168)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4199,f1032])).
% 24.66/4.13 thf(f4211,plain,(
% 24.66/4.13 (sF168 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f4204,f1166])).
% 24.66/4.13 thf(f4216,plain,(
% 24.66/4.13 (sF168 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4211])).
% 24.66/4.13 thf(f4217,plain,(
% 24.66/4.13 (sF168 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4216])).
% 24.66/4.13 thf(f4225,plain,(
% 24.66/4.13 (((setminusERneg => sF167)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1456,f4217])).
% 24.66/4.13 thf(f4226,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => sF167)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4225,f914])).
% 24.66/4.13 thf(f4231,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => $true)) = $false) | (sF167 = $false)),
% 24.66/4.13 inference(superposition,[],[f4226,f1166])).
% 24.66/4.13 thf(f4234,plain,(
% 24.66/4.13 (sF167 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4231])).
% 24.66/4.13 thf(f4235,plain,(
% 24.66/4.13 (sF167 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4234])).
% 24.66/4.13 thf(f4239,plain,(
% 24.66/4.13 ($false = ((setminusELneg => sF166)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1454,f4235])).
% 24.66/4.13 thf(f4246,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => sF166)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4239,f950])).
% 24.66/4.13 thf(f4247,plain,(
% 24.66/4.13 (sF166 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4246])).
% 24.66/4.13 thf(f4257,plain,(
% 24.66/4.13 (((setminusILneg => sF165)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1453,f4247])).
% 24.66/4.13 thf(f4260,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => sF165)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4257,f1060])).
% 24.66/4.13 thf(f4265,plain,(
% 24.66/4.13 (sF165 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => $true)))),
% 24.66/4.13 inference(superposition,[],[f4260,f1166])).
% 24.66/4.13 thf(f4268,plain,(
% 24.66/4.13 ($true = $false) | (sF165 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4265])).
% 24.66/4.13 thf(f4269,plain,(
% 24.66/4.13 (sF165 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4268])).
% 24.66/4.13 thf(f4273,plain,(
% 24.66/4.13 (((setminusIRneg => sF164)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1452,f4269])).
% 24.66/4.13 thf(f4278,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => sF164)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4273,f1080])).
% 24.66/4.13 thf(f4283,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => $true))) | ($false = sF164)),
% 24.66/4.13 inference(superposition,[],[f4278,f1166])).
% 24.66/4.13 thf(f4286,plain,(
% 24.66/4.13 ($true = $false) | ($false = sF164)),
% 24.66/4.13 inference(boolean_simplification,[],[f4283])).
% 24.66/4.13 thf(f4287,plain,(
% 24.66/4.13 ($false = sF164)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4286])).
% 24.66/4.13 thf(f4291,plain,(
% 24.66/4.13 (((setminusLsub => sF163)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1450,f4287])).
% 24.66/4.13 thf(f4296,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => sF163)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4291,f1058])).
% 24.66/4.13 thf(f4305,plain,(
% 24.66/4.13 (sF163 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f4296,f1166])).
% 24.66/4.13 thf(f4310,plain,(
% 24.66/4.13 (sF163 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4305])).
% 24.66/4.13 thf(f4311,plain,(
% 24.66/4.13 (sF163 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4310])).
% 24.66/4.13 thf(f4317,plain,(
% 24.66/4.13 (((setminusSubset1 => sF162)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1448,f4311])).
% 24.66/4.13 thf(f4318,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => sF162)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4317,f922])).
% 24.66/4.13 thf(f4321,plain,(
% 24.66/4.13 ($false = sF162) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f4318,f1166])).
% 24.66/4.13 thf(f4324,plain,(
% 24.66/4.13 ($true = $false) | ($false = sF162)),
% 24.66/4.13 inference(boolean_simplification,[],[f4321])).
% 24.66/4.13 thf(f4325,plain,(
% 24.66/4.13 ($false = sF162)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4324])).
% 24.66/4.13 thf(f4329,plain,(
% 24.66/4.13 (((symdiffE => sF161)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1446,f4325])).
% 24.66/4.13 thf(f4336,plain,(
% 24.66/4.13 (sF161 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4329])).
% 24.66/4.13 thf(f4346,plain,(
% 24.66/4.13 ($false = ((symdiffI1 => sF160)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1444,f4336])).
% 24.66/4.13 thf(f4353,plain,(
% 24.66/4.13 (sF160 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4346])).
% 24.66/4.13 thf(f4367,plain,(
% 24.66/4.13 (((symdiffI2 => sF159)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1443,f4353])).
% 24.66/4.13 thf(f4370,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => sF159)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4367,f1140])).
% 24.66/4.13 thf(f4397,plain,(
% 24.66/4.13 (sF159 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4370])).
% 24.66/4.13 thf(f4407,plain,(
% 24.66/4.13 (((symdiffIneg1 => sF158)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1442,f4397])).
% 24.66/4.13 thf(f4412,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))) => sF158)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4407,f1086])).
% 24.66/4.13 thf(f4417,plain,(
% 24.66/4.13 (sF158 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4412])).
% 24.66/4.13 thf(f4427,plain,(
% 24.66/4.13 (((symdiffIneg2 => sF157)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1440,f4417])).
% 24.66/4.13 thf(f4434,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => sF157)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4427,f920])).
% 24.66/4.13 thf(f4437,plain,(
% 24.66/4.13 (sF157 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4434])).
% 24.66/4.13 thf(f4447,plain,(
% 24.66/4.13 (((secondinupair => sF156)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1438,f4437])).
% 24.66/4.13 thf(f4454,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => sF156)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4447,f1051])).
% 24.66/4.13 thf(f4459,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)) = $false) | (sF156 = $false)),
% 24.66/4.13 inference(superposition,[],[f4454,f1166])).
% 24.66/4.13 thf(f4462,plain,(
% 24.66/4.13 ($true = $false) | (sF156 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4459])).
% 24.66/4.13 thf(f4463,plain,(
% 24.66/4.13 (sF156 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4462])).
% 24.66/4.13 thf(f4467,plain,(
% 24.66/4.13 (((setukpairIL => sF155)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1436,f4463])).
% 24.66/4.13 thf(f4474,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => sF155)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4467,f988])).
% 24.66/4.13 thf(f4477,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => $true)) = $false) | (sF155 = $false)),
% 24.66/4.13 inference(superposition,[],[f4474,f1166])).
% 24.66/4.13 thf(f4482,plain,(
% 24.66/4.13 ($true = $false) | (sF155 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4477])).
% 24.66/4.13 thf(f4483,plain,(
% 24.66/4.13 (sF155 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4482])).
% 24.66/4.13 thf(f4491,plain,(
% 24.66/4.13 (((setukpairIR => sF154)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1434,f4483])).
% 24.66/4.13 thf(f4492,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => sF154)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4491,f981])).
% 24.66/4.13 thf(f4495,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => $true)) = $false) | (sF154 = $false)),
% 24.66/4.13 inference(superposition,[],[f4492,f1166])).
% 24.66/4.13 thf(f4498,plain,(
% 24.66/4.13 (sF154 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4495])).
% 24.66/4.13 thf(f4499,plain,(
% 24.66/4.13 (sF154 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4498])).
% 24.66/4.13 thf(f4503,plain,(
% 24.66/4.13 (((kpairiskpair => sF153)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1432,f4499])).
% 24.66/4.13 thf(f4510,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => sF153)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4503,f1088])).
% 24.66/4.13 thf(f4513,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => $true)) = $false) | (sF153 = $false)),
% 24.66/4.13 inference(superposition,[],[f4510,f1166])).
% 24.66/4.13 thf(f4516,plain,(
% 24.66/4.13 (sF153 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4513])).
% 24.66/4.13 thf(f4517,plain,(
% 24.66/4.13 (sF153 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4516])).
% 24.66/4.13 thf(f4523,plain,(
% 24.66/4.13 ($false = ((kpairp => sF152)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1430,f4517])).
% 24.66/4.13 thf(f4526,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => sF152)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4523,f1154])).
% 24.66/4.13 thf(f4527,plain,(
% 24.66/4.13 ($false = sF152)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4526])).
% 24.66/4.13 thf(f4541,plain,(
% 24.66/4.13 (((singletonsubset => sF151)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1429,f4527])).
% 24.66/4.13 thf(f4544,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => sF151)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4541,f1029])).
% 24.66/4.13 thf(f4545,plain,(
% 24.66/4.13 (sF151 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4544])).
% 24.66/4.13 thf(f4561,plain,(
% 24.66/4.13 (((singletoninpowerset => sF150)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1427,f4545])).
% 24.66/4.13 thf(f4562,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => sF150)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4561,f891])).
% 24.66/4.13 thf(f4563,plain,(
% 24.66/4.13 ($false = sF150)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4562])).
% 24.66/4.13 thf(f4573,plain,(
% 24.66/4.13 (((singletoninpowunion => sF149)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1426,f4563])).
% 24.66/4.13 thf(f4576,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0)))))))))) => sF149)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4573,f1147])).
% 24.66/4.13 thf(f4581,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0)))))))))) => $true)) = $false) | (sF149 = $false)),
% 24.66/4.13 inference(superposition,[],[f4576,f1166])).
% 24.66/4.13 thf(f4585,plain,(
% 24.66/4.13 ($true = $false) | (sF149 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4581])).
% 24.66/4.13 thf(f4586,plain,(
% 24.66/4.13 (sF149 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4585])).
% 24.66/4.13 thf(f4589,plain,(
% 24.66/4.13 (((upairset2E => sF148)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1424,f4586])).
% 24.66/4.13 thf(f4596,plain,(
% 24.66/4.13 (((upairset2E => (upairsubunion => sF147))) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4589,f1422])).
% 24.66/4.13 thf(f4601,plain,(
% 24.66/4.13 (sF147 = $false) | ($false = ((upairset2E => (upairsubunion => $true))))),
% 24.66/4.13 inference(superposition,[],[f4596,f1166])).
% 24.66/4.13 thf(f4609,plain,(
% 24.66/4.13 (sF147 = $false) | (((upairset2E => $true)) = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4601])).
% 24.66/4.13 thf(f4610,plain,(
% 24.66/4.13 (sF147 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4609])).
% 24.66/4.13 thf(f4611,plain,(
% 24.66/4.13 (sF147 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4610])).
% 24.66/4.13 thf(f4619,plain,(
% 24.66/4.13 (((upairinpowunion => sF146)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1421,f4611])).
% 24.66/4.13 thf(f4631,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y1))))))))))))) => sF146)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4619,f927])).
% 24.66/4.13 thf(f4659,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y1))))))))))))) => $true)) = $false) | (sF146 = $false)),
% 24.66/4.13 inference(superposition,[],[f4631,f1166])).
% 24.66/4.13 thf(f4664,plain,(
% 24.66/4.13 (sF146 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4659])).
% 24.66/4.13 thf(f4665,plain,(
% 24.66/4.13 (sF146 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4664])).
% 24.66/4.13 thf(f4667,plain,(
% 24.66/4.13 (((ubforcartprodlem1 => sF145)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1419,f4665])).
% 24.66/4.13 thf(f4670,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y1))))))))))))) => sF145)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4667,f1128])).
% 24.66/4.13 thf(f4675,plain,(
% 24.66/4.13 (sF145 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4670])).
% 24.66/4.13 thf(f4689,plain,(
% 24.66/4.13 (((ubforcartprodlem2 => sF144)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1418,f4675])).
% 24.66/4.13 thf(f4690,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => sF144)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4689,f1135])).
% 24.66/4.13 thf(f4693,plain,(
% 24.66/4.13 ($false = sF144) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f4690,f1166])).
% 24.66/4.13 thf(f4698,plain,(
% 24.66/4.13 ($false = sF144) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4693])).
% 24.66/4.13 thf(f4699,plain,(
% 24.66/4.13 ($false = sF144)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4698])).
% 24.66/4.13 thf(f4707,plain,(
% 24.66/4.13 (((ubforcartprodlem3 => sF143)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1416,f4699])).
% 24.66/4.13 thf(f4708,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => sF143)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4707,f946])).
% 24.66/4.13 thf(f4711,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => $true)) = $false) | (sF143 = $false)),
% 24.66/4.13 inference(superposition,[],[f4708,f1166])).
% 24.66/4.13 thf(f4714,plain,(
% 24.66/4.13 ($true = $false) | (sF143 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4711])).
% 24.66/4.13 thf(f4715,plain,(
% 24.66/4.13 (sF143 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4714])).
% 24.66/4.13 thf(f4719,plain,(
% 24.66/4.13 ($false = ((cartprodpairin => sF142)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1414,f4715])).
% 24.66/4.13 thf(f4726,plain,(
% 24.66/4.13 ($false = sF142)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4719])).
% 24.66/4.13 thf(f4736,plain,(
% 24.66/4.13 (((cartprodmempair1 => sF141)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1413,f4726])).
% 24.66/4.13 thf(f4741,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((kpair @ Y3 @ Y4) = Y0)))) & (in @ Y3 @ Y2))))))))))) => sF141)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4736,f1044])).
% 24.66/4.13 thf(f4763,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((kpair @ Y3 @ Y4) = Y0)))) & (in @ Y3 @ Y2))))))))))) => $true))) | (sF141 = $false)),
% 24.66/4.13 inference(superposition,[],[f4741,f1166])).
% 24.66/4.13 thf(f4766,plain,(
% 24.66/4.13 ($true = $false) | (sF141 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4763])).
% 24.66/4.13 thf(f4767,plain,(
% 24.66/4.13 (sF141 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4766])).
% 24.66/4.13 thf(f4771,plain,(
% 24.66/4.13 (((cartprodmempair => sF140)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1411,f4767])).
% 24.66/4.13 thf(f4782,plain,(
% 24.66/4.13 (sF140 = $false) | ($false = ((cartprodmempair => $true)))),
% 24.66/4.13 inference(superposition,[],[f4771,f1166])).
% 24.66/4.13 thf(f4786,plain,(
% 24.66/4.13 (sF140 = $false) | ($true = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4782])).
% 24.66/4.13 thf(f4787,plain,(
% 24.66/4.13 (sF140 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4786])).
% 24.66/4.13 thf(f4790,plain,(
% 24.66/4.13 (((setunionE2 => sF139)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1409,f4787])).
% 24.66/4.13 thf(f4793,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => sF139)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4790,f1125])).
% 24.66/4.13 thf(f4813,plain,(
% 24.66/4.13 (sF139 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4793])).
% 24.66/4.13 thf(f4823,plain,(
% 24.66/4.13 (((setunionsingleton1 => sF138)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1407,f4813])).
% 24.66/4.13 thf(f4830,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => sF138)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4823,f1068])).
% 24.66/4.13 thf(f4833,plain,(
% 24.66/4.13 (sF138 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4830])).
% 24.66/4.13 thf(f4843,plain,(
% 24.66/4.13 (((setunionsingleton2 => sF137)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1406,f4833])).
% 24.66/4.13 thf(f4850,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => sF137)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4843,f933])).
% 24.66/4.13 thf(f4851,plain,(
% 24.66/4.13 (sF137 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4850])).
% 24.66/4.13 thf(f4861,plain,(
% 24.66/4.13 (((setunionsingleton => sF136)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1404,f4851])).
% 24.66/4.13 thf(f4864,plain,(
% 24.66/4.13 ($false = (((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => sF136)))),
% 24.66/4.13 inference(forward_demodulation,[],[f4861,f1028])).
% 24.66/4.13 thf(f4871,plain,(
% 24.66/4.13 ($false = sF136) | ((((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f4864,f1166])).
% 24.66/4.13 thf(f4876,plain,(
% 24.66/4.13 ($true = $false) | ($false = sF136)),
% 24.66/4.13 inference(boolean_simplification,[],[f4871])).
% 24.66/4.13 thf(f4877,plain,(
% 24.66/4.13 ($false = sF136)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4876])).
% 24.66/4.13 thf(f4879,plain,(
% 24.66/4.13 (((singletonprop => sF135)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1403,f4877])).
% 24.66/4.13 thf(f4886,plain,(
% 24.66/4.13 (sF135 = $false) | (((singletonprop => $true)) = $false)),
% 24.66/4.13 inference(superposition,[],[f4879,f1166])).
% 24.66/4.13 thf(f4889,plain,(
% 24.66/4.13 ($true = $false) | (sF135 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4886])).
% 24.66/4.13 thf(f4890,plain,(
% 24.66/4.13 (sF135 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4889])).
% 24.66/4.13 thf(f4896,plain,(
% 24.66/4.13 (((ex1E1 => sF134)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1401,f4890])).
% 24.66/4.13 thf(f4899,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => sF134)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4896,f1698])).
% 24.66/4.13 thf(f4900,plain,(
% 24.66/4.13 (sF134 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4899])).
% 24.66/4.13 thf(f4912,plain,(
% 24.66/4.13 (((ex1I => sF133)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1400,f4900])).
% 24.66/4.13 thf(f4915,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y2 @ Y1)))))))))) => sF133)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4912,f1704])).
% 24.66/4.13 thf(f4916,plain,(
% 24.66/4.13 (sF133 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4915])).
% 24.66/4.13 thf(f4926,plain,(
% 24.66/4.13 ($false = ((ex1I2 => sF132)))),
% 24.66/4.13 inference(backward_demodulation,[],[f1398,f4916])).
% 24.66/4.13 thf(f4929,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ Y0))))))) => sF132)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4926,f1710])).
% 24.66/4.13 thf(f4965,plain,(
% 24.66/4.13 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ Y0))))))) => $true)) = $false) | (sF132 = $false)),
% 24.66/4.13 inference(superposition,[],[f4929,f1166])).
% 24.66/4.13 thf(f4969,plain,(
% 24.66/4.13 ($true = $false) | (sF132 = $false)),
% 24.66/4.13 inference(boolean_simplification,[],[f4965])).
% 24.66/4.13 thf(f4970,plain,(
% 24.66/4.13 (sF132 = $false)),
% 24.66/4.13 inference(trivial_inequality_removal,[],[f4969])).
% 24.66/4.13 thf(f4977,plain,(
% 24.66/4.13 (((singletonsuniq => sF131)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1397,f4970])).
% 24.66/4.13 thf(f4980,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => sF131)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4977,f1158])).
% 24.66/4.13 thf(f4983,plain,(
% 24.66/4.13 (sF131 = $false)),
% 24.66/4.13 inference(imp_proxy_clausification,[],[f4980])).
% 24.66/4.13 thf(f4993,plain,(
% 24.66/4.13 (((setukpairinjL1 => sF130)) = $false)),
% 24.66/4.13 inference(backward_demodulation,[],[f1396,f4983])).
% 24.66/4.13 thf(f4998,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))) => sF130)) = $false)),
% 24.66/4.13 inference(forward_demodulation,[],[f4993,f1040])).
% 24.66/4.13 thf(f5003,plain,(
% 24.66/4.13 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))) => $true)) = $false) | (sF130 = $false)),
% 24.66/4.14 inference(superposition,[],[f4998,f1166])).
% 24.66/4.14 thf(f5006,plain,(
% 24.66/4.14 ($true = $false) | (sF130 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5003])).
% 24.66/4.14 thf(f5007,plain,(
% 24.66/4.14 (sF130 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5006])).
% 24.66/4.14 thf(f5011,plain,(
% 24.66/4.14 (((kfstsingleton => sF129)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1395,f5007])).
% 24.66/4.14 thf(f5018,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))) => sF129)))),
% 24.66/4.14 inference(forward_demodulation,[],[f5011,f1133])).
% 24.66/4.14 thf(f5021,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))) => (theprop => sF128))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5018,f1393])).
% 24.66/4.14 thf(f5024,plain,(
% 24.66/4.14 (sF128 = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))) => (theprop => $true))) = $false)),
% 24.66/4.14 inference(superposition,[],[f5021,f1166])).
% 24.66/4.14 thf(f5034,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))) => $true)) = $false) | (sF128 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5024])).
% 24.66/4.14 thf(f5035,plain,(
% 24.66/4.14 (sF128 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5034])).
% 24.66/4.14 thf(f5036,plain,(
% 24.66/4.14 (sF128 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5035])).
% 24.66/4.14 thf(f5046,plain,(
% 24.66/4.14 ($false = ((kfstpairEq => sF127)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1392,f5036])).
% 24.66/4.14 thf(f5052,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => sF127)))),
% 24.66/4.14 inference(forward_demodulation,[],[f5046,f1075])).
% 24.66/4.14 thf(f5057,plain,(
% 24.66/4.14 (sF127 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f5052,f1166])).
% 24.66/4.14 thf(f5062,plain,(
% 24.66/4.14 ($true = $false) | (sF127 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5057])).
% 24.66/4.14 thf(f5063,plain,(
% 24.66/4.14 (sF127 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5062])).
% 24.66/4.14 thf(f5071,plain,(
% 24.66/4.14 (((cartprodfstin => sF126)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1391,f5063])).
% 24.66/4.14 thf(f5072,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => sF126)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5071,f1062])).
% 24.66/4.14 thf(f5073,plain,(
% 24.66/4.14 ($false = sF126)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5072])).
% 24.66/4.14 thf(f5083,plain,(
% 24.66/4.14 ($false = ((setukpairinjL2 => sF125)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1390,f5073])).
% 24.66/4.14 thf(f5088,plain,(
% 24.66/4.14 (((setukpairinjL2 => (setukpairinjL => sF124))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5083,f1388])).
% 24.66/4.14 thf(f5089,plain,(
% 24.66/4.14 (((setukpairinjL2 => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y2) = (kpair @ Y3 @ Y1)) => (Y3 = Y0)))))))))) => sF124))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5088,f1151])).
% 24.66/4.14 thf(f5092,plain,(
% 24.66/4.14 (((setukpairinjL2 => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y2) = (kpair @ Y3 @ Y1)) => (Y3 = Y0)))))))))) => $true))) = $false) | ($false = sF124)),
% 24.66/4.14 inference(superposition,[],[f5089,f1166])).
% 24.66/4.14 thf(f5098,plain,(
% 24.66/4.14 ($false = sF124) | (((setukpairinjL2 => $true)) = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5092])).
% 24.66/4.14 thf(f5099,plain,(
% 24.66/4.14 ($false = sF124) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5098])).
% 24.66/4.14 thf(f5100,plain,(
% 24.66/4.14 ($false = sF124)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5099])).
% 24.66/4.14 thf(f5112,plain,(
% 24.66/4.14 (((setukpairinjR11 => sF123)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1387,f5100])).
% 24.66/4.14 thf(f5131,plain,(
% 24.66/4.14 (sF123 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5112])).
% 24.66/4.14 thf(f5145,plain,(
% 24.66/4.14 (((setukpairinjR12 => sF122)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1385,f5131])).
% 24.66/4.14 thf(f5146,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => sF122)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5145,f893])).
% 24.66/4.14 thf(f5158,plain,(
% 24.66/4.14 (sF122 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => $true)))),
% 24.66/4.14 inference(superposition,[],[f5146,f1166])).
% 24.66/4.14 thf(f5162,plain,(
% 24.66/4.14 (sF122 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5158])).
% 24.66/4.14 thf(f5163,plain,(
% 24.66/4.14 (sF122 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5162])).
% 24.66/4.14 thf(f5168,plain,(
% 24.66/4.14 (((setukpairinjR1 => sF121)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1383,f5163])).
% 24.66/4.14 thf(f5169,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y0))))))))))) => sF121)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5168,f1036])).
% 24.66/4.14 thf(f5183,plain,(
% 24.66/4.14 (sF121 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5169])).
% 24.66/4.14 thf(f5193,plain,(
% 24.66/4.14 (((upairequniteq => sF120)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1381,f5183])).
% 24.66/4.14 thf(f5200,plain,(
% 24.66/4.14 ($false = ((upairequniteq => (setukpairinjR2 => sF119))))),
% 24.66/4.14 inference(forward_demodulation,[],[f5193,f1380])).
% 24.66/4.14 thf(f5205,plain,(
% 24.66/4.14 (sF119 = $false) | (((upairequniteq => (setukpairinjR2 => $true))) = $false)),
% 24.66/4.14 inference(superposition,[],[f5200,f1166])).
% 24.66/4.14 thf(f5212,plain,(
% 24.66/4.14 (sF119 = $false) | (((upairequniteq => $true)) = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5205])).
% 24.66/4.14 thf(f5213,plain,(
% 24.66/4.14 ($true = $false) | (sF119 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5212])).
% 24.66/4.14 thf(f5214,plain,(
% 24.66/4.14 (sF119 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5213])).
% 24.66/4.14 thf(f5226,plain,(
% 24.66/4.14 (((setukpairinjR => sF118)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1378,f5214])).
% 24.66/4.14 thf(f5240,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y2 @ Y0)) => (Y3 = Y0)))))))))) => sF118)))),
% 24.66/4.14 inference(forward_demodulation,[],[f5226,f875])).
% 24.66/4.14 thf(f5255,plain,(
% 24.66/4.14 (sF118 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5240])).
% 24.66/4.14 thf(f5267,plain,(
% 24.66/4.14 (((ksndsingleton => sF117)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1376,f5255])).
% 24.66/4.14 thf(f5270,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))) => sF117)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5267,f1153])).
% 24.66/4.14 thf(f5271,plain,(
% 24.66/4.14 (sF117 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5270])).
% 24.66/4.14 thf(f5285,plain,(
% 24.66/4.14 ($false = ((ksndpairEq => sF116)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1375,f5271])).
% 24.66/4.14 thf(f5286,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1))))) => sF116)))),
% 24.66/4.14 inference(forward_demodulation,[],[f5285,f924])).
% 24.66/4.14 thf(f5287,plain,(
% 24.66/4.14 (sF116 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5286])).
% 24.66/4.14 thf(f5297,plain,(
% 24.66/4.14 ($false = ((kpairsurjEq => sF115)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1374,f5287])).
% 24.66/4.14 thf(f5302,plain,(
% 24.66/4.14 (sF115 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5297])).
% 24.66/4.14 thf(f5312,plain,(
% 24.66/4.14 ($false = ((cartprodsndin => sF114)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1373,f5302])).
% 24.66/4.14 thf(f5319,plain,(
% 24.66/4.14 ($false = sF114) | (((cartprodsndin => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f5312,f1166])).
% 24.66/4.14 thf(f5323,plain,(
% 24.66/4.14 ($true = $false) | ($false = sF114)),
% 24.66/4.14 inference(boolean_simplification,[],[f5319])).
% 24.66/4.14 thf(f5324,plain,(
% 24.66/4.14 ($false = sF114)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5323])).
% 24.66/4.14 thf(f5327,plain,(
% 24.66/4.14 (((cartprodpairmemEL => sF113)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1372,f5324])).
% 24.66/4.14 thf(f5334,plain,(
% 24.66/4.14 ($false = ((cartprodpairmemEL => $true))) | ($false = sF113)),
% 24.66/4.14 inference(superposition,[],[f5327,f1166])).
% 24.66/4.14 thf(f5338,plain,(
% 24.66/4.14 ($true = $false) | ($false = sF113)),
% 24.66/4.14 inference(boolean_simplification,[],[f5334])).
% 24.66/4.14 thf(f5339,plain,(
% 24.66/4.14 ($false = sF113)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5338])).
% 24.66/4.14 thf(f5346,plain,(
% 24.66/4.14 (((cartprodpairmemER => sF112)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1370,f5339])).
% 24.66/4.14 thf(f5347,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))))) => sF112)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5346,f1071])).
% 24.66/4.14 thf(f5391,plain,(
% 24.66/4.14 ($false = sF112)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5347])).
% 24.66/4.14 thf(f5405,plain,(
% 24.66/4.14 ($false = ((cartprodmempaircEq => sF111)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1368,f5391])).
% 24.66/4.14 thf(f5408,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF111)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5405,f1685])).
% 24.66/4.14 thf(f5409,plain,(
% 24.66/4.14 (sF111 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5408])).
% 24.66/4.14 thf(f5421,plain,(
% 24.66/4.14 (((cartprodfstpairEq => sF110)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1366,f5409])).
% 24.66/4.14 thf(f5424,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => sF110)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5421,f1137])).
% 24.66/4.14 thf(f5425,plain,(
% 24.66/4.14 (sF110 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5424])).
% 24.66/4.14 thf(f5435,plain,(
% 24.66/4.14 (((cartprodsndpairEq => sF109)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1364,f5425])).
% 24.66/4.14 thf(f5440,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => sF109)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5435,f945])).
% 24.66/4.14 thf(f5447,plain,(
% 24.66/4.14 (sF109 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5440])).
% 24.66/4.14 thf(f5461,plain,(
% 24.66/4.14 (((cartprodpairsurjEq => sF108)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1363,f5447])).
% 24.66/4.14 thf(f5464,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))))) => sF108)))),
% 24.66/4.14 inference(forward_demodulation,[],[f5461,f997])).
% 24.66/4.14 thf(f5465,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))))) => (dpsetconstrI => sF107))))),
% 24.66/4.14 inference(forward_demodulation,[],[f5464,f1362])).
% 24.66/4.14 thf(f5468,plain,(
% 24.66/4.14 (sF107 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))))) => (dpsetconstrI => $true))))),
% 24.66/4.14 inference(superposition,[],[f5465,f1166])).
% 24.66/4.14 thf(f5473,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))))) => $true))) | (sF107 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5468])).
% 24.66/4.14 thf(f5474,plain,(
% 24.66/4.14 ($true = $false) | (sF107 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5473])).
% 24.66/4.14 thf(f5475,plain,(
% 24.66/4.14 (sF107 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5474])).
% 24.66/4.14 thf(f5485,plain,(
% 24.66/4.14 (((dpsetconstrSub => sF106)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1361,f5475])).
% 24.66/4.14 thf(f5498,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => sF106)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5485,f1671])).
% 24.66/4.14 thf(f5503,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => (setOfPairsIsBReln => sF105))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5498,f1360])).
% 24.66/4.14 thf(f5508,plain,(
% 24.66/4.14 ($false = sF105) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => (setOfPairsIsBReln => $true))) = $false)),
% 24.66/4.14 inference(superposition,[],[f5503,f1166])).
% 24.66/4.14 thf(f5513,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => $true))) | ($false = sF105)),
% 24.66/4.14 inference(boolean_simplification,[],[f5508])).
% 24.66/4.14 thf(f5514,plain,(
% 24.66/4.14 ($false = sF105) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5513])).
% 24.66/4.14 thf(f5515,plain,(
% 24.66/4.14 ($false = sF105)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5514])).
% 24.66/4.14 thf(f5523,plain,(
% 24.66/4.14 ($false = ((dpsetconstrERa => sF104)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1358,f5515])).
% 24.66/4.14 thf(f5550,plain,(
% 24.66/4.14 (((dpsetconstrERa => $true)) = $false) | (sF104 = $false)),
% 24.66/4.14 inference(superposition,[],[f5523,f1166])).
% 24.66/4.14 thf(f5554,plain,(
% 24.66/4.14 (sF104 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5550])).
% 24.66/4.14 thf(f5555,plain,(
% 24.66/4.14 (sF104 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5554])).
% 24.66/4.14 thf(f5558,plain,(
% 24.66/4.14 ($false = ((dpsetconstrEL1 => sF103)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1357,f5555])).
% 24.66/4.14 thf(f5563,plain,(
% 24.66/4.14 (((dpsetconstrEL1 => (dpsetconstrEL2 => sF102))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5558,f1356])).
% 24.66/4.14 thf(f5566,plain,(
% 24.66/4.14 ($false = sF102) | (((dpsetconstrEL1 => (dpsetconstrEL2 => $true))) = $false)),
% 24.66/4.14 inference(superposition,[],[f5563,f1166])).
% 24.66/4.14 thf(f5571,plain,(
% 24.66/4.14 (((dpsetconstrEL1 => $true)) = $false) | ($false = sF102)),
% 24.66/4.14 inference(boolean_simplification,[],[f5566])).
% 24.66/4.14 thf(f5572,plain,(
% 24.66/4.14 ($false = sF102) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5571])).
% 24.66/4.14 thf(f5573,plain,(
% 24.66/4.14 ($false = sF102)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5572])).
% 24.66/4.14 thf(f5582,plain,(
% 24.66/4.14 (((dpsetconstrER => sF101)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1354,f5573])).
% 24.66/4.14 thf(f5597,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3)) => (Y3 @ Y0 @ Y4)))))))))))) => sF101)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5582,f1657])).
% 24.66/4.14 thf(f5603,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3)) => (Y3 @ Y0 @ Y4)))))))))))) => (funcImageSingleton => sF100))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5597,f1352])).
% 24.66/4.14 thf(f5629,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3)) => (Y3 @ Y0 @ Y4)))))))))))) => (funcImageSingleton => $true))) = $false) | (sF100 = $false)),
% 24.66/4.14 inference(superposition,[],[f5603,f1166])).
% 24.66/4.14 thf(f5639,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3)) => (Y3 @ Y0 @ Y4)))))))))))) => $true)) = $false) | (sF100 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5629])).
% 24.66/4.14 thf(f5640,plain,(
% 24.66/4.14 (sF100 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5639])).
% 24.66/4.14 thf(f5641,plain,(
% 24.66/4.14 (sF100 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5640])).
% 24.66/4.14 thf(f5653,plain,(
% 24.66/4.14 (((apProp => sF99)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1350,f5641])).
% 24.66/4.14 thf(f5661,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))) @ Y0))))))))))) => sF99)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5653,f1038])).
% 24.66/4.14 thf(f5666,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))) @ Y0))))))))))) => $true)) = $false) | (sF99 = $false)),
% 24.66/4.14 inference(superposition,[],[f5661,f1166])).
% 24.66/4.14 thf(f5671,plain,(
% 24.66/4.14 (sF99 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5666])).
% 24.66/4.14 thf(f5672,plain,(
% 24.66/4.14 (sF99 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5671])).
% 24.66/4.14 thf(f5674,plain,(
% 24.66/4.14 (((app => sF98)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1348,f5672])).
% 24.66/4.14 thf(f5681,plain,(
% 24.66/4.14 (sF98 = $false) | (((app => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f5674,f1166])).
% 24.66/4.14 thf(f5684,plain,(
% 24.66/4.14 (sF98 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5681])).
% 24.66/4.14 thf(f5685,plain,(
% 24.66/4.14 (sF98 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5684])).
% 24.66/4.14 thf(f5691,plain,(
% 24.66/4.14 (((infuncsetfunc => sF97)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1347,f5685])).
% 24.66/4.14 thf(f5696,plain,(
% 24.66/4.14 (((infuncsetfunc => $true)) = $false) | ($false = sF97)),
% 24.66/4.14 inference(superposition,[],[f5691,f1166])).
% 24.66/4.14 thf(f5700,plain,(
% 24.66/4.14 ($false = sF97) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5696])).
% 24.66/4.14 thf(f5701,plain,(
% 24.66/4.14 ($false = sF97)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5700])).
% 24.66/4.14 thf(f5708,plain,(
% 24.66/4.14 (((ap2p => sF96)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1346,f5701])).
% 24.66/4.14 thf(f5709,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))) => sF96)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5708,f970])).
% 24.66/4.14 thf(f5740,plain,(
% 24.66/4.14 (sF96 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f5709,f1166])).
% 24.66/4.14 thf(f5743,plain,(
% 24.66/4.14 (sF96 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5740])).
% 24.66/4.14 thf(f5744,plain,(
% 24.66/4.14 (sF96 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5743])).
% 24.66/4.14 thf(f5748,plain,(
% 24.66/4.14 (((funcinfuncset => sF95)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1344,f5744])).
% 24.66/4.14 thf(f5753,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (in @ Y1 @ (funcSet @ Y2 @ Y0))))))))) => sF95)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5748,f961])).
% 24.66/4.14 thf(f5760,plain,(
% 24.66/4.14 (sF95 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (in @ Y1 @ (funcSet @ Y2 @ Y0))))))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f5753,f1166])).
% 24.66/4.14 thf(f5765,plain,(
% 24.66/4.14 (sF95 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5760])).
% 24.66/4.14 thf(f5766,plain,(
% 24.66/4.14 (sF95 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5765])).
% 24.66/4.14 thf(f5772,plain,(
% 24.66/4.14 (((lamProp => sF94)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1343,f5766])).
% 24.66/4.14 thf(f5775,plain,(
% 24.66/4.14 ($false = ((lamProp => $true))) | (sF94 = $false)),
% 24.66/4.14 inference(superposition,[],[f5772,f1166])).
% 24.66/4.14 thf(f5779,plain,(
% 24.66/4.14 (sF94 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5775])).
% 24.66/4.14 thf(f5780,plain,(
% 24.66/4.14 (sF94 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5779])).
% 24.66/4.14 thf(f5787,plain,(
% 24.66/4.14 (((lamp => sF93)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1342,f5780])).
% 24.66/4.14 thf(f5792,plain,(
% 24.66/4.14 (((lamp => $true)) = $false) | (sF93 = $false)),
% 24.66/4.14 inference(superposition,[],[f5787,f1166])).
% 24.66/4.14 thf(f5795,plain,(
% 24.66/4.14 (sF93 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5792])).
% 24.66/4.14 thf(f5796,plain,(
% 24.66/4.14 (sF93 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5795])).
% 24.66/4.14 thf(f5800,plain,(
% 24.66/4.14 (((lam2p => sF92)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1340,f5796])).
% 24.66/4.14 thf(f5809,plain,(
% 24.66/4.14 (sF92 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5800])).
% 24.66/4.14 thf(f5819,plain,(
% 24.66/4.14 (((brelnall1 => sF91)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1338,f5809])).
% 24.66/4.14 thf(f5824,plain,(
% 24.66/4.14 ($false = ((brelnall1 => (brelnall2 => sF90))))),
% 24.66/4.14 inference(forward_demodulation,[],[f5819,f1337])).
% 24.66/4.14 thf(f5827,plain,(
% 24.66/4.14 (sF90 = $false) | ($false = ((brelnall1 => (brelnall2 => $true))))),
% 24.66/4.14 inference(superposition,[],[f5824,f1166])).
% 24.66/4.14 thf(f5835,plain,(
% 24.66/4.14 (((brelnall1 => $true)) = $false) | (sF90 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5827])).
% 24.66/4.14 thf(f5836,plain,(
% 24.66/4.14 (sF90 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f5835])).
% 24.66/4.14 thf(f5837,plain,(
% 24.66/4.14 (sF90 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f5836])).
% 24.66/4.14 thf(f5845,plain,(
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% 24.66/4.14 inference(backward_demodulation,[],[f1335,f5837])).
% 24.66/4.14 thf(f5857,plain,(
% 24.66/4.14 ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3)))))))))))))) => sF89)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f5845,f1702])).
% 24.66/4.14 thf(f5945,plain,(
% 24.66/4.14 (sF89 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f5857])).
% 24.66/4.14 thf(f5955,plain,(
% 24.66/4.14 (((funcGraphProp1 => sF88)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1334,f5945])).
% 24.66/4.14 thf(f5960,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) => sF88)))),
% 24.66/4.14 inference(forward_demodulation,[],[f5955,f912])).
% 24.66/4.14 thf(f5967,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) => $true))) | (sF88 = $false)),
% 24.66/4.14 inference(superposition,[],[f5960,f1166])).
% 24.66/4.14 thf(f5971,plain,(
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% 24.66/4.14 thf(f5972,plain,(
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% 24.66/4.14 inference(trivial_inequality_removal,[],[f5971])).
% 24.66/4.14 thf(f5979,plain,(
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% 24.66/4.14 inference(backward_demodulation,[],[f1332,f5972])).
% 24.66/4.14 thf(f5986,plain,(
% 24.66/4.14 ($false = ((funcGraphProp3 => $true))) | (sF87 = $false)),
% 24.66/4.14 inference(superposition,[],[f5979,f1166])).
% 24.66/4.14 thf(f5991,plain,(
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% 24.66/4.14 thf(f5992,plain,(
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% 24.66/4.14 inference(trivial_inequality_removal,[],[f5991])).
% 24.66/4.14 thf(f6000,plain,(
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% 24.66/4.14 inference(backward_demodulation,[],[f1331,f5992])).
% 24.66/4.14 thf(f6001,plain,(
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% 24.66/4.14 inference(imp_proxy_clausification,[],[f6000])).
% 24.66/4.14 thf(f6011,plain,(
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% 24.66/4.14 inference(backward_demodulation,[],[f1330,f6001])).
% 24.66/4.14 thf(f6020,plain,(
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% 24.66/4.14 inference(superposition,[],[f6011,f1166])).
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% 24.66/4.14 thf(f6026,plain,(
% 24.66/4.14 (sF85 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6025])).
% 24.66/4.14 thf(f6032,plain,(
% 24.66/4.14 ($false = ((funcGraphProp4 => sF84)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1329,f6026])).
% 24.66/4.14 thf(f6033,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => ((ap @ Y0 @ Y2 @ Y1 @ Y3) = Y4))))))))))))))) => sF84)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6032,f1034])).
% 24.66/4.14 thf(f6083,plain,(
% 24.66/4.14 ($false = sF84)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6033])).
% 24.66/4.14 thf(f6093,plain,(
% 24.66/4.14 ($false = ((subbreln => sF83)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1328,f6083])).
% 24.66/4.14 thf(f6100,plain,(
% 24.66/4.14 (((subbreln => (eqbreln => sF82))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6093,f1327])).
% 24.66/4.14 thf(f6102,plain,(
% 24.66/4.14 (subbreln = $true)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6100])).
% 24.66/4.14 thf(f6103,plain,(
% 24.66/4.14 ($false = ((subbreln => (eqbreln => $true)))) | (sF82 = $false)),
% 24.66/4.14 inference(superposition,[],[f6100,f1166])).
% 24.66/4.14 thf(f6108,plain,(
% 24.66/4.14 (sF82 = $false) | (((subbreln => $true)) = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6103])).
% 24.66/4.14 thf(f6109,plain,(
% 24.66/4.14 ($true = $false) | (sF82 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6108])).
% 24.66/4.14 thf(f6110,plain,(
% 24.66/4.14 (sF82 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6109])).
% 24.66/4.14 thf(f6118,plain,(
% 24.66/4.14 (((funcext => sF81)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1325,f6110])).
% 24.66/4.14 thf(f6121,plain,(
% 24.66/4.14 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y2 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))))))),
% 24.66/4.14 inference(backward_demodulation,[],[f1645,f6102])).
% 24.66/4.14 thf(f6141,plain,(
% 24.66/4.14 (sF81 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6118])).
% 24.66/4.14 thf(f6151,plain,(
% 24.66/4.14 (((funcext2 => sF80)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1323,f6141])).
% 24.66/4.14 thf(f6158,plain,(
% 24.66/4.14 (sF80 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6151])).
% 24.66/4.14 thf(f6172,plain,(
% 24.66/4.14 (((ap2apEq1 => sF79)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1321,f6158])).
% 24.66/4.14 thf(f6175,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y0 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF79)))),
% 24.66/4.14 inference(forward_demodulation,[],[f6172,f1693])).
% 24.66/4.14 thf(f6176,plain,(
% 24.66/4.14 ($false = sF79)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6175])).
% 24.66/4.14 thf(f6186,plain,(
% 24.66/4.14 (((ap2apEq2 => sF78)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1319,f6176])).
% 24.66/4.14 thf(f6191,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => sF78)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6186,f1678])).
% 24.66/4.14 thf(f6196,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ($true)))))))))) => $true)) = $false) | ($false = sF78)),
% 24.66/4.14 inference(superposition,[],[f6191,f1166])).
% 24.66/4.14 thf(f6199,plain,(
% 24.66/4.14 ($false = sF78) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6196])).
% 24.66/4.14 thf(f6200,plain,(
% 24.66/4.14 ($false = sF78)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6199])).
% 24.66/4.14 thf(f6204,plain,(
% 24.66/4.14 ($false = ((beta1 => sF77)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1317,f6200])).
% 24.66/4.14 thf(f6209,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y2 @ Y3) @ Y0)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y0 @ (lam @ Y1 @ Y0 @ Y2) @ Y3) = (Y2 @ Y3)))))))))))) => sF77)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6204,f1660])).
% 24.66/4.14 thf(f6214,plain,(
% 24.66/4.14 (sF77 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6209])).
% 24.66/4.14 thf(f6224,plain,(
% 24.66/4.14 (((eta1 => sF76)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1315,f6214])).
% 24.66/4.14 thf(f6229,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (Y0 = (lam @ Y2 @ Y1 @ (ap @ Y2 @ Y1 @ Y0)))))))))) => sF76)))),
% 24.66/4.14 inference(forward_demodulation,[],[f6224,f1659])).
% 24.66/4.14 thf(f6234,plain,(
% 24.66/4.14 (sF76 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6229])).
% 24.66/4.14 thf(f6250,plain,(
% 24.66/4.14 (((lam2lamEq => sF75)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1314,f6234])).
% 24.66/4.14 thf(f6251,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ($true))))))) => sF75)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6250,f1674])).
% 24.66/4.14 thf(f6254,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ($true))))))) => $true))) | (sF75 = $false)),
% 24.66/4.14 inference(superposition,[],[f6251,f1166])).
% 24.66/4.14 thf(f6258,plain,(
% 24.66/4.14 (sF75 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6254])).
% 24.66/4.14 thf(f6259,plain,(
% 24.66/4.14 (sF75 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6258])).
% 24.66/4.14 thf(f6262,plain,(
% 24.66/4.14 ($false = ((beta2 => sF74)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1312,f6259])).
% 24.66/4.14 thf(f6265,plain,(
% 24.66/4.14 (((beta2 => (eta2 => sF73))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6262,f1311])).
% 24.66/4.14 thf(f6272,plain,(
% 24.66/4.14 (((beta2 => (eta2 => $true))) = $false) | (sF73 = $false)),
% 24.66/4.14 inference(superposition,[],[f6265,f1166])).
% 24.66/4.14 thf(f6282,plain,(
% 24.66/4.14 (((beta2 => $true)) = $false) | (sF73 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6272])).
% 24.66/4.14 thf(f6283,plain,(
% 24.66/4.14 ($true = $false) | (sF73 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6282])).
% 24.66/4.14 thf(f6284,plain,(
% 24.66/4.14 (sF73 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6283])).
% 24.66/4.14 thf(f6294,plain,(
% 24.66/4.14 (((iffalseProp1 => sF72)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1309,f6284])).
% 24.66/4.14 thf(f6300,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((Y3 = Y4) & (~ Y1)) | ((Y0 = Y4) & Y1)))))))))))))))) => sF72)))),
% 24.66/4.14 inference(forward_demodulation,[],[f6294,f1064])).
% 24.66/4.14 thf(f6301,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((Y3 = Y4) & (~ Y1)) | ((Y0 = Y4) & Y1)))))))))))))))) => (iffalseProp2 => sF71))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6300,f1308])).
% 24.66/4.14 thf(f6317,plain,(
% 24.66/4.14 (sF71 = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((Y3 = Y4) & (~ Y1)) | ((Y0 = Y4) & Y1)))))))))))))))) => (iffalseProp2 => $true))))),
% 24.66/4.14 inference(superposition,[],[f6301,f1166])).
% 24.66/4.14 thf(f6322,plain,(
% 24.66/4.14 (sF71 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((Y3 = Y4) & (~ Y1)) | ((Y0 = Y4) & Y1)))))))))))))))) => $true)) = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6317])).
% 24.66/4.14 thf(f6323,plain,(
% 24.66/4.14 ($true = $false) | (sF71 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6322])).
% 24.66/4.14 thf(f6324,plain,(
% 24.66/4.14 (sF71 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6323])).
% 24.66/4.14 thf(f6331,plain,(
% 24.66/4.14 (((iftrueProp1 => sF70)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1307,f6324])).
% 24.66/4.14 thf(f6348,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (Y1 => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (((~ Y1) & (Y3 = Y4)) | ((Y0 = Y4) & Y1)))))))))))))))) => sF70)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6331,f1027])).
% 24.66/4.14 thf(f6354,plain,(
% 24.66/4.14 (sF70 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6348])).
% 24.66/4.14 thf(f6364,plain,(
% 24.66/4.14 (((iftrueProp2 => sF69)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1305,f6354])).
% 24.66/4.14 thf(f6371,plain,(
% 24.66/4.14 ($false = sF69)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6364])).
% 24.66/4.14 thf(f6385,plain,(
% 24.66/4.14 (((ifSingleton => sF68)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1303,f6371])).
% 24.66/4.14 thf(f6388,plain,(
% 24.66/4.14 (sF68 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6385])).
% 24.66/4.14 thf(f6398,plain,(
% 24.66/4.14 (((ifp => sF67)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1301,f6388])).
% 24.66/4.14 thf(f6401,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (if @ Y0 @ Y2 @ Y1 @ Y3) @ Y0))))))))))) => sF67)))),
% 24.66/4.14 inference(forward_demodulation,[],[f6398,f1159])).
% 24.66/4.14 thf(f6404,plain,(
% 24.66/4.14 ($false = sF67)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6401])).
% 24.66/4.14 thf(f6414,plain,(
% 24.66/4.14 ($false = ((theeq => sF66)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1299,f6404])).
% 24.66/4.14 thf(f6419,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1))))))) => sF66)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6414,f1072])).
% 24.66/4.14 thf(f6424,plain,(
% 24.66/4.14 (sF66 = $false) | ((((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1))))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f6419,f1166])).
% 24.66/4.14 thf(f6428,plain,(
% 24.66/4.14 ($true = $false) | (sF66 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6424])).
% 24.66/4.14 thf(f6429,plain,(
% 24.66/4.14 (sF66 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6428])).
% 24.66/4.14 thf(f6436,plain,(
% 24.66/4.14 (((iftrue => sF65)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1298,f6429])).
% 24.66/4.14 thf(f6439,plain,(
% 24.66/4.14 (((iftrue => (iffalse => sF64))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6436,f1297])).
% 24.66/4.14 thf(f6444,plain,(
% 24.66/4.14 (sF64 = $false) | (((iftrue => (iffalse => $true))) = $false)),
% 24.66/4.14 inference(superposition,[],[f6439,f1166])).
% 24.66/4.14 thf(f6452,plain,(
% 24.66/4.14 (sF64 = $false) | (((iftrue => $true)) = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6444])).
% 24.66/4.14 thf(f6453,plain,(
% 24.66/4.14 ($true = $false) | (sF64 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6452])).
% 24.66/4.14 thf(f6454,plain,(
% 24.66/4.14 (sF64 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6453])).
% 24.66/4.14 thf(f6468,plain,(
% 24.66/4.14 (((iftrueorfalse => sF63)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1296,f6454])).
% 24.66/4.14 thf(f6482,plain,(
% 24.66/4.14 (((iftrueorfalse => $true)) = $false) | ($false = sF63)),
% 24.66/4.14 inference(superposition,[],[f6468,f1166])).
% 24.66/4.14 thf(f6486,plain,(
% 24.66/4.14 ($true = $false) | ($false = sF63)),
% 24.66/4.14 inference(boolean_simplification,[],[f6482])).
% 24.66/4.14 thf(f6487,plain,(
% 24.66/4.14 ($false = sF63)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6486])).
% 24.66/4.14 thf(f6494,plain,(
% 24.66/4.14 (((binintersectT_lem => sF62)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1294,f6487])).
% 24.66/4.14 thf(f6497,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ Y0)))))))))) => sF62)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6494,f1005])).
% 24.66/4.14 thf(f6498,plain,(
% 24.66/4.14 (sF62 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6497])).
% 24.66/4.14 thf(f6510,plain,(
% 24.66/4.14 (((binunionT_lem => sF61)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1292,f6498])).
% 24.66/4.14 thf(f6513,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (binunion @ Y1 @ Y2) @ (powerset @ Y0)))))))))) => sF61)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6510,f900])).
% 24.66/4.14 thf(f6514,plain,(
% 24.66/4.14 ($false = sF61)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6513])).
% 24.66/4.14 thf(f6524,plain,(
% 24.66/4.14 ($false = ((powersetT_lem => sF60)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1290,f6514])).
% 24.66/4.14 thf(f6527,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (powerset @ Y0) @ (powerset @ (powerset @ Y1)))))))) => sF60)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6524,f943])).
% 24.66/4.14 thf(f6530,plain,(
% 24.66/4.14 (sF60 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6527])).
% 24.66/4.14 thf(f6544,plain,(
% 24.66/4.14 (((setminusT_lem => sF59)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1288,f6530])).
% 24.66/4.14 thf(f6545,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y1 @ Y2) @ (powerset @ Y0)))))))))) => sF59)))),
% 24.66/4.14 inference(forward_demodulation,[],[f6544,f1016])).
% 24.66/4.14 thf(f6548,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y1 @ Y2) @ (powerset @ Y0)))))))))) => $true)) = $false) | (sF59 = $false)),
% 24.66/4.14 inference(superposition,[],[f6545,f1166])).
% 24.66/4.14 thf(f6551,plain,(
% 24.66/4.14 ($true = $false) | (sF59 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6548])).
% 24.66/4.14 thf(f6552,plain,(
% 24.66/4.14 (sF59 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6551])).
% 24.66/4.14 thf(f6556,plain,(
% 24.66/4.14 (((complementT_lem => sF58)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1286,f6552])).
% 24.66/4.14 thf(f6563,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))) => sF58)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6556,f1001])).
% 24.66/4.14 thf(f6568,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1))))))) => $true)) = $false) | (sF58 = $false)),
% 24.66/4.14 inference(superposition,[],[f6563,f1166])).
% 24.66/4.14 thf(f6571,plain,(
% 24.66/4.14 (sF58 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6568])).
% 24.66/4.14 thf(f6572,plain,(
% 24.66/4.14 (sF58 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6571])).
% 24.66/4.14 thf(f6576,plain,(
% 24.66/4.14 (((setextT => sF57)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1285,f6572])).
% 24.66/4.14 thf(f6585,plain,(
% 24.66/4.14 ($false = sF57)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6576])).
% 24.66/4.14 thf(f6601,plain,(
% 24.66/4.14 (((subsetTI => sF56)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1283,f6585])).
% 24.66/4.14 thf(f6602,plain,(
% 24.66/4.14 (sF56 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6601])).
% 24.66/4.14 thf(f6614,plain,(
% 24.66/4.14 (((powersetTI1 => sF55)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1281,f6602])).
% 24.66/4.14 thf(f6617,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2))))))))))) => sF55)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6614,f937])).
% 24.66/4.14 thf(f6688,plain,(
% 24.66/4.14 (sF55 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2))))))))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f6617,f1166])).
% 24.66/4.14 thf(f6692,plain,(
% 24.66/4.14 (sF55 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6688])).
% 24.66/4.14 thf(f6693,plain,(
% 24.66/4.14 (sF55 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6692])).
% 24.66/4.14 thf(f6696,plain,(
% 24.66/4.14 (((powersetTE1 => sF54)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1280,f6693])).
% 24.66/4.14 thf(f6701,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2)))))))))))))) => sF54)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6696,f1122])).
% 24.66/4.14 thf(f6704,plain,(
% 24.66/4.14 (sF54 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2)))))))))))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f6701,f1166])).
% 24.66/4.14 thf(f6707,plain,(
% 24.66/4.14 (sF54 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6704])).
% 24.66/4.14 thf(f6708,plain,(
% 24.66/4.14 (sF54 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6707])).
% 24.66/4.14 thf(f6712,plain,(
% 24.66/4.14 ($false = ((complementTI1 => sF53)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1278,f6708])).
% 24.66/4.14 thf(f6721,plain,(
% 24.66/4.14 (sF53 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6712])).
% 24.66/4.14 thf(f6731,plain,(
% 24.66/4.14 ($false = ((complementTE1 => sF52)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1277,f6721])).
% 24.66/4.14 thf(f6740,plain,(
% 24.66/4.14 (((complementTE1 => $true)) = $false) | ($false = sF52)),
% 24.66/4.14 inference(superposition,[],[f6731,f1166])).
% 24.66/4.14 thf(f6743,plain,(
% 24.66/4.14 ($false = sF52) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6740])).
% 24.66/4.14 thf(f6744,plain,(
% 24.66/4.14 ($false = sF52)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6743])).
% 24.66/4.14 thf(f6748,plain,(
% 24.66/4.14 (((binintersectTELcontra => sF51)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1276,f6744])).
% 24.66/4.14 thf(f6753,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2))))))))))))))) => sF51)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6748,f1134])).
% 24.66/4.14 thf(f6758,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2))))))))))))))) => (binintersectTERcontra => sF50))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6753,f1274])).
% 24.66/4.14 thf(f6789,plain,(
% 24.66/4.14 ($false = sF50) | ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2))))))))))))))) => (binintersectTERcontra => $true))))),
% 24.66/4.14 inference(superposition,[],[f6758,f1166])).
% 24.66/4.14 thf(f6795,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ Y0)) => (~ (in @ Y3 @ (binintersect @ Y0 @ Y2))))))))))))))) => $true)) = $false) | ($false = sF50)),
% 24.66/4.14 inference(boolean_simplification,[],[f6789])).
% 24.66/4.14 thf(f6796,plain,(
% 24.66/4.14 ($false = sF50) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6795])).
% 24.66/4.14 thf(f6797,plain,(
% 24.66/4.14 ($false = sF50)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6796])).
% 24.66/4.14 thf(f6805,plain,(
% 24.66/4.14 ($false = ((contrasubsetT => sF49)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1272,f6797])).
% 24.66/4.14 thf(f6831,plain,(
% 24.66/4.14 (((contrasubsetT => $true)) = $false) | ($false = sF49)),
% 24.66/4.14 inference(superposition,[],[f6805,f1166])).
% 24.66/4.14 thf(f6836,plain,(
% 24.66/4.14 ($true = $false) | ($false = sF49)),
% 24.66/4.14 inference(boolean_simplification,[],[f6831])).
% 24.66/4.14 thf(f6837,plain,(
% 24.66/4.14 ($false = sF49)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6836])).
% 24.66/4.14 thf(f6839,plain,(
% 24.66/4.14 (((contrasubsetT1 => sF48)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1270,f6837])).
% 24.66/4.14 thf(f6842,plain,(
% 24.66/4.14 (((contrasubsetT1 => (contrasubsetT2 => sF47))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6839,f1268])).
% 24.66/4.14 thf(f6847,plain,(
% 24.66/4.14 (((contrasubsetT1 => (contrasubsetT2 => $true))) = $false) | ($false = sF47)),
% 24.66/4.14 inference(superposition,[],[f6842,f1166])).
% 24.66/4.14 thf(f6854,plain,(
% 24.66/4.14 ($false = ((contrasubsetT1 => $true))) | ($false = sF47)),
% 24.66/4.14 inference(boolean_simplification,[],[f6847])).
% 24.66/4.14 thf(f6855,plain,(
% 24.66/4.14 ($false = sF47) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6854])).
% 24.66/4.14 thf(f6856,plain,(
% 24.66/4.14 ($false = sF47)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6855])).
% 24.66/4.14 thf(f6867,plain,(
% 24.66/4.14 (((contrasubsetT3 => sF46)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1266,f6856])).
% 24.66/4.14 thf(f6877,plain,(
% 24.66/4.14 (sF46 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6867])).
% 24.66/4.14 thf(f6887,plain,(
% 24.66/4.14 ($false = ((doubleComplementI1 => sF45)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1264,f6877])).
% 24.66/4.14 thf(f6892,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => sF45)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6887,f1103])).
% 24.66/4.14 thf(f6912,plain,(
% 24.66/4.14 (sF45 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ (setminus @ Y1 @ (setminus @ Y1 @ Y0)))))))))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f6892,f1166])).
% 24.66/4.14 thf(f6916,plain,(
% 24.66/4.14 ($true = $false) | (sF45 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6912])).
% 24.66/4.14 thf(f6917,plain,(
% 24.66/4.14 (sF45 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6916])).
% 24.66/4.14 thf(f6920,plain,(
% 24.66/4.14 (((doubleComplementE1 => sF44)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1263,f6917])).
% 24.66/4.14 thf(f6929,plain,(
% 24.66/4.14 (sF44 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6920])).
% 24.66/4.14 thf(f6941,plain,(
% 24.66/4.14 (((doubleComplementSub1 => sF43)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1261,f6929])).
% 24.66/4.14 thf(f6942,plain,(
% 24.66/4.14 (sF43 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f6941])).
% 24.66/4.14 thf(f6952,plain,(
% 24.66/4.14 (((doubleComplementSub2 => sF42)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1260,f6942])).
% 24.66/4.14 thf(f6955,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ (setminus @ Y0 @ Y1)) @ Y1)))))) => sF42)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6952,f888])).
% 24.66/4.14 thf(f6975,plain,(
% 24.66/4.14 ($false = sF42) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ (setminus @ Y0 @ (setminus @ Y0 @ Y1)) @ Y1)))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f6955,f1166])).
% 24.66/4.14 thf(f6978,plain,(
% 24.66/4.14 ($true = $false) | ($false = sF42)),
% 24.66/4.14 inference(boolean_simplification,[],[f6975])).
% 24.66/4.14 thf(f6979,plain,(
% 24.66/4.14 ($false = sF42)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6978])).
% 24.66/4.14 thf(f6985,plain,(
% 24.66/4.14 (((doubleComplementEq => sF41)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1259,f6979])).
% 24.66/4.14 thf(f6988,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))) => sF41)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f6985,f975])).
% 24.66/4.14 thf(f6991,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((setminus @ Y0 @ (setminus @ Y0 @ Y1)) = Y1)))))) => $true)) = $false) | (sF41 = $false)),
% 24.66/4.14 inference(superposition,[],[f6988,f1166])).
% 24.66/4.14 thf(f6995,plain,(
% 24.66/4.14 (sF41 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f6991])).
% 24.66/4.14 thf(f6996,plain,(
% 24.66/4.14 (sF41 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f6995])).
% 24.66/4.14 thf(f6999,plain,(
% 24.66/4.14 (((complementTnotintersectT => sF40)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1257,f6996])).
% 24.66/4.14 thf(f7006,plain,(
% 24.66/4.14 (((complementTnotintersectT => $true)) = $false) | (sF40 = $false)),
% 24.66/4.14 inference(superposition,[],[f6999,f1166])).
% 24.66/4.14 thf(f7009,plain,(
% 24.66/4.14 ($true = $false) | (sF40 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7006])).
% 24.66/4.14 thf(f7010,plain,(
% 24.66/4.14 (sF40 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7009])).
% 24.66/4.14 thf(f7014,plain,(
% 24.66/4.14 (((complementImpComplementIntersect => sF39)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1255,f7010])).
% 24.66/4.14 thf(f7019,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))))))) => sF39)))),
% 24.66/4.14 inference(forward_demodulation,[],[f7014,f1123])).
% 24.66/4.14 thf(f7076,plain,(
% 24.66/4.14 (sF39 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7019])).
% 24.66/4.14 thf(f7086,plain,(
% 24.66/4.14 (((complementSubsetComplementIntersect => sF38)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1253,f7076])).
% 24.66/4.14 thf(f7091,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (subset @ (setminus @ Y1 @ Y0) @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2))))))))))) => sF38)))),
% 24.66/4.14 inference(forward_demodulation,[],[f7086,f1136])).
% 24.66/4.14 thf(f7094,plain,(
% 24.66/4.14 (sF38 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7091])).
% 24.66/4.14 thf(f7108,plain,(
% 24.66/4.14 ($false = ((complementInPowersetComplementIntersect => sF37)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1252,f7094])).
% 24.66/4.14 thf(f7109,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2)))))))))))) => sF37)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7108,f1056])).
% 24.66/4.14 thf(f7112,plain,(
% 24.66/4.14 (sF37 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ Y1) @ (powerset @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2)))))))))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f7109,f1166])).
% 24.66/4.14 thf(f7117,plain,(
% 24.66/4.14 (sF37 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7112])).
% 24.66/4.14 thf(f7118,plain,(
% 24.66/4.14 (sF37 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7117])).
% 24.66/4.14 thf(f7126,plain,(
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% 24.66/4.14 inference(backward_demodulation,[],[f1251,f7118])).
% 24.66/4.14 thf(f7127,plain,(
% 24.66/4.14 (((contraSubsetComplement => (complementTcontraSubset => sF35))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7126,f1249])).
% 24.66/4.14 thf(f7130,plain,(
% 24.66/4.14 (((contraSubsetComplement => (complementTcontraSubset => $true))) = $false) | (sF35 = $false)),
% 24.66/4.14 inference(superposition,[],[f7127,f1166])).
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% 24.66/4.14 inference(boolean_simplification,[],[f7130])).
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% 24.66/4.14 inference(boolean_simplification,[],[f7138])).
% 24.66/4.14 thf(f7140,plain,(
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% 24.66/4.14 inference(trivial_inequality_removal,[],[f7139])).
% 24.66/4.14 thf(f7148,plain,(
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% 24.66/4.14 inference(backward_demodulation,[],[f1248,f7140])).
% 24.66/4.14 thf(f7166,plain,(
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% 24.66/4.14 inference(superposition,[],[f7148,f1166])).
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% 24.66/4.14 inference(trivial_inequality_removal,[],[f7169])).
% 24.66/4.14 thf(f7174,plain,(
% 24.66/4.14 (((binunionTIRcontra => sF33)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1246,f7170])).
% 24.66/4.14 thf(f7185,plain,(
% 24.66/4.14 (sF33 = $false) | (((binunionTIRcontra => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f7174,f1166])).
% 24.66/4.14 thf(f7188,plain,(
% 24.66/4.14 (sF33 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7185])).
% 24.66/4.14 thf(f7189,plain,(
% 24.66/4.14 (sF33 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7188])).
% 24.66/4.14 thf(f7193,plain,(
% 24.66/4.14 ($false = ((inIntersectImpInUnion => sF32)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1245,f7189])).
% 24.66/4.14 thf(f7204,plain,(
% 24.66/4.14 (sF32 = $false) | (((inIntersectImpInUnion => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f7193,f1166])).
% 24.66/4.14 thf(f7207,plain,(
% 24.66/4.14 (sF32 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7204])).
% 24.66/4.14 thf(f7208,plain,(
% 24.66/4.14 (sF32 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7207])).
% 24.66/4.14 thf(f7214,plain,(
% 24.66/4.14 (((inIntersectImpInUnion2 => sF31)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1244,f7208])).
% 24.66/4.14 thf(f7219,plain,(
% 24.66/4.14 (sF31 = $false) | (((inIntersectImpInUnion2 => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f7214,f1166])).
% 24.66/4.14 thf(f7222,plain,(
% 24.66/4.14 ($true = $false) | (sF31 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7219])).
% 24.66/4.14 thf(f7223,plain,(
% 24.66/4.14 (sF31 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7222])).
% 24.66/4.14 thf(f7227,plain,(
% 24.66/4.14 (((inIntersectImpInIntersectUnions => sF30)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1243,f7223])).
% 24.66/4.14 thf(f7236,plain,(
% 24.66/4.14 (sF30 = $false) | (((inIntersectImpInIntersectUnions => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f7227,f1166])).
% 24.66/4.14 thf(f7240,plain,(
% 24.66/4.14 ($true = $false) | (sF30 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7236])).
% 24.66/4.14 thf(f7241,plain,(
% 24.66/4.14 (sF30 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7240])).
% 24.66/4.14 thf(f7248,plain,(
% 24.66/4.14 (((intersectInPowersetIntersectUnions => sF29)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1241,f7241])).
% 24.66/4.14 thf(f7251,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y0 @ Y3) @ (binunion @ Y2 @ Y3))))))))))))))) => sF29)))),
% 24.66/4.14 inference(forward_demodulation,[],[f7248,f1037])).
% 24.66/4.14 thf(f7252,plain,(
% 24.66/4.14 (((woz1_3 => sF29)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7251,f935])).
% 24.66/4.14 thf(f7253,plain,(
% 24.66/4.14 (sF29 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7252])).
% 24.66/4.14 thf(f7254,plain,(
% 24.66/4.14 (woz1_3 = $true)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7252])).
% 24.66/4.14 thf(f7263,plain,(
% 24.66/4.14 (sF8 = (($true => sF7)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1207,f7254])).
% 24.66/4.14 thf(f7265,plain,(
% 24.66/4.14 (sF8 = sF7)),
% 24.66/4.14 inference(boolean_simplification,[],[f7263])).
% 24.66/4.14 thf(f7267,plain,(
% 24.66/4.14 (((inComplementUnionImpNotIn1 => sF28)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1239,f7253])).
% 24.66/4.14 thf(f7270,plain,(
% 24.66/4.14 (((woz1_4 => sF6)) = sF8)),
% 24.66/4.14 inference(backward_demodulation,[],[f1205,f7265])).
% 24.66/4.14 thf(f7280,plain,(
% 24.66/4.14 (sF28 = $false) | (((inComplementUnionImpNotIn1 => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f7267,f1166])).
% 24.66/4.14 thf(f7284,plain,(
% 24.66/4.14 (sF28 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7280])).
% 24.66/4.14 thf(f7285,plain,(
% 24.66/4.14 (sF28 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7284])).
% 24.66/4.14 thf(f7292,plain,(
% 24.66/4.14 (((inComplementUnionImpInComplement1 => sF27)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1237,f7285])).
% 24.66/4.14 thf(f7297,plain,(
% 24.66/4.14 (sF8 = ((woz1_4 => $true))) | (sF6 = $false)),
% 24.66/4.14 inference(superposition,[],[f7270,f1166])).
% 24.66/4.14 thf(f7301,plain,(
% 24.66/4.14 (sF8 = $true) | (sF6 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7297])).
% 24.66/4.14 thf(f7307,plain,(
% 24.66/4.14 ($false = ((inComplementUnionImpInComplement1 => $true))) | ($false = sF27)),
% 24.66/4.14 inference(superposition,[],[f7292,f1166])).
% 24.66/4.14 thf(f7311,plain,(
% 24.66/4.14 ($true = $false) | ($false = sF27)),
% 24.66/4.14 inference(boolean_simplification,[],[f7307])).
% 24.66/4.14 thf(f7312,plain,(
% 24.66/4.14 ($false = sF27)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7311])).
% 24.66/4.14 thf(f7315,plain,(
% 24.66/4.14 ($false = ((binunionTE => sF26)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1236,f7312])).
% 24.66/4.14 thf(f7324,plain,(
% 24.66/4.14 ($false = sF26)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7315])).
% 24.66/4.14 thf(f7336,plain,(
% 24.66/4.14 ($false = ((binunionTEcontra => sF25)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1235,f7324])).
% 24.66/4.14 thf(f7339,plain,(
% 24.66/4.14 ($false = sF25)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7336])).
% 24.66/4.14 thf(f7349,plain,(
% 24.66/4.14 (((demorgan2a1 => sF24)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1234,f7339])).
% 24.66/4.14 thf(f7352,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ Y1)))))))))))))) => sF24)))),
% 24.66/4.14 inference(forward_demodulation,[],[f7349,f898])).
% 24.66/4.14 thf(f7426,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2))) => (in @ Y3 @ (setminus @ Y0 @ Y1)))))))))))))) => $true)) = $false) | (sF24 = $false)),
% 24.66/4.14 inference(superposition,[],[f7352,f1166])).
% 24.66/4.14 thf(f7429,plain,(
% 24.66/4.14 (sF24 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7426])).
% 24.66/4.14 thf(f7430,plain,(
% 24.66/4.14 (sF24 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7429])).
% 24.66/4.14 thf(f7434,plain,(
% 24.66/4.14 (((complementUnionInPowersetComplement => sF23)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1232,f7430])).
% 24.66/4.14 thf(f7441,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ (binunion @ Y0 @ Y2)) @ (powerset @ (setminus @ Y1 @ Y0))))))))))) => sF23)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7434,f1156])).
% 24.66/4.14 thf(f7442,plain,(
% 24.66/4.14 ($false = sF23)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7441])).
% 24.66/4.14 thf(f7443,plain,(
% 24.66/4.14 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ (binunion @ Y0 @ Y2)) @ (powerset @ (setminus @ Y1 @ Y0)))))))))))) = $true)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7441])).
% 24.66/4.14 thf(f7452,plain,(
% 24.66/4.14 (((demorgan2a2 => sF22)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1231,f7442])).
% 24.66/4.14 thf(f7454,plain,(
% 24.66/4.14 (woz1_5 = $true)),
% 24.66/4.14 inference(backward_demodulation,[],[f1008,f7443])).
% 24.66/4.14 thf(f7460,plain,(
% 24.66/4.14 (sF6 = (($true => sF5)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1203,f7454])).
% 24.66/4.14 thf(f7461,plain,(
% 24.66/4.14 (sF6 = sF5)),
% 24.66/4.14 inference(boolean_simplification,[],[f7460])).
% 24.66/4.14 thf(f7462,plain,(
% 24.66/4.14 ($false = sF5) | (sF8 = $true)),
% 24.66/4.14 inference(backward_demodulation,[],[f7301,f7461])).
% 24.66/4.14 thf(f7473,plain,(
% 24.66/4.14 (((demorgan2a2 => $true)) = $false) | (sF22 = $false)),
% 24.66/4.14 inference(superposition,[],[f7452,f1166])).
% 24.66/4.14 thf(f7476,plain,(
% 24.66/4.14 (sF22 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7473])).
% 24.66/4.14 thf(f7477,plain,(
% 24.66/4.14 (sF22 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7476])).
% 24.66/4.14 thf(f7483,plain,(
% 24.66/4.14 (((demorgan1a => sF21)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1229,f7477])).
% 24.66/4.14 thf(f7486,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))) => (in @ Y3 @ (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))))))) => sF21)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7483,f1110])).
% 24.66/4.14 thf(f7583,plain,(
% 24.66/4.14 (sF21 = $false) | ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ (binintersect @ Y1 @ Y2))) => (in @ Y3 @ (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))))))) => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f7486,f1166])).
% 24.66/4.14 thf(f7587,plain,(
% 24.66/4.14 (sF21 = $false) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7583])).
% 24.66/4.14 thf(f7588,plain,(
% 24.66/4.14 (sF21 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7587])).
% 24.66/4.14 thf(f7595,plain,(
% 24.66/4.14 (((demorgan1b => sF20)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1228,f7588])).
% 24.66/4.14 thf(f7598,plain,(
% 24.66/4.14 ($false = sF20) | (((demorgan1b => $true)) = $false)),
% 24.66/4.14 inference(superposition,[],[f7595,f1166])).
% 24.66/4.14 thf(f7603,plain,(
% 24.66/4.14 ($true = $false) | ($false = sF20)),
% 24.66/4.14 inference(boolean_simplification,[],[f7598])).
% 24.66/4.14 thf(f7604,plain,(
% 24.66/4.14 ($false = sF20)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7603])).
% 24.66/4.14 thf(f7606,plain,(
% 24.66/4.14 ($false = ((demorgan1 => sF19)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1226,f7604])).
% 24.66/4.14 thf(f7609,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((setminus @ Y0 @ (binintersect @ Y1 @ Y2)) = (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))) => sF19)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7606,f1039])).
% 24.66/4.14 thf(f7612,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((setminus @ Y0 @ (binintersect @ Y1 @ Y2)) = (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))) => (demorgan2a => sF18))) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7609,f1225])).
% 24.66/4.14 thf(f7615,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((setminus @ Y0 @ (binintersect @ Y1 @ Y2)) = (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))) => (demorgan2a => $true))) = $false) | (sF18 = $false)),
% 24.66/4.14 inference(superposition,[],[f7612,f1166])).
% 24.66/4.14 thf(f7623,plain,(
% 24.66/4.14 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((setminus @ Y0 @ (binintersect @ Y1 @ Y2)) = (binunion @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2))))))))))) => $true))) | (sF18 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7615])).
% 24.66/4.14 thf(f7624,plain,(
% 24.66/4.14 ($true = $false) | (sF18 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7623])).
% 24.66/4.14 thf(f7625,plain,(
% 24.66/4.14 (sF18 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7624])).
% 24.66/4.14 thf(f7633,plain,(
% 24.66/4.14 (((demorgan2b2 => sF17)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1224,f7625])).
% 24.66/4.14 thf(f7643,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (setminus @ Y0 @ Y1)) => ((in @ Y3 @ (setminus @ Y0 @ Y2)) => (in @ Y3 @ (setminus @ Y0 @ (binunion @ Y1 @ Y2)))))))))))))))) => sF17)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7633,f1041])).
% 24.66/4.14 thf(f7674,plain,(
% 24.66/4.14 ($false = sF17)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7643])).
% 24.66/4.14 thf(f7684,plain,(
% 24.66/4.14 (((demorgan2b => sF16)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1222,f7674])).
% 24.66/4.14 thf(f7695,plain,(
% 24.66/4.14 (((demorgan2b => $true)) = $false) | ($false = sF16)),
% 24.66/4.14 inference(superposition,[],[f7684,f1166])).
% 24.66/4.14 thf(f7698,plain,(
% 24.66/4.14 ($false = sF16) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7695])).
% 24.66/4.14 thf(f7699,plain,(
% 24.66/4.14 ($false = sF16)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7698])).
% 24.66/4.14 thf(f7703,plain,(
% 24.66/4.14 (((demorgan2 => sF15)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1220,f7699])).
% 24.66/4.14 thf(f7710,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((binintersect @ (setminus @ Y0 @ Y1) @ (setminus @ Y0 @ Y2)) = (setminus @ Y0 @ (binunion @ Y1 @ Y2))))))))))) => sF15)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7703,f996])).
% 24.66/4.14 thf(f7713,plain,(
% 24.66/4.14 ($false = sF15)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7710])).
% 24.66/4.14 thf(f7723,plain,(
% 24.66/4.14 (((woz13rule0 => sF14)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1218,f7713])).
% 24.66/4.14 thf(f7730,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y1 @ Y2)) => (in @ Y3 @ Y0)))))))))))) => sF14)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7723,f1160])).
% 24.66/4.14 thf(f7733,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binintersect @ Y1 @ Y2)) => (in @ Y3 @ Y0)))))))))))) => $true)) = $false) | (sF14 = $false)),
% 24.66/4.14 inference(superposition,[],[f7730,f1166])).
% 24.66/4.14 thf(f7736,plain,(
% 24.66/4.14 ($true = $false) | (sF14 = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7733])).
% 24.66/4.14 thf(f7737,plain,(
% 24.66/4.14 (sF14 = $false)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7736])).
% 24.66/4.14 thf(f7741,plain,(
% 24.66/4.14 ($false = ((woz13rule1 => sF13)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1216,f7737])).
% 24.66/4.14 thf(f7748,plain,(
% 24.66/4.14 (sF13 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7741])).
% 24.66/4.14 thf(f7762,plain,(
% 24.66/4.14 (((woz13rule2 => sF12)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1215,f7748])).
% 24.66/4.14 thf(f7763,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => ((subset @ Y2 @ Y3) => (subset @ (binintersect @ Y1 @ Y2) @ Y3))))))))))))) => sF12)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7762,f1082])).
% 24.66/4.14 thf(f7777,plain,(
% 24.66/4.14 (sF12 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7763])).
% 24.66/4.14 thf(f7793,plain,(
% 24.66/4.14 ($false = ((woz13rule3 => sF11)))),
% 24.66/4.14 inference(backward_demodulation,[],[f1213,f7777])).
% 24.66/4.14 thf(f7794,plain,(
% 24.66/4.14 (sF11 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7793])).
% 24.66/4.14 thf(f7804,plain,(
% 24.66/4.14 (((woz13rule4 => sF10)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1212,f7794])).
% 24.66/4.14 thf(f7811,plain,(
% 24.66/4.14 (((woz13rule4 => $true)) = $false) | ($false = sF10)),
% 24.66/4.14 inference(superposition,[],[f7804,f1166])).
% 24.66/4.14 thf(f7816,plain,(
% 24.66/4.14 ($false = sF10) | ($true = $false)),
% 24.66/4.14 inference(boolean_simplification,[],[f7811])).
% 24.66/4.14 thf(f7817,plain,(
% 24.66/4.14 ($false = sF10)),
% 24.66/4.14 inference(trivial_inequality_removal,[],[f7816])).
% 24.66/4.14 thf(f7819,plain,(
% 24.66/4.14 (((woz1_1 => sF9)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1211,f7817])).
% 24.66/4.14 thf(f7822,plain,(
% 24.66/4.14 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))) => sF9)) = $false)),
% 24.66/4.14 inference(forward_demodulation,[],[f7819,f1010])).
% 24.66/4.14 thf(f7827,plain,(
% 24.66/4.14 (sF9 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7822])).
% 24.66/4.14 thf(f7837,plain,(
% 24.66/4.14 (((woz1_2 => sF8)) = $false)),
% 24.66/4.14 inference(backward_demodulation,[],[f1209,f7827])).
% 24.66/4.14 thf(f7846,plain,(
% 24.66/4.14 (sF8 = $false)),
% 24.66/4.14 inference(imp_proxy_clausification,[],[f7837])).
% 24.66/4.15 thf(f7858,plain,(
% 24.66/4.15 ($false = sF5) | ($true = $false)),
% 24.66/4.15 inference(backward_demodulation,[],[f7462,f7846])).
% 24.66/4.15 thf(f7861,plain,(
% 24.66/4.15 ($false = sF5)),
% 24.66/4.15 inference(trivial_inequality_removal,[],[f7858])).
% 24.66/4.15 thf(f7869,plain,(
% 24.66/4.15 ($false = ((breln1all2 => sF4)))),
% 24.66/4.15 inference(backward_demodulation,[],[f1202,f7861])).
% 24.66/4.15 thf(f7945,plain,(
% 24.66/4.15 (sF4 = $false)),
% 24.66/4.15 inference(imp_proxy_clausification,[],[f7869])).
% 24.66/4.15 thf(f7955,plain,(
% 24.66/4.15 (((breln1SetBreln1 => sF3)) = $false)),
% 24.66/4.15 inference(backward_demodulation,[],[f1200,f7945])).
% 24.66/4.15 thf(f7964,plain,(
% 24.66/4.15 (sF3 = $false) | (((breln1SetBreln1 => $true)) = $false)),
% 24.66/4.15 inference(superposition,[],[f7955,f1166])).
% 24.66/4.15 thf(f7968,plain,(
% 24.66/4.15 ($true = $false) | (sF3 = $false)),
% 24.66/4.15 inference(boolean_simplification,[],[f7964])).
% 24.66/4.15 thf(f7969,plain,(
% 24.66/4.15 (sF3 = $false)),
% 24.66/4.15 inference(trivial_inequality_removal,[],[f7968])).
% 24.66/4.15 thf(f7972,plain,(
% 24.66/4.15 (((choice2fnsingleton => sF2)) = $false)),
% 24.66/4.15 inference(backward_demodulation,[],[f1198,f7969])).
% 24.66/4.15 thf(f7975,plain,(
% 24.66/4.15 (((choice2fnsingleton => (setOfPairsIsBReln1 => sF1))) = $false)),
% 24.66/4.15 inference(forward_demodulation,[],[f7972,f1197])).
% 24.66/4.15 thf(f7980,plain,(
% 24.66/4.15 ($false = ((choice2fnsingleton => (setOfPairsIsBReln1 => $true)))) | (sF1 = $false)),
% 24.66/4.15 inference(superposition,[],[f7975,f1166])).
% 24.66/4.15 thf(f7990,plain,(
% 24.66/4.15 (((choice2fnsingleton => $true)) = $false) | (sF1 = $false)),
% 24.66/4.15 inference(boolean_simplification,[],[f7980])).
% 24.66/4.15 thf(f7991,plain,(
% 24.66/4.15 (sF1 = $false) | ($true = $false)),
% 24.66/4.15 inference(boolean_simplification,[],[f7990])).
% 24.66/4.15 thf(f7992,plain,(
% 24.66/4.15 (sF1 = $false)),
% 24.66/4.15 inference(trivial_inequality_removal,[],[f7991])).
% 24.66/4.15 thf(f8002,plain,(
% 24.66/4.15 ($false = ((breln1all1 => sF0)))),
% 24.66/4.15 inference(backward_demodulation,[],[f1196,f7992])).
% 24.66/4.15 thf(f8010,plain,(
% 24.66/4.15 (sF0 = $false)),
% 24.66/4.15 inference(imp_proxy_clausification,[],[f8002])).
% 24.66/4.15 thf(f8024,plain,(
% 24.66/4.15 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))))) = $false)),
% 24.66/4.15 inference(backward_demodulation,[],[f1670,f8010])).
% 24.66/4.15 thf(f8156,plain,(
% 24.66/4.15 ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y1 @ Y2))))))))) @ sK291)) = $false)),
% 24.66/4.15 inference(sigma_proxy_clausification,[],[f8024])).
% 24.66/4.15 thf(f8158,plain,(
% 24.66/4.15 (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK291 @ sK291)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ sK291 @ sK291)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK291) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK291) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ Y0 @ Y1))))))))) = $false)),
% 24.66/4.15 inference(beta-eta_normalization,[],[f8156])).
% 24.66/4.15 thf(f8160,plain,(
% 24.66/4.15 ((((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK291 @ sK291)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ sK291 @ sK291)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK291) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK291) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ Y0 @ Y1))))))) @ sK292)) = $false)),
% 24.66/4.15 inference(sigma_proxy_clausification,[],[f8158])).
% 24.66/4.15 thf(f8163,plain,(
% 24.66/4.15 ((((subset @ sK292 @ (cartprod @ sK291 @ sK291)) => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK291 @ sK291)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK291) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK291) => ((in @ (kpair @ Y1 @ Y2) @ sK292) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK292 @ Y0))))))) = $false)),
% 24.66/4.15 inference(beta-eta_normalization,[],[f8160])).
% 24.66/4.15 thf(f8165,plain,(
% 24.66/4.15 (((subset @ sK292 @ (cartprod @ sK291 @ sK291))) = $true)),
% 24.66/4.15 inference(imp_proxy_clausification,[],[f8163])).
% 24.66/4.15 thf(f8166,plain,(
% 24.66/4.15 ((((subset @ sK292 @ (cartprod @ sK291 @ sK291)) => $true)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK291 @ sK291)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK291) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK291) => ((in @ (kpair @ Y1 @ Y2) @ sK292) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK292 @ Y0)))))) = $false)),
% 24.66/4.15 inference(superposition,[],[f8163,f1166])).
% 24.66/4.15 thf(f8170,plain,(
% 24.66/4.15 (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK291 @ sK291)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK291) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK291) => ((in @ (kpair @ Y1 @ Y2) @ sK292) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK292 @ Y0)))))) = $false) | ($true = $false)),
% 24.66/4.15 inference(boolean_simplification,[],[f8166])).
% 24.66/4.15 thf(f8171,plain,(
% 24.66/4.15 (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK291 @ sK291)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK291) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK291) => ((in @ (kpair @ Y1 @ Y2) @ sK292) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK292 @ Y0)))))) = $false)),
% 24.66/4.15 inference(trivial_inequality_removal,[],[f8170])).
% 24.66/4.15 thf(f8216,plain,(
% 24.66/4.15 ( ! [X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y2 @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))) @ X1)) = $true)) )),
% 24.66/4.15 inference(pi_proxy_clausification,[],[f6121])).
% 24.66/4.15 thf(f8217,plain,(
% 24.66/4.15 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ (cartprod @ Y1 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y1 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ X1 @ Y2))))))))))) = $true)) )),
% 24.66/4.15 inference(beta-eta_normalization,[],[f8216])).
% 24.66/4.15 thf(f8218,plain,(
% 24.66/4.15 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ (cartprod @ Y1 @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y1 @ Y0)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ X1 @ Y2))))))))) @ X2)))) )),
% 24.66/4.15 inference(pi_proxy_clausification,[],[f8217])).
% 24.66/4.15 thf(f8219,plain,(
% 24.66/4.15 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ X2)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ X1 @ Y1))))))))))) )),
% 24.66/4.15 inference(beta-eta_normalization,[],[f8218])).
% 24.66/4.15 thf(f8220,plain,(
% 24.66/4.15 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ Y0 @ X2)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ X1 @ Y1))))))) @ X3)))) )),
% 24.66/4.15 inference(pi_proxy_clausification,[],[f8219])).
% 24.66/4.15 thf(f8221,plain,(
% 24.66/4.15 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((subset @ X1 @ (cartprod @ X3 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X3 @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0))))))) = $true)) )),
% 24.66/4.15 inference(beta-eta_normalization,[],[f8220])).
% 24.66/4.15 thf(f9608,plain,(
% 24.66/4.15 ($true = (($true => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK291 @ sK291)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK291) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK291) => ((in @ (kpair @ Y1 @ Y2) @ sK292) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK292 @ Y0))))))))),
% 24.66/4.15 inference(superposition,[],[f8221,f8165])).
% 24.66/4.15 thf(f9628,plain,(
% 24.66/4.15 ($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK291 @ sK291)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK291) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK291) => ((in @ (kpair @ Y1 @ Y2) @ sK292) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK292 @ Y0)))))))),
% 24.66/4.15 inference(boolean_simplification,[],[f9608])).
% 24.66/4.15 thf(f9629,plain,(
% 24.66/4.15 ($true = $false)),
% 24.66/4.15 inference(forward_demodulation,[],[f9628,f8171])).
% 24.66/4.15 thf(f9630,plain,(
% 24.66/4.15 $false),
% 24.66/4.15 inference(trivial_inequality_removal,[],[f9629])).
% 24.66/4.15 % SZS output end Proof for theBenchmark
% 24.66/4.15 % (1367293)------------------------------
% 24.66/4.15 % (1367293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.66/4.15 % (1367293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.66/4.15 % (1367293)CaDiCaL version: 2.1.3
% 24.66/4.15 % (1367293)Termination reason: Refutation
% 24.66/4.15 % (1367293)Time elapsed: 1.227 s
% 24.66/4.15 % (1367293)Peak memory usage: 23 MB
% 24.66/4.15 % (1367293)Instructions burned: 1323 (million)
% 24.66/4.15 % (1367102)Success in time 3.78 s
% 24.66/4.15 % Vampire exiting
%------------------------------------------------------------------------------