%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU717^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:56 AM UTC 2026
% Result : Theorem 1.24s 0.55s
% Output : Refutation 1.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU717^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:14:32 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.43 % (783116)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.43 % (783125)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3431694989:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.43 % (783127)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.43 % (783127)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
% 0.54/0.43 % (783125)Instruction limit reached!
% 0.54/0.43 % (783125)------------------------------
% 0.54/0.43 % (783125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.43 % (783125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.43 % (783125)CaDiCaL version: 2.1.3
% 0.54/0.43 % (783125)Termination reason: Instruction limit
% 0.54/0.43 % (783125)Termination phase: Property scanning
% 0.54/0.43 % (783125)Time elapsed: 0.006 s
% 0.54/0.43 % (783125)Peak memory usage: 10 MB
% 0.54/0.43 % (783125)Instructions burned: 25 (million)
% 0.54/0.43 % (783121)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1072569238:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.43 % (783123)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4226440444:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.43 % (783124)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=3797007754: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)
% 0.54/0.43 % (783126)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4231899158:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.43 % (783127)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=1221142790:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.43 % (783123)Instruction limit reached!
% 0.54/0.43 % (783123)------------------------------
% 0.54/0.43 % (783123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.43 % (783123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.43 % (783123)CaDiCaL version: 2.1.3
% 0.54/0.43 % (783123)Termination reason: Instruction limit
% 0.54/0.43 % (783123)Termination phase: shuffling
% 0.54/0.43 % (783123)Time elapsed: 0.003 s
% 0.54/0.43 % (783123)Peak memory usage: 10 MB
% 0.54/0.43 % (783123)Instructions burned: 5 (million)
% 0.54/0.43 % (783122)lrs+10_16_si=on:nwc=1.5:random_seed=3082751968:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.43 % (783132)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2756068666:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.43 % (783132)Instruction limit reached!
% 0.54/0.43 % (783132)------------------------------
% 0.54/0.43 % (783132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.43 % (783132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.43 % (783132)CaDiCaL version: 2.1.3
% 0.54/0.43 % (783132)Termination reason: Instruction limit
% 0.54/0.43 % (783132)Termination phase: shuffling
% 0.54/0.43 % (783132)Time elapsed: 0.003 s
% 0.54/0.43 % (783132)Peak memory usage: 10 MB
% 0.54/0.43 % (783132)Instructions burned: 11 (million)
% 0.54/0.43 % (783122)Instruction limit reached!
% 0.54/0.43 % (783122)------------------------------
% 0.54/0.43 % (783122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.43 % (783122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.43 % (783122)CaDiCaL version: 2.1.3
% 0.54/0.43 % (783122)Termination reason: Instruction limit
% 0.54/0.43 % (783122)Termination phase: shuffling
% 0.54/0.43 % (783122)Time elapsed: 0.013 s
% 0.54/0.43 % (783122)Peak memory usage: 10 MB
% 0.54/0.43 % (783122)Instructions burned: 19 (million)
% 0.54/0.43 % (783138)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.43 % (783138)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1238919482:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.47 % (783138)Instruction limit reached!
% 0.54/0.47 % (783138)------------------------------
% 0.54/0.47 % (783138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.47 % (783138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.47 % (783138)CaDiCaL version: 2.1.3
% 0.54/0.47 % (783138)Termination reason: Instruction limit
% 0.54/0.47 % (783138)Termination phase: shuffling
% 0.54/0.47 % (783138)Time elapsed: 0.002 s
% 0.54/0.47 % (783138)Peak memory usage: 10 MB
% 0.54/0.47 % (783138)Instructions burned: 10 (million)
% 0.54/0.47 % (783126)Instruction limit reached!
% 0.54/0.47 % (783126)------------------------------
% 0.54/0.47 % (783126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.47 % (783126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.47 % (783126)CaDiCaL version: 2.1.3
% 0.54/0.47 % (783126)Termination reason: Instruction limit
% 0.54/0.47 % (783126)Termination phase: Preprocessing 3
% 0.54/0.47 % (783126)Time elapsed: 0.035 s
% 0.54/0.47 % (783126)Peak memory usage: 12 MB
% 0.54/0.47 % (783126)Instructions burned: 76 (million)
% 0.54/0.47 % (783141)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
% 0.54/0.47 % (783141)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.47 % (783135)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1834668844:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.47 % (783141)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3278020113:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.47 % (783139)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1991316279:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.47 % (783121)Instruction limit reached!
% 0.54/0.47 % (783121)------------------------------
% 0.54/0.47 % (783121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.47 % (783121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.47 % (783121)CaDiCaL version: 2.1.3
% 0.54/0.47 % (783121)Termination reason: Instruction limit
% 0.54/0.47 % (783121)Termination phase: Preprocessing 3
% 0.54/0.47 % (783121)Time elapsed: 0.041 s
% 0.54/0.47 % (783121)Peak memory usage: 13 MB
% 0.54/0.47 % (783121)Instructions burned: 87 (million)
% 0.54/0.47 % (783135)Instruction limit reached!
% 0.54/0.47 % (783135)------------------------------
% 0.54/0.47 % (783135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.47 % (783135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.47 % (783135)CaDiCaL version: 2.1.3
% 0.54/0.47 % (783135)Termination reason: Instruction limit
% 0.54/0.47 % (783135)Termination phase: shuffling
% 0.54/0.47 % (783135)Time elapsed: 0.003 s
% 0.54/0.47 % (783135)Peak memory usage: 10 MB
% 0.54/0.47 % (783135)Instructions burned: 5 (million)
% 0.54/0.47 % (783139)Instruction limit reached!
% 0.54/0.47 % (783139)------------------------------
% 0.54/0.47 % (783139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.47 % (783139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.47 % (783139)CaDiCaL version: 2.1.3
% 0.54/0.47 % (783139)Termination reason: Instruction limit
% 0.54/0.47 % (783139)Termination phase: shuffling
% 0.54/0.47 % (783139)Time elapsed: 0.006 s
% 0.54/0.47 % (783139)Peak memory usage: 10 MB
% 0.54/0.47 % (783139)Instructions burned: 12 (million)
% 0.54/0.47 % (783141)Instruction limit reached!
% 0.54/0.47 % (783141)------------------------------
% 0.54/0.47 % (783141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.47 % (783141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.47 % (783141)CaDiCaL version: 2.1.3
% 0.54/0.47 % (783141)Termination reason: Instruction limit
% 0.54/0.47 % (783141)Termination phase: shuffling
% 0.54/0.47 % (783141)Time elapsed: 0.007 s
% 0.54/0.47 % (783141)Peak memory usage: 10 MB
% 1.24/0.50 % (783141)Instructions burned: 33 (million)
% 1.24/0.50 % (783142)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=3494214988:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.24/0.50 % (783147)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.24/0.50 % (783149)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=864513630:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.24/0.50 % (783146)lrs+10_1_si=on:cs=on:random_seed=3633226140:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.24/0.50 % (783147)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=2565921932:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.24/0.50 % (783146)Instruction limit reached!
% 1.24/0.50 % (783146)------------------------------
% 1.24/0.50 % (783146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.50 % (783146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.50 % (783146)CaDiCaL version: 2.1.3
% 1.24/0.50 % (783146)Termination reason: Instruction limit
% 1.24/0.50 % (783146)Termination phase: shuffling
% 1.24/0.50 % (783146)Time elapsed: 0.004 s
% 1.24/0.50 % (783146)Peak memory usage: 10 MB
% 1.24/0.50 % (783146)Instructions burned: 9 (million)
% 1.24/0.50 % (783148)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3877434398:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.24/0.50 % (783147)Instruction limit reached!
% 1.24/0.50 % (783147)------------------------------
% 1.24/0.50 % (783147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.50 % (783147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.50 % (783147)CaDiCaL version: 2.1.3
% 1.24/0.50 % (783147)Termination reason: Instruction limit
% 1.24/0.50 % (783147)Termination phase: shuffling
% 1.24/0.50 % (783147)Time elapsed: 0.003 s
% 1.24/0.50 % (783147)Peak memory usage: 10 MB
% 1.24/0.50 % (783147)Instructions burned: 6 (million)
% 1.24/0.50 % (783127)Instruction limit reached!
% 1.24/0.50 % (783127)------------------------------
% 1.24/0.50 % (783127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.50 % (783127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.50 % (783127)CaDiCaL version: 2.1.3
% 1.24/0.50 % (783127)Termination reason: Instruction limit
% 1.24/0.50 % (783127)Termination phase: Saturation
% 1.24/0.50 % (783127)Time elapsed: 0.081 s
% 1.24/0.50 % (783127)Peak memory usage: 13 MB
% 1.24/0.50 % (783127)Instructions burned: 159 (million)
% 1.24/0.50 % (783148)Instruction limit reached!
% 1.24/0.50 % (783148)------------------------------
% 1.24/0.50 % (783148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.50 % (783148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.50 % (783148)CaDiCaL version: 2.1.3
% 1.24/0.50 % (783148)Termination reason: Instruction limit
% 1.24/0.50 % (783148)Termination phase: SInE selection
% 1.24/0.50 % (783148)Time elapsed: 0.017 s
% 1.24/0.50 % (783148)Peak memory usage: 11 MB
% 1.24/0.50 % (783155)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2570163755:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.24/0.50 % (783156)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2148839530:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.24/0.50 % (783148)Instructions burned: 48 (million)
% 1.24/0.50 % (783156)Instruction limit reached!
% 1.24/0.50 % (783156)------------------------------
% 1.24/0.50 % (783156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.50 % (783156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.50 % (783156)CaDiCaL version: 2.1.3
% 1.24/0.50 % (783156)Termination reason: Instruction limit
% 1.24/0.50 % (783156)Termination phase: shuffling
% 1.24/0.50 % (783156)Time elapsed: 0.007 s
% 1.24/0.50 % (783156)Peak memory usage: 10 MB
% 1.24/0.50 % (783156)Instructions burned: 14 (million)
% 1.24/0.50 % (783142)Instruction limit reached!
% 1.24/0.50 % (783142)------------------------------
% 1.24/0.55 % (783142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783142)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783142)Termination reason: Instruction limit
% 1.24/0.55 % (783142)Termination phase: Property scanning
% 1.24/0.55 % (783142)Time elapsed: 0.036 s
% 1.24/0.55 % (783142)Peak memory usage: 11 MB
% 1.24/0.55 % (783142)Instructions burned: 88 (million)
% 1.24/0.55 % (783155)Instruction limit reached!
% 1.24/0.55 % (783155)------------------------------
% 1.24/0.55 % (783155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783155)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783155)Termination reason: Instruction limit
% 1.24/0.55 % (783155)Termination phase: Property scanning
% 1.24/0.55 % (783155)Time elapsed: 0.012 s
% 1.24/0.55 % (783155)Peak memory usage: 10 MB
% 1.24/0.55 % (783155)Instructions burned: 26 (million)
% 1.24/0.55 % (783157)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2055273162:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.24/0.55 % (783160)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2150992959:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.24/0.55 % (783161)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2074506973:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.24/0.55 % (783162)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1369058870:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.24/0.55 % (783160)Instruction limit reached!
% 1.24/0.55 % (783160)------------------------------
% 1.24/0.55 % (783160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783160)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783160)Termination reason: Instruction limit
% 1.24/0.55 % (783160)Termination phase: shuffling
% 1.24/0.55 % (783160)Time elapsed: 0.007 s
% 1.24/0.55 % (783160)Peak memory usage: 10 MB
% 1.24/0.55 % (783160)Instructions burned: 15 (million)
% 1.24/0.55 % (783161)Instruction limit reached!
% 1.24/0.55 % (783161)------------------------------
% 1.24/0.55 % (783161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783161)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783161)Termination reason: Instruction limit
% 1.24/0.55 % (783161)Termination phase: shuffling
% 1.24/0.55 % (783161)Time elapsed: 0.002 s
% 1.24/0.55 % (783161)Peak memory usage: 10 MB
% 1.24/0.55 % (783161)Instructions burned: 4 (million)
% 1.24/0.55 % (783163)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3757908537:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.24/0.55 % (783149)Instruction limit reached!
% 1.24/0.55 % (783149)------------------------------
% 1.24/0.55 % (783149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783149)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783149)Termination reason: Instruction limit
% 1.24/0.55 % (783149)Termination phase: Saturation
% 1.24/0.55 % (783149)Time elapsed: 0.059 s
% 1.24/0.55 % (783149)Peak memory usage: 15 MB
% 1.24/0.55 % (783149)Instructions burned: 252 (million)
% 1.24/0.55 % (783162)Instruction limit reached!
% 1.24/0.55 % (783162)------------------------------
% 1.24/0.55 % (783162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783162)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783162)Termination reason: Instruction limit
% 1.24/0.55 % (783162)Termination phase: shuffling
% 1.24/0.55 % (783162)Time elapsed: 0.012 s
% 1.24/0.55 % (783162)Peak memory usage: 10 MB
% 1.24/0.55 % (783162)Instructions burned: 28 (million)
% 1.24/0.55 % (783171)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.24/0.55 % (783171)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=3056831951:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.24/0.55 % (783163)Instruction limit reached!
% 1.24/0.55 % (783163)------------------------------
% 1.24/0.55 % (783163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783163)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783163)Termination reason: Instruction limit
% 1.24/0.55 % (783163)Termination phase: shuffling
% 1.24/0.55 % (783163)Time elapsed: 0.015 s
% 1.24/0.55 % (783163)Peak memory usage: 10 MB
% 1.24/0.55 % (783163)Instructions burned: 24 (million)
% 1.24/0.55 % (783171)Instruction limit reached!
% 1.24/0.55 % (783171)------------------------------
% 1.24/0.55 % (783171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783171)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783171)Termination reason: Instruction limit
% 1.24/0.55 % (783171)Termination phase: shuffling
% 1.24/0.55 % (783171)Time elapsed: 0.002 s
% 1.24/0.55 % (783171)Peak memory usage: 10 MB
% 1.24/0.55 % (783171)Instructions burned: 9 (million)
% 1.24/0.55 % (783168)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1051228941:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.24/0.55 % (783175)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=184364362:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.24/0.55 % (783170)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.24/0.55 % (783170)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.24/0.55 % (783172)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=960773827:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.24/0.55 % (783175)Instruction limit reached!
% 1.24/0.55 % (783175)------------------------------
% 1.24/0.55 % (783175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783175)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783175)Termination reason: Instruction limit
% 1.24/0.55 % (783175)Termination phase: shuffling
% 1.24/0.55 % (783175)Time elapsed: 0.006 s
% 1.24/0.55 % (783175)Peak memory usage: 10 MB
% 1.24/0.55 % (783175)Instructions burned: 26 (million)
% 1.24/0.55 % (783174)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=107656897:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.24/0.55 % (783170)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=1517587445:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.24/0.55 % (783174)Instruction limit reached!
% 1.24/0.55 % (783174)------------------------------
% 1.24/0.55 % (783174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783174)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783174)Termination reason: Instruction limit
% 1.24/0.55 % (783174)Termination phase: shuffling
% 1.24/0.55 % (783174)Time elapsed: 0.004 s
% 1.24/0.55 % (783174)Peak memory usage: 10 MB
% 1.24/0.55 % (783174)Instructions burned: 9 (million)
% 1.24/0.55 % (783179)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1665881299:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.24/0.55 % (783172)Instruction limit reached!
% 1.24/0.55 % (783172)------------------------------
% 1.24/0.55 % (783172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783172)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783172)Termination reason: Instruction limit
% 1.24/0.55 % (783172)Termination phase: shuffling
% 1.24/0.55 % (783172)Time elapsed: 0.015 s
% 1.24/0.55 % (783172)Peak memory usage: 10 MB
% 1.24/0.55 % (783172)Instructions burned: 33 (million)
% 1.24/0.55 % (783168)Instruction limit reached!
% 1.24/0.55 % (783168)------------------------------
% 1.24/0.55 % (783168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783168)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783168)Termination reason: Instruction limit
% 1.24/0.55 % (783168)Termination phase: Preprocessing 3
% 1.24/0.55 % (783168)Time elapsed: 0.028 s
% 1.24/0.55 % (783168)Peak memory usage: 12 MB
% 1.24/0.55 % (783168)Instructions burned: 61 (million)
% 1.24/0.55 % (783170)Instruction limit reached!
% 1.24/0.55 % (783170)------------------------------
% 1.24/0.55 % (783170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783170)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783170)Termination reason: Instruction limit
% 1.24/0.55 % (783170)Termination phase: shuffling
% 1.24/0.55 % (783170)Time elapsed: 0.013 s
% 1.24/0.55 % (783170)Peak memory usage: 10 MB
% 1.24/0.55 % (783170)Instructions burned: 14 (million)
% 1.24/0.55 % (783179)Instruction limit reached!
% 1.24/0.55 % (783179)------------------------------
% 1.24/0.55 % (783179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783179)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783179)Termination reason: Instruction limit
% 1.24/0.55 % (783179)Termination phase: shuffling
% 1.24/0.55 % (783179)Time elapsed: 0.005 s
% 1.24/0.55 % (783179)Peak memory usage: 10 MB
% 1.24/0.55 % (783179)Instructions burned: 22 (million)
% 1.24/0.55 % (783182)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1827158945:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.24/0.55 % (783187)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.24/0.55 % (783184)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=808139039:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.24/0.55 % (783185)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1505959155:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.24/0.55 % (783186)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1008288836:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.24/0.55 % (783187)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2013160583:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.24/0.55 % (783187)Instruction limit reached!
% 1.24/0.55 % (783187)------------------------------
% 1.24/0.55 % (783187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783187)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783187)Termination reason: Instruction limit
% 1.24/0.55 % (783187)Termination phase: shuffling
% 1.24/0.55 % (783187)Time elapsed: 0.003 s
% 1.24/0.55 % (783187)Peak memory usage: 10 MB
% 1.24/0.55 % (783187)Instructions burned: 7 (million)
% 1.24/0.55 % (783186)Instruction limit reached!
% 1.24/0.55 % (783186)------------------------------
% 1.24/0.55 % (783186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783124) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-783116-783124"...
% 1.24/0.55 % (783186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783186)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783186)Termination reason: Instruction limit
% 1.24/0.55 % (783186)Termination phase: Property scanning
% 1.24/0.55 % (783186)Time elapsed: 0.019 s
% 1.24/0.55 % (783186)Peak memory usage: 11 MB
% 1.24/0.55 % (783186)Instructions burned: 44 (million)
% 1.24/0.55 % (783193)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2929560535:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.24/0.55 % (783124)...printing done.
% 1.24/0.55 % (783124)Refutation found. Thanks to Tanya!
% 1.24/0.55 % SZS status Theorem for theBenchmark
% 1.24/0.55 % SZS output start Proof for theBenchmark
% 1.24/0.55 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.24/0.55 thf(func_def_0, type, in: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 1.24/0.55 thf(func_def_3, type, setextAx: $o).
% 1.24/0.55 thf(func_def_5, type, emptysetAx: $o).
% 1.24/0.55 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_7, type, setadjoinAx: $o).
% 1.24/0.55 thf(func_def_8, type, powerset: ($i > $i)).
% 1.24/0.55 thf(func_def_9, type, powersetAx: $o).
% 1.24/0.55 thf(func_def_10, type, setunion: ($i > $i)).
% 1.24/0.55 thf(func_def_11, type, setunionAx: $o).
% 1.24/0.55 thf(func_def_13, type, omega0Ax: $o).
% 1.24/0.55 thf(func_def_14, type, omegaSAx: $o).
% 1.24/0.55 thf(func_def_15, type, omegaIndAx: $o).
% 1.24/0.55 thf(func_def_16, type, replAx: $o).
% 1.24/0.55 thf(func_def_17, type, foundationAx: $o).
% 1.24/0.55 thf(func_def_18, type, wellorderingAx: $o).
% 1.24/0.55 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 1.24/0.55 thf(func_def_20, type, descrp: $o).
% 1.24/0.55 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_22, type, dsetconstrI: $o).
% 1.24/0.55 thf(func_def_23, type, dsetconstrEL: $o).
% 1.24/0.55 thf(func_def_24, type, dsetconstrER: $o).
% 1.24/0.55 thf(func_def_25, type, exuE1: $o).
% 1.24/0.55 thf(func_def_26, type, prop2set: ($o > $i)).
% 1.24/0.55 thf(func_def_27, type, prop2setE: $o).
% 1.24/0.55 thf(func_def_28, type, emptysetE: $o).
% 1.24/0.55 thf(func_def_29, type, emptysetimpfalse: $o).
% 1.24/0.55 thf(func_def_30, type, notinemptyset: $o).
% 1.24/0.55 thf(func_def_31, type, exuE3e: $o).
% 1.24/0.55 thf(func_def_32, type, setext: $o).
% 1.24/0.55 thf(func_def_33, type, emptyI: $o).
% 1.24/0.55 thf(func_def_34, type, noeltsimpempty: $o).
% 1.24/0.55 thf(func_def_35, type, setbeta: $o).
% 1.24/0.55 thf(func_def_36, type, nonempty: ($i > $o)).
% 1.24/0.55 thf(func_def_37, type, nonemptyE1: $o).
% 1.24/0.55 thf(func_def_38, type, nonemptyI: $o).
% 1.24/0.55 thf(func_def_39, type, nonemptyI1: $o).
% 1.24/0.55 thf(func_def_40, type, setadjoinIL: $o).
% 1.24/0.55 thf(func_def_41, type, emptyinunitempty: $o).
% 1.24/0.55 thf(func_def_42, type, setadjoinIR: $o).
% 1.24/0.55 thf(func_def_43, type, setadjoinE: $o).
% 1.24/0.55 thf(func_def_44, type, setadjoinOr: $o).
% 1.24/0.55 thf(func_def_45, type, setoftrueEq: $o).
% 1.24/0.55 thf(func_def_46, type, powersetI: $o).
% 1.24/0.55 thf(func_def_47, type, emptyinPowerset: $o).
% 1.24/0.55 thf(func_def_48, type, emptyInPowerset: $o).
% 1.24/0.55 thf(func_def_49, type, powersetE: $o).
% 1.24/0.55 thf(func_def_50, type, setunionI: $o).
% 1.24/0.55 thf(func_def_51, type, setunionE: $o).
% 1.24/0.55 thf(func_def_52, type, subPowSU: $o).
% 1.24/0.55 thf(func_def_53, type, exuE2: $o).
% 1.24/0.55 thf(func_def_54, type, nonemptyImpWitness: $o).
% 1.24/0.55 thf(func_def_55, type, uniqinunit: $o).
% 1.24/0.55 thf(func_def_56, type, notinsingleton: $o).
% 1.24/0.55 thf(func_def_57, type, eqinunit: $o).
% 1.24/0.55 thf(func_def_58, type, singletonsswitch: $o).
% 1.24/0.55 thf(func_def_59, type, upairsetE: $o).
% 1.24/0.55 thf(func_def_60, type, upairsetIL: $o).
% 1.24/0.55 thf(func_def_61, type, upairsetIR: $o).
% 1.24/0.55 thf(func_def_62, type, emptyE1: $o).
% 1.24/0.55 thf(func_def_63, type, vacuousDall: $o).
% 1.24/0.55 thf(func_def_64, type, quantDeMorgan1: $o).
% 1.24/0.55 thf(func_def_65, type, quantDeMorgan2: $o).
% 1.24/0.55 thf(func_def_66, type, quantDeMorgan3: $o).
% 1.24/0.55 thf(func_def_67, type, quantDeMorgan4: $o).
% 1.24/0.55 thf(func_def_68, type, prop2setI: $o).
% 1.24/0.55 thf(func_def_69, type, set2prop: ($i > $o)).
% 1.24/0.55 thf(func_def_70, type, prop2set2propI: $o).
% 1.24/0.55 thf(func_def_71, type, notdexE: $o).
% 1.24/0.55 thf(func_def_72, type, notdallE: $o).
% 1.24/0.55 thf(func_def_73, type, exuI1: $o).
% 1.24/0.55 thf(func_def_74, type, exuI3: $o).
% 1.24/0.55 thf(func_def_75, type, exuI2: $o).
% 1.24/0.55 thf(func_def_76, type, inCongP: $o).
% 1.24/0.55 thf(func_def_77, type, in__Cong: $o).
% 1.24/0.55 thf(func_def_78, type, exuE3u: $o).
% 1.24/0.55 thf(func_def_79, type, exu__Cong: $o).
% 1.24/0.55 thf(func_def_80, type, emptyset__Cong: $o).
% 1.24/0.55 thf(func_def_81, type, setadjoin__Cong: $o).
% 1.24/0.55 thf(func_def_82, type, powerset__Cong: $o).
% 1.24/0.55 thf(func_def_83, type, setunion__Cong: $o).
% 1.24/0.55 thf(func_def_84, type, omega__Cong: $o).
% 1.24/0.55 thf(func_def_85, type, exuEu: $o).
% 1.24/0.55 thf(func_def_86, type, descr__Cong: $o).
% 1.24/0.55 thf(func_def_87, type, dsetconstr__Cong: $o).
% 1.24/0.55 thf(func_def_88, type, subset: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_91, type, subsetI1: $o).
% 1.24/0.55 thf(func_def_92, type, eqimpsubset2: $o).
% 1.24/0.55 thf(func_def_93, type, eqimpsubset1: $o).
% 1.24/0.55 thf(func_def_94, type, subsetI2: $o).
% 1.24/0.55 thf(func_def_95, type, emptysetsubset: $o).
% 1.24/0.55 thf(func_def_96, type, subsetE: $o).
% 1.24/0.55 thf(func_def_97, type, subsetE2: $o).
% 1.24/0.55 thf(func_def_98, type, notsubsetI: $o).
% 1.24/0.55 thf(func_def_99, type, notequalI1: $o).
% 1.24/0.55 thf(func_def_100, type, notequalI2: $o).
% 1.24/0.55 thf(func_def_101, type, subsetRefl: $o).
% 1.24/0.55 thf(func_def_102, type, subsetTrans: $o).
% 1.24/0.55 thf(func_def_103, type, setadjoinSub: $o).
% 1.24/0.55 thf(func_def_104, type, setadjoinSub2: $o).
% 1.24/0.55 thf(func_def_105, type, subset2powerset: $o).
% 1.24/0.55 thf(func_def_106, type, setextsub: $o).
% 1.24/0.55 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 1.24/0.55 thf(func_def_108, type, powersetI1: $o).
% 1.24/0.55 thf(func_def_109, type, powersetE1: $o).
% 1.24/0.55 thf(func_def_110, type, inPowerset: $o).
% 1.24/0.55 thf(func_def_111, type, powersetsubset: $o).
% 1.24/0.55 thf(func_def_112, type, sepInPowerset: $o).
% 1.24/0.55 thf(func_def_113, type, sepSubset: $o).
% 1.24/0.55 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_115, type, binunionIL: $o).
% 1.24/0.55 thf(func_def_116, type, upairset2IR: $o).
% 1.24/0.55 thf(func_def_117, type, binunionIR: $o).
% 1.24/0.55 thf(func_def_118, type, binunionEcases: $o).
% 1.24/0.55 thf(func_def_119, type, binunionE: $o).
% 1.24/0.55 thf(func_def_120, type, binunionLsub: $o).
% 1.24/0.55 thf(func_def_121, type, binunionRsub: $o).
% 1.24/0.55 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_123, type, binintersectI: $o).
% 1.24/0.55 thf(func_def_124, type, binintersectSubset5: $o).
% 1.24/0.55 thf(func_def_125, type, binintersectEL: $o).
% 1.24/0.55 thf(func_def_126, type, binintersectLsub: $o).
% 1.24/0.55 thf(func_def_127, type, binintersectSubset2: $o).
% 1.24/0.55 thf(func_def_128, type, binintersectSubset3: $o).
% 1.24/0.55 thf(func_def_129, type, binintersectER: $o).
% 1.24/0.55 thf(func_def_130, type, disjointsetsI1: $o).
% 1.24/0.55 thf(func_def_131, type, binintersectRsub: $o).
% 1.24/0.55 thf(func_def_132, type, binintersectSubset4: $o).
% 1.24/0.55 thf(func_def_133, type, binintersectSubset1: $o).
% 1.24/0.55 thf(func_def_134, type, bs114d: $o).
% 1.24/0.55 thf(func_def_135, type, regular: ($i > $o)).
% 1.24/0.55 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_137, type, setminusI: $o).
% 1.24/0.55 thf(func_def_138, type, setminusEL: $o).
% 1.24/0.55 thf(func_def_139, type, setminusER: $o).
% 1.24/0.55 thf(func_def_140, type, setminusSubset2: $o).
% 1.24/0.55 thf(func_def_141, type, setminusERneg: $o).
% 1.24/0.55 thf(func_def_142, type, setminusELneg: $o).
% 1.24/0.55 thf(func_def_143, type, setminusILneg: $o).
% 1.24/0.55 thf(func_def_144, type, setminusIRneg: $o).
% 1.24/0.55 thf(func_def_145, type, setminusLsub: $o).
% 1.24/0.55 thf(func_def_146, type, setminusSubset1: $o).
% 1.24/0.55 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_148, type, symdiffE: $o).
% 1.24/0.55 thf(func_def_149, type, symdiffI1: $o).
% 1.24/0.55 thf(func_def_150, type, symdiffI2: $o).
% 1.24/0.55 thf(func_def_151, type, symdiffIneg1: $o).
% 1.24/0.55 thf(func_def_152, type, symdiffIneg2: $o).
% 1.24/0.55 thf(func_def_153, type, iskpair: ($i > $o)).
% 1.24/0.55 thf(func_def_154, type, secondinupair: $o).
% 1.24/0.55 thf(func_def_155, type, setukpairIL: $o).
% 1.24/0.55 thf(func_def_156, type, setukpairIR: $o).
% 1.24/0.55 thf(func_def_157, type, kpairiskpair: $o).
% 1.24/0.55 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_159, type, kpairp: $o).
% 1.24/0.55 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_161, type, singletonsubset: $o).
% 1.24/0.55 thf(func_def_162, type, singletoninpowerset: $o).
% 1.24/0.55 thf(func_def_163, type, singletoninpowunion: $o).
% 1.24/0.55 thf(func_def_164, type, upairset2E: $o).
% 1.24/0.55 thf(func_def_165, type, upairsubunion: $o).
% 1.24/0.55 thf(func_def_166, type, upairinpowunion: $o).
% 1.24/0.55 thf(func_def_167, type, ubforcartprodlem1: $o).
% 1.24/0.55 thf(func_def_168, type, ubforcartprodlem2: $o).
% 1.24/0.55 thf(func_def_169, type, ubforcartprodlem3: $o).
% 1.24/0.55 thf(func_def_170, type, cartprodpairin: $o).
% 1.24/0.55 thf(func_def_171, type, cartprodmempair1: $o).
% 1.24/0.55 thf(func_def_172, type, cartprodmempair: $o).
% 1.24/0.55 thf(func_def_173, type, setunionE2: $o).
% 1.24/0.55 thf(func_def_174, type, setunionsingleton1: $o).
% 1.24/0.55 thf(func_def_175, type, setunionsingleton2: $o).
% 1.24/0.55 thf(func_def_176, type, setunionsingleton: $o).
% 1.24/0.55 thf(func_def_177, type, singleton: ($i > $o)).
% 1.24/0.55 thf(func_def_178, type, singletonprop: $o).
% 1.24/0.55 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 1.24/0.55 thf(func_def_180, type, ex1E1: $o).
% 1.24/0.55 thf(func_def_181, type, ex1I: $o).
% 1.24/0.55 thf(func_def_182, type, ex1I2: $o).
% 1.24/0.55 thf(func_def_183, type, singletonsuniq: $o).
% 1.24/0.55 thf(func_def_184, type, atmost1p: ($i > $o)).
% 1.24/0.55 thf(func_def_185, type, atleast2p: ($i > $o)).
% 1.24/0.55 thf(func_def_186, type, atmost2p: ($i > $o)).
% 1.24/0.55 thf(func_def_187, type, upairsetp: ($i > $o)).
% 1.24/0.55 thf(func_def_188, type, setukpairinjL1: $o).
% 1.24/0.55 thf(func_def_189, type, kfstsingleton: $o).
% 1.24/0.55 thf(func_def_190, type, theprop: $o).
% 1.24/0.55 thf(func_def_191, type, kfst: ($i > $i)).
% 1.24/0.55 thf(func_def_192, type, kfstpairEq: $o).
% 1.24/0.55 thf(func_def_193, type, cartprodfstin: $o).
% 1.24/0.55 thf(func_def_194, type, setukpairinjL2: $o).
% 1.24/0.55 thf(func_def_195, type, setukpairinjL: $o).
% 1.24/0.55 thf(func_def_196, type, setukpairinjR11: $o).
% 1.24/0.55 thf(func_def_197, type, setukpairinjR12: $o).
% 1.24/0.55 thf(func_def_198, type, setukpairinjR1: $o).
% 1.24/0.55 thf(func_def_199, type, upairequniteq: $o).
% 1.24/0.55 thf(func_def_200, type, setukpairinjR2: $o).
% 1.24/0.55 thf(func_def_201, type, setukpairinjR: $o).
% 1.24/0.55 thf(func_def_202, type, ksndsingleton: $o).
% 1.24/0.55 thf(func_def_203, type, ksnd: ($i > $i)).
% 1.24/0.55 thf(func_def_204, type, ksndpairEq: $o).
% 1.24/0.55 thf(func_def_205, type, kpairsurjEq: $o).
% 1.24/0.55 thf(func_def_206, type, cartprodsndin: $o).
% 1.24/0.55 thf(func_def_207, type, cartprodpairmemEL: $o).
% 1.24/0.55 thf(func_def_208, type, cartprodpairmemER: $o).
% 1.24/0.55 thf(func_def_209, type, cartprodmempaircEq: $o).
% 1.24/0.55 thf(func_def_210, type, cartprodfstpairEq: $o).
% 1.24/0.55 thf(func_def_211, type, cartprodsndpairEq: $o).
% 1.24/0.55 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 1.24/0.55 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 1.24/0.55 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 1.24/0.55 thf(func_def_215, type, dpsetconstrI: $o).
% 1.24/0.55 thf(func_def_216, type, dpsetconstrSub: $o).
% 1.24/0.55 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 1.24/0.55 thf(func_def_218, type, dpsetconstrERa: $o).
% 1.24/0.55 thf(func_def_219, type, dpsetconstrEL1: $o).
% 1.24/0.55 thf(func_def_220, type, dpsetconstrEL2: $o).
% 1.24/0.55 thf(func_def_221, type, dpsetconstrER: $o).
% 1.24/0.55 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 1.24/0.55 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_224, type, funcImageSingleton: $o).
% 1.24/0.55 thf(func_def_225, type, apProp: $o).
% 1.24/0.55 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_227, type, app: $o).
% 1.24/0.55 thf(func_def_228, type, infuncsetfunc: $o).
% 1.24/0.55 thf(func_def_229, type, ap2p: $o).
% 1.24/0.55 thf(func_def_230, type, funcinfuncset: $o).
% 1.24/0.55 thf(func_def_231, type, lamProp: $o).
% 1.24/0.55 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 1.24/0.55 thf(func_def_233, type, lamp: $o).
% 1.24/0.55 thf(func_def_234, type, lam2p: $o).
% 1.24/0.55 thf(func_def_235, type, brelnall1: $o).
% 1.24/0.55 thf(func_def_236, type, brelnall2: $o).
% 1.24/0.55 thf(func_def_237, type, ex1E2: $o).
% 1.24/0.55 thf(func_def_238, type, funcGraphProp1: $o).
% 1.24/0.55 thf(func_def_239, type, funcGraphProp3: $o).
% 1.24/0.55 thf(func_def_240, type, funcGraphProp2: $o).
% 1.24/0.55 thf(func_def_241, type, funcextLem: $o).
% 1.24/0.55 thf(func_def_242, type, funcGraphProp4: $o).
% 1.24/0.55 thf(func_def_243, type, subbreln: $o).
% 1.24/0.55 thf(func_def_244, type, eqbreln: $o).
% 1.24/0.55 thf(func_def_245, type, funcext: $o).
% 1.24/0.55 thf(func_def_246, type, funcext2: $o).
% 1.24/0.55 thf(func_def_247, type, ap2apEq1: $o).
% 1.24/0.55 thf(func_def_248, type, ap2apEq2: $o).
% 1.24/0.55 thf(func_def_249, type, beta1: $o).
% 1.24/0.55 thf(func_def_250, type, eta1: $o).
% 1.24/0.55 thf(func_def_251, type, lam2lamEq: $o).
% 1.24/0.55 thf(func_def_252, type, beta2: $o).
% 1.24/0.55 thf(func_def_253, type, eta2: $o).
% 1.24/0.55 thf(func_def_254, type, iffalseProp1: $o).
% 1.24/0.55 thf(func_def_255, type, iffalseProp2: $o).
% 1.24/0.55 thf(func_def_256, type, iftrueProp1: $o).
% 1.24/0.55 thf(func_def_257, type, iftrueProp2: $o).
% 1.24/0.55 thf(func_def_258, type, ifSingleton: $o).
% 1.24/0.55 thf(func_def_259, type, if: ($i > $o > $i > $i > $i)).
% 1.24/0.55 thf(func_def_260, type, ifp: $o).
% 1.24/0.55 thf(func_def_261, type, theeq: $o).
% 1.24/0.55 thf(func_def_262, type, iftrue: $o).
% 1.24/0.55 thf(func_def_263, type, iffalse: $o).
% 1.24/0.55 thf(func_def_264, type, iftrueorfalse: $o).
% 1.24/0.55 thf(func_def_265, type, binintersectT_lem: $o).
% 1.24/0.55 thf(func_def_266, type, binunionT_lem: $o).
% 1.24/0.55 thf(func_def_267, type, powersetT_lem: $o).
% 1.24/0.55 thf(func_def_268, type, setminusT_lem: $o).
% 1.24/0.55 thf(func_def_269, type, complementT_lem: $o).
% 1.24/0.55 thf(func_def_270, type, setextT: $o).
% 1.24/0.55 thf(func_def_271, type, subsetTI: $o).
% 1.24/0.55 thf(func_def_274, type, db0: !>[X0: $tType]:(X0)).
% 1.24/0.55 thf(func_def_275, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.24/0.55 thf(func_def_276, type, db1: !>[X0: $tType]:(X0)).
% 1.24/0.55 thf(func_def_277, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.24/0.55 thf(func_def_278, type, vAND: ($o > $o > $o)).
% 1.24/0.55 thf(func_def_279, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.24/0.55 thf(func_def_280, type, vIMP: ($o > $o > $o)).
% 1.24/0.55 thf(func_def_281, type, db2: !>[X0: $tType]:(X0)).
% 1.24/0.55 thf(func_def_282, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.24/0.55 thf(func_def_283, type, vNOT: ($o > $o)).
% 1.24/0.55 thf(func_def_284, type, vOR: ($o > $o > $o)).
% 1.24/0.55 thf(func_def_285, type, sP0: $o).
% 1.24/0.55 thf(func_def_286, type, sP1: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_287, type, sP2: ($i > $o)).
% 1.24/0.55 thf(func_def_288, type, sP3: $o).
% 1.24/0.55 thf(func_def_291, type, sK6: $o).
% 1.24/0.55 thf(func_def_308, type, sK23: ($i > $o)).
% 1.24/0.55 thf(func_def_316, type, sK31: (($i > $o) > $i)).
% 1.24/0.55 thf(func_def_317, type, sK32: ($i > $o)).
% 1.24/0.55 thf(func_def_318, type, sK33: ($i > $i)).
% 1.24/0.55 thf(func_def_322, type, sK37: $o).
% 1.24/0.55 thf(func_def_345, type, sK60: (($i > $o) > $i)).
% 1.24/0.55 thf(func_def_346, type, sK61: ($i > $o)).
% 1.24/0.55 thf(func_def_347, type, sK62: ($i > $i)).
% 1.24/0.55 thf(func_def_349, type, sK64: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_360, type, sK75: ($i > $i)).
% 1.24/0.55 thf(func_def_363, type, sK78: ($i > ($i > $i) > $i > $i)).
% 1.24/0.55 thf(func_def_367, type, sK82: ($i > $i > ($i > $i) > $i)).
% 1.24/0.55 thf(func_def_368, type, sK83: ($i > $i)).
% 1.24/0.55 thf(func_def_394, type, sK109: ($i > $i > ($i > $i) > $i)).
% 1.24/0.55 thf(func_def_395, type, sK110: ($i > $i)).
% 1.24/0.55 thf(func_def_404, type, sK119: $o).
% 1.24/0.55 thf(func_def_407, type, sK122: ($i > $o)).
% 1.24/0.55 thf(func_def_411, type, sK126: ($i > $o)).
% 1.24/0.55 thf(func_def_412, type, sK127: ($i > $o)).
% 1.24/0.55 thf(func_def_413, type, sK128: (($i > $o) > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_414, type, sK129: (($i > $o) > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_422, type, sK137: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_430, type, sK145: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_431, type, sK146: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_432, type, sK147: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_433, type, sK148: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_438, type, sK153: ($i > $i)).
% 1.24/0.55 thf(func_def_449, type, sK164: ($i > $i)).
% 1.24/0.55 thf(func_def_450, type, sK165: (($i > $i) > $i > $i > $i)).
% 1.24/0.55 thf(func_def_456, type, sK171: ($i > $o)).
% 1.24/0.55 thf(func_def_457, type, sK172: ($i > $o)).
% 1.24/0.55 thf(func_def_458, type, sK173: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 1.24/0.55 thf(func_def_459, type, sK174: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 1.24/0.55 thf(func_def_460, type, sK175: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_469, type, sK184: ($i > $o)).
% 1.24/0.55 thf(func_def_471, type, sK186: ($i > ($i > $o) > $i > $i)).
% 1.24/0.55 thf(func_def_476, type, sK191: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_483, type, sK198: $o).
% 1.24/0.55 thf(func_def_490, type, sK205: ($i > $o)).
% 1.24/0.55 thf(func_def_498, type, sK213: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_501, type, sK216: $o).
% 1.24/0.55 thf(func_def_507, type, sK222: ($i > $i)).
% 1.24/0.55 thf(func_def_508, type, sK223: $o).
% 1.24/0.55 thf(func_def_518, type, sK233: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_527, type, sK242: ($i > $o)).
% 1.24/0.55 thf(func_def_529, type, sK244: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_545, type, sK260: ($i > ($i > $i > $o) > $i)).
% 1.24/0.55 thf(func_def_546, type, sK261: ($i > ($i > $i > $o) > $i)).
% 1.24/0.55 thf(func_def_547, type, sK262: ($i > $i > ($i > $i > $o) > $i)).
% 1.24/0.55 thf(func_def_548, type, sK263: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_550, type, sK265: ($i > $i)).
% 1.24/0.55 thf(func_def_551, type, sK266: ($i > $i)).
% 1.24/0.55 thf(func_def_559, type, sK274: ($i > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_560, type, sK275: ($i > $o)).
% 1.24/0.55 thf(func_def_568, type, sK283: $o).
% 1.24/0.55 thf(func_def_576, type, sK291: ($i > $o)).
% 1.24/0.55 thf(func_def_578, type, sK293: ($i > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_581, type, sK296: $o).
% 1.24/0.55 thf(func_def_584, type, sK299: ($i > $o)).
% 1.24/0.55 thf(func_def_591, type, sK306: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_601, type, sK316: ($i > $o)).
% 1.24/0.55 thf(func_def_603, type, sK318: (($i > $o) > $i > $i)).
% 1.24/0.55 thf(func_def_604, type, sK319: (($i > $o) > $i > $i)).
% 1.24/0.55 thf(func_def_609, type, sK324: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_614, type, sK329: (($i > $i) > $i > $i > $i)).
% 1.24/0.55 thf(func_def_617, type, sK332: ($i > $i)).
% 1.24/0.55 thf(func_def_621, type, sK336: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_623, type, sK338: ($i > $o)).
% 1.24/0.55 thf(func_def_625, type, sK340: ($i > $o)).
% 1.24/0.55 thf(func_def_628, type, sK343: ($o > $i > $i > $i)).
% 1.24/0.55 thf(func_def_631, type, sK346: $o).
% 1.24/0.55 thf(func_def_632, type, sK347: ($i > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_633, type, sK348: ($i > $o)).
% 1.24/0.55 thf(func_def_637, type, sK352: $o).
% 1.24/0.55 thf(func_def_652, type, sK367: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_659, type, sK374: ($i > $o)).
% 1.24/0.55 thf(func_def_661, type, sK376: (($i > $o) > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_662, type, sK377: (($i > $o) > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_663, type, sK378: ($i > $o)).
% 1.24/0.55 thf(func_def_666, type, sK381: ($i > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_685, type, sK400: $o).
% 1.24/0.55 thf(func_def_695, type, sK410: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_703, type, sK418: $o).
% 1.24/0.55 thf(func_def_707, type, sK422: ($i > $i)).
% 1.24/0.55 thf(func_def_708, type, sK423: ($i > $i)).
% 1.24/0.55 thf(func_def_709, type, sK424: ($i > $i)).
% 1.24/0.55 thf(func_def_710, type, sK425: ($i > $i)).
% 1.24/0.55 thf(func_def_711, type, sK426: ($i > $i)).
% 1.24/0.55 thf(func_def_712, type, sK427: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_713, type, sK428: ($i > $i)).
% 1.24/0.55 thf(func_def_714, type, sK429: ($i > $i)).
% 1.24/0.55 thf(func_def_715, type, sK430: ($i > $i)).
% 1.24/0.55 thf(func_def_716, type, sK431: ($i > $i)).
% 1.24/0.55 thf(func_def_717, type, sK432: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_718, type, sK433: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_719, type, sK434: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_720, type, sK435: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_721, type, sK436: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_722, type, sK437: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_723, type, sK438: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_724, type, sK439: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_732, type, sK447: $o).
% 1.24/0.55 thf(func_def_743, type, sK458: ($i > $o)).
% 1.24/0.55 thf(func_def_746, type, sK461: ($i > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_748, type, sK463: ($i > $o)).
% 1.24/0.55 thf(func_def_750, type, sK465: (($i > $o) > $i > $i)).
% 1.24/0.55 thf(func_def_751, type, sK466: (($i > $o) > $i > $i)).
% 1.24/0.55 thf(func_def_756, type, sK471: ($i > $i)).
% 1.24/0.55 thf(func_def_759, type, sK474: ($i > $i)).
% 1.24/0.55 thf(func_def_761, type, sK476: $o).
% 1.24/0.55 thf(func_def_763, type, sK478: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_764, type, sK479: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_772, type, sK487: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_778, type, sK493: ($i > $o)).
% 1.24/0.55 thf(func_def_788, type, sK503: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_791, type, sK506: ($i > $o)).
% 1.24/0.55 thf(func_def_792, type, sK507: (($i > $o) > $i)).
% 1.24/0.55 thf(func_def_812, type, sK527: ($i > $o)).
% 1.24/0.55 thf(func_def_813, type, sK528: (($i > $o) > $i > $i)).
% 1.24/0.55 thf(func_def_824, type, sK539: ($i > $o)).
% 1.24/0.55 thf(func_def_828, type, sK543: ($i > $o)).
% 1.24/0.55 thf(func_def_835, type, sK550: ($i > $o)).
% 1.24/0.55 thf(func_def_854, type, sK569: ($i > $o)).
% 1.24/0.55 thf(func_def_857, type, sK572: $o).
% 1.24/0.55 thf(func_def_858, type, sK573: ($i > $o)).
% 1.24/0.55 thf(func_def_861, type, sK576: ($i > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_868, type, sK583: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_872, type, sK587: ($i > $i)).
% 1.24/0.55 thf(func_def_882, type, sK597: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_887, type, sK602: $o).
% 1.24/0.55 thf(func_def_899, type, sK614: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_900, type, sK615: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_906, type, sK621: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_912, type, sK627: ($i > $i)).
% 1.24/0.55 thf(func_def_914, type, sK629: (($i > $i) > $i > $i > $i)).
% 1.24/0.55 thf(func_def_925, type, sK640: ($i > $o)).
% 1.24/0.55 thf(func_def_927, type, sK642: (($i > $o) > $i > $i)).
% 1.24/0.55 thf(func_def_928, type, sK643: (($i > $o) > $i > $i)).
% 1.24/0.55 thf(func_def_930, type, sK645: ($i > $o)).
% 1.24/0.55 thf(func_def_932, type, sK647: (($i > $o) > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_933, type, sK648: (($i > $o) > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_937, type, sK652: ($i > $o)).
% 1.24/0.55 thf(func_def_941, type, sK656: ($i > $i > $o)).
% 1.24/0.55 thf(func_def_951, type, sK666: (($i > $o) > $i)).
% 1.24/0.55 thf(func_def_952, type, sK667: (($i > $o) > $i)).
% 1.24/0.55 thf(func_def_953, type, sK668: ($i > $o)).
% 1.24/0.55 thf(func_def_955, type, sK670: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_956, type, sK671: ($i > $i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_963, type, sK678: $o).
% 1.24/0.55 thf(func_def_971, type, sK686: ($i > $i > $i)).
% 1.24/0.55 thf(func_def_976, type, sK691: ($i > $o)).
% 1.24/0.55 thf(func_def_988, type, sK703: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_989, type, sK704: ($i > $i > $i > $i)).
% 1.24/0.55 thf(func_def_994, type, sK709: ($i > $i)).
% 1.24/0.55 thf(func_def_996, type, sK711: ($i > $i)).
% 1.24/0.55 thf(func_def_997, type, sK712: (($i > $o) > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_998, type, sK713: (($i > $o) > ($i > $o) > $i)).
% 1.24/0.55 thf(func_def_999, type, sK714: ($i > $o)).
% 1.24/0.55 thf(func_def_1000, type, sK715: ($i > $o)).
% 1.24/0.55 thf(f81,axiom,(
% 1.24/0.55 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.24/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 1.24/0.55 thf(f95,axiom,(
% 1.24/0.55 (powersetI1 = ! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 1.24/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1)).
% 1.24/0.55 thf(f96,axiom,(
% 1.24/0.55 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)) = powersetE1)),
% 1.24/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1)).
% 1.24/0.55 thf(f110,axiom,(
% 1.24/0.55 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)) = binintersectEL)),
% 1.24/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL)).
% 1.24/0.55 thf(f117,axiom,(
% 1.24/0.55 (binintersectSubset4 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X0 @ X1)) = X1)))),
% 1.24/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4)).
% 1.24/0.55 thf(f238,conjecture,(
% 1.24/0.55 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 => ! [X1 : $i,X0 : $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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.24/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1)).
% 1.24/0.55 thf(f239,negated_conjecture,(
% 1.24/0.55 ~(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 => ! [X1 : $i,X0 : $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.24/0.55 inference(negated_conjecture,[status(cth)],[f238])).
% 1.24/0.55 thf(f275,plain,(
% 1.24/0.55 (binintersectSubset4 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (((binintersect @ X0 @ X1)) = X1)))),
% 1.24/0.55 inference(rectify,[],[f117])).
% 1.24/0.55 thf(f276,plain,(
% 1.24/0.55 (binintersectSubset4 = $true) <=> ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) => (((binintersect @ X0 @ X1)) = X1))),
% 1.24/0.55 inference(fool_elimination,[],[f275])).
% 1.24/0.55 thf(f311,plain,(
% 1.24/0.55 (powersetI1 = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 1.24/0.55 inference(rectify,[],[f95])).
% 1.24/0.55 thf(f312,plain,(
% 1.24/0.55 (powersetI1 = $true) <=> ! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) => (((in @ X0 @ (powerset @ X1))) = $true))),
% 1.24/0.55 inference(fool_elimination,[],[f311])).
% 1.24/0.55 thf(f328,plain,(
% 1.24/0.55 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 1.24/0.55 inference(rectify,[],[f81])).
% 1.24/0.55 thf(f329,plain,(
% 1.24/0.55 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true)) <=> (subsetI2 = $true)),
% 1.24/0.55 inference(fool_elimination,[],[f328])).
% 1.24/0.55 thf(f341,plain,(
% 1.24/0.55 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (in @ X0 @ (powerset @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.24/0.55 inference(rectify,[],[f239])).
% 1.24/0.55 thf(f342,plain,(
% 1.24/0.55 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X2)) = $true))) => (((in @ X0 @ (powerset @ X2))) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.24/0.55 inference(fool_elimination,[],[f341])).
% 1.24/0.55 thf(f459,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)) = powersetE1)),
% 1.24/0.55 inference(rectify,[],[f96])).
% 1.24/0.55 thf(f460,plain,(
% 1.24/0.55 ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => (((subset @ X0 @ X1)) = $true)) <=> (powersetE1 = $true)),
% 1.24/0.55 inference(fool_elimination,[],[f459])).
% 1.24/0.55 thf(f627,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X2 @ X1)) => (in @ X0 @ X2)) = binintersectEL)),
% 1.24/0.55 inference(rectify,[],[f110])).
% 1.24/0.55 thf(f628,plain,(
% 1.24/0.55 ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) = $true) => (((in @ X0 @ X2)) = $true)) <=> (binintersectEL = $true)),
% 1.24/0.55 inference(fool_elimination,[],[f627])).
% 1.24/0.55 thf(f758,plain,(
% 1.24/0.55 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((((in @ X0 @ (powerset @ X2))) != $true) & ! [X3 : $i] : (((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X0)) != $true)) | (((in @ X3 @ X1)) != $true))) & (((in @ X2 @ (powerset @ X1))) = $true)) & (((in @ X0 @ (powerset @ X1))) = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 1.24/0.55 inference(ennf_transformation,[],[f342])).
% 1.24/0.55 thf(f759,plain,(
% 1.24/0.55 (setadjoinE = $true) & (exuE3e = $true) & (vacuousDall = $true) & (setunionE2 = $true) & (iftrueProp1 = $true) & (setadjoinIR = $true) & (beta2 = $true) & (setukpairinjL = $true) & (dsetconstrI = $true) & (prop2setI = $true) & (upairsetIR = $true) & (ksndpairEq = $true) & (lam2lamEq = $true) & (emptyinunitempty = $true) & (powersetsubset = $true) & (powersetI = $true) & (upairsetIL = $true) & (upairsetE = $true) & (lam2p = $true) & (cartprodmempair1 = $true) & (binunionE = $true) & (upairset2E = $true) & (infuncsetfunc = $true) & (dpsetconstrERa = $true) & (cartprodfstin = $true) & (setunionsingleton2 = $true) & (binunionEcases = $true) & (eta1 = $true) & (iffalseProp2 = $true) & (brelnall2 = $true) & (setukpairinjR12 = $true) & (setadjoinOr = $true) & (cartprodsndpairEq = $true) & (funcext = $true) & (notinemptyset = $true) & (singletonsuniq = $true) & (setminusT_lem = $true) & (setadjoin__Cong = $true) & (cartprodmempair = $true) & (symdiffI1 = $true) & (quantDeMorgan1 = $true) & (nonemptyI1 = $true) & (subPowSU = $true) & (eqimpsubset2 = $true) & (emptysetimpfalse = $true) & (setminusI = $true) & (funcext2 = $true) & (subsetI1 = $true) & (prop2set2propI = $true) & (inCongP = $true) & (setukpairinjR2 = $true) & (emptyI = $true) & (setminusIRneg = $true) & (noeltsimpempty = $true) & (dsetconstrEL = $true) & (exuE3u = $true) & (funcGraphProp1 = $true) & (setukpairIR = $true) & (setunion__Cong = $true) & (emptysetAx = $true) & (prop2setE = $true) & (setminusER = $true) & (singletoninpowunion = $true) & (eqinunit = $true) & (setukpairinjR = $true) & (nonemptyE1 = $true) & (upairset2IR = $true) & (powerset__Cong = $true) & (iffalseProp1 = $true) & (descrp = $true) & (powersetAx = $true) & (ap2p = $true) & (setukpairinjR1 = $true) & (sepSubset = $true) & (iftrueProp2 = $true) & (setadjoinSub = $true) & (setminusSubset1 = $true) & (setminusILneg = $true) & (binunionIR = $true) & (emptyE1 = $true) & (subsetTrans = $true) & (exuE2 = $true) & (bs114d = $true) & (ap2apEq1 = $true) & (powersetT_lem = $true) & (emptyInPowerset = $true) & (setadjoinIL = $true) & (binintersectSubset1 = $true) & (dsetconstr__Cong = $true) & (funcGraphProp4 = $true) & (dsetconstrER = $true) & (upairequniteq = $true) & (setukpairinjR11 = $true) & (setunionI = $true) & (kpairiskpair = $true) & (setukpairIL = $true) & (setminusEL = $true) & (subset2powerset = $true) & (app = $true) & (notdallE = $true) & (setextAx = $true) & (emptyinPowerset = $true) & (setukpairinjL1 = $true) & (setadjoinAx = $true) & (dpsetconstrSub = $true) & (nonemptyImpWitness = $true) & (subsetE = $true) & (ex1E2 = $true) & (descr__Cong = $true) & (binintersectI = $true) & (ubforcartprodlem3 = $true) & (binunionT_lem = $true) & (setunionAx = $true) & (dpsetconstrI = $true) & (powersetE = $true) & (omegaIndAx = $true) & (binintersectER = $true) & (notequalI1 = $true) & (ap2apEq2 = $true) & (ex1I = $true) & (emptyset__Cong = $true) & (powersetI1 = $true) & (singletonsswitch = $true) & (setbeta = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & ? [X2 : $i] : ((((in @ X0 @ (powerset @ X2))) != $true) & (((in @ X2 @ (powerset @ X1))) = $true) & ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true)))) & (kpairp = $true) & (setunionE = $true) & (ubforcartprodlem2 = $true) & (quantDeMorgan3 = $true) & (binintersectSubset4 = $true) & (ifSingleton = $true) & (setextT = $true) & (exuEu = $true) & (setukpairinjL2 = $true) & (subsetI2 = $true) & (exuI1 = $true) & (replAx = $true) & (dpsetconstrEL1 = $true) & (symdiffIneg2 = $true) & (binintersectSubset3 = $true) & (setminusELneg = $true) & (omega__Cong = $true) & (funcinfuncset = $true) & (foundationAx = $true) & (kpairsurjEq = $true) & (symdiffI2 = $true) & (emptysetsubset = $true) & (omega0Ax = $true) & (cartprodpairmemER = $true) & (notdexE = $true) & (quantDeMorgan4 = $true) & (binintersectRsub = $true) & (omegaSAx = $true) & (secondinupair = $true) & (nonemptyI = $true) & (ex1E1 = $true) & (emptysetE = $true) & (lamp = $true) & (binunionLsub = $true) & (kfstsingleton = $true) & (symdiffIneg1 = $true) & (notinsingleton = $true) & (setminusLsub = $true) & (lamProp = $true) & (setminusERneg = $true) & (symdiffE = $true) & (setOfPairsIsBReln = $true) & (upairinpowunion = $true) & (subsetRefl = $true) & (subsetemptysetimpeq = $true) & (funcGraphProp2 = $true) & (singletonsubset = $true) & (ksndsingleton = $true) & (theeq = $true) & (quantDeMorgan2 = $true) & (ifp = $true) & (cartprodpairin = $true) & (eqbreln = $true) & (singletonprop = $true) & (setunionsingleton1 = $true) & (binintersectLsub = $true) & (setadjoinSub2 = $true) & (in__Cong = $true) & (cartprodpairmemEL = $true) & (iftrue = $true) & (setext = $true) & (funcImageSingleton = $true) & (setunionsingleton = $true) & (dpsetconstrEL2 = $true) & (ex1I2 = $true) & (subbreln = $true) & (disjointsetsI1 = $true) & (binintersectSubset2 = $true) & (apProp = $true) & (eqimpsubset1 = $true) & (binunionRsub = $true) & (cartprodsndin = $true) & (binunionIL = $true) & (notsubsetI = $true) & (subsetTI = $true) & (funcextLem = $true) & (sepInPowerset = $true) & (funcGraphProp3 = $true) & (exuI2 = $true) & (complementT_lem = $true) & (uniqinunit = $true) & (kfstpairEq = $true) & (brelnall1 = $true) & (iffalse = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (exuE1 = $true) & (dpsetconstrER = $true) & (subsetE2 = $true) & (ubforcartprodlem1 = $true) & (cartprodpairsurjEq = $true) & (setoftrueEq = $true) & (upairsubunion = $true) & (cartprodfstpairEq = $true) & (beta1 = $true) & (setminusSubset2 = $true) & (cartprodmempaircEq = $true) & (exuI3 = $true) & (eta2 = $true) & (notequalI2 = $true) & (binintersectSubset5 = $true) & (theprop = $true) & (wellorderingAx = $true) & (exu__Cong = $true) & (binintersectEL = $true) & (singletoninpowerset = $true) & (inPowerset = $true) & (setextsub = $true) & (powersetE1 = $true)),
% 1.24/0.55 inference(flattening,[],[f758])).
% 1.24/0.55 thf(f818,plain,(
% 1.24/0.55 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true))),
% 1.24/0.55 inference(ennf_transformation,[],[f329])).
% 1.24/0.55 thf(f876,plain,(
% 1.24/0.55 (powersetI1 = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) | (((subset @ X0 @ X1)) != $true))),
% 1.24/0.55 inference(ennf_transformation,[],[f312])).
% 1.24/0.55 thf(f888,plain,(
% 1.24/0.55 ! [X1 : $i,X0 : $i] : ((((binintersect @ X0 @ X1)) = X1) | (((subset @ X1 @ X0)) != $true)) <=> (binintersectSubset4 = $true)),
% 1.24/0.55 inference(ennf_transformation,[],[f276])).
% 1.24/0.55 thf(f910,plain,(
% 1.24/0.55 ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) != $true) | (((in @ X0 @ X2)) = $true)) <=> (binintersectEL = $true)),
% 1.24/0.55 inference(ennf_transformation,[],[f628])).
% 1.24/0.55 thf(f966,plain,(
% 1.24/0.55 ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) <=> (powersetE1 = $true)),
% 1.24/0.55 inference(ennf_transformation,[],[f460])).
% 1.24/0.55 thf(f1183,plain,(
% 1.24/0.55 ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & (((subset @ X1 @ X0)) != $true))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI2 != $true))),
% 1.24/0.55 inference(nnf_transformation,[],[f818])).
% 1.24/0.55 thf(f1184,plain,(
% 1.24/0.55 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : ((((in @ X5 @ X4)) != $true) & (((in @ X5 @ X3)) = $true)) | (((subset @ X3 @ X4)) = $true)) | (subsetI2 != $true))),
% 1.24/0.55 inference(rectify,[],[f1183])).
% 1.24/0.55 thf(f1185,plain,(
% 1.24/0.55 ((subsetI2 = $true) | (! [X2 : $i] : ((((in @ X2 @ sK190)) = $true) | (((in @ X2 @ sK189)) != $true)) & (((subset @ sK189 @ sK190)) != $true))) & (! [X3 : $i,X4 : $i] : (((((in @ (sK191 @ X4 @ X3) @ X4)) != $true) & ($true = ((in @ (sK191 @ X4 @ X3) @ X3)))) | (((subset @ X3 @ X4)) = $true)) | (subsetI2 != $true))),
% 1.24/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK189,sK190,vAPP]),skolemize(X0,sK189),skolemize(X1,sK190),skolemize(X5,sK33 @ X4)],[f1184])).
% 1.24/0.55 thf(f1244,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (powersetE1 != $true)) & ((powersetE1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & (((in @ X0 @ (powerset @ X1))) = $true)))),
% 1.24/0.55 inference(nnf_transformation,[],[f966])).
% 1.24/0.55 thf(f1245,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (powersetE1 != $true)) & ((powersetE1 = $true) | ? [X2 : $i,X3 : $i] : ((((subset @ X2 @ X3)) != $true) & (((in @ X2 @ (powerset @ X3))) = $true)))),
% 1.24/0.55 inference(rectify,[],[f1244])).
% 1.24/0.55 thf(f1246,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (powersetE1 != $true)) & ((powersetE1 = $true) | ((((subset @ sK248 @ sK249)) != $true) & (((in @ sK248 @ (powerset @ sK249))) = $true)))),
% 1.24/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK248,sK249]),skolemize(X2,sK248),skolemize(X3,sK249)],[f1245])).
% 1.24/0.55 thf(f1377,plain,(
% 1.24/0.55 (! [X1 : $i,X0 : $i] : ((((binintersect @ X0 @ X1)) = X1) | (((subset @ X1 @ X0)) != $true)) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | ? [X1 : $i,X0 : $i] : ((((binintersect @ X0 @ X1)) != X1) & (((subset @ X1 @ X0)) = $true)))),
% 1.24/0.55 inference(nnf_transformation,[],[f888])).
% 1.24/0.55 thf(f1378,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i] : ((((binintersect @ X1 @ X0)) = X0) | (((subset @ X0 @ X1)) != $true)) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | ? [X2 : $i,X3 : $i] : ((((binintersect @ X3 @ X2)) != X2) & (((subset @ X2 @ X3)) = $true)))),
% 1.24/0.55 inference(rectify,[],[f1377])).
% 1.24/0.55 thf(f1379,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i] : ((((binintersect @ X1 @ X0)) = X0) | (((subset @ X0 @ X1)) != $true)) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | ((sK392 != ((binintersect @ sK393 @ sK392))) & (((subset @ sK392 @ sK393)) = $true)))),
% 1.24/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK392,sK393]),skolemize(X2,sK392),skolemize(X3,sK393)],[f1378])).
% 1.24/0.55 thf(f1436,plain,(
% 1.24/0.55 (! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) != $true) | (((in @ X0 @ X2)) = $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) = $true) & (((in @ X0 @ X2)) != $true)))),
% 1.24/0.55 inference(nnf_transformation,[],[f910])).
% 1.24/0.55 thf(f1437,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) != $true) | (((in @ X0 @ X1)) = $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ (binintersect @ X4 @ X5))) = $true) & (((in @ X3 @ X4)) != $true)))),
% 1.24/0.55 inference(rectify,[],[f1436])).
% 1.24/0.55 thf(f1438,plain,(
% 1.24/0.55 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) != $true) | (((in @ X0 @ X1)) = $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ((((in @ sK455 @ (binintersect @ sK456 @ sK457))) = $true) & (((in @ sK455 @ sK456)) != $true)))),
% 1.24/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK455,sK456,sK457]),skolemize(X3,sK455),skolemize(X4,sK456),skolemize(X5,sK457)],[f1437])).
% 1.24/0.55 thf(f1511,plain,(
% 1.24/0.55 (setadjoinE = $true) & (exuE3e = $true) & (vacuousDall = $true) & (setunionE2 = $true) & (iftrueProp1 = $true) & (setadjoinIR = $true) & (beta2 = $true) & (setukpairinjL = $true) & (dsetconstrI = $true) & (prop2setI = $true) & (upairsetIR = $true) & (ksndpairEq = $true) & (lam2lamEq = $true) & (emptyinunitempty = $true) & (powersetsubset = $true) & (powersetI = $true) & (upairsetIL = $true) & (upairsetE = $true) & (lam2p = $true) & (cartprodmempair1 = $true) & (binunionE = $true) & (upairset2E = $true) & (infuncsetfunc = $true) & (dpsetconstrERa = $true) & (cartprodfstin = $true) & (setunionsingleton2 = $true) & (binunionEcases = $true) & (eta1 = $true) & (iffalseProp2 = $true) & (brelnall2 = $true) & (setukpairinjR12 = $true) & (setadjoinOr = $true) & (cartprodsndpairEq = $true) & (funcext = $true) & (notinemptyset = $true) & (singletonsuniq = $true) & (setminusT_lem = $true) & (setadjoin__Cong = $true) & (cartprodmempair = $true) & (symdiffI1 = $true) & (quantDeMorgan1 = $true) & (nonemptyI1 = $true) & (subPowSU = $true) & (eqimpsubset2 = $true) & (emptysetimpfalse = $true) & (setminusI = $true) & (funcext2 = $true) & (subsetI1 = $true) & (prop2set2propI = $true) & (inCongP = $true) & (setukpairinjR2 = $true) & (emptyI = $true) & (setminusIRneg = $true) & (noeltsimpempty = $true) & (dsetconstrEL = $true) & (exuE3u = $true) & (funcGraphProp1 = $true) & (setukpairIR = $true) & (setunion__Cong = $true) & (emptysetAx = $true) & (prop2setE = $true) & (setminusER = $true) & (singletoninpowunion = $true) & (eqinunit = $true) & (setukpairinjR = $true) & (nonemptyE1 = $true) & (upairset2IR = $true) & (powerset__Cong = $true) & (iffalseProp1 = $true) & (descrp = $true) & (powersetAx = $true) & (ap2p = $true) & (setukpairinjR1 = $true) & (sepSubset = $true) & (iftrueProp2 = $true) & (setadjoinSub = $true) & (setminusSubset1 = $true) & (setminusILneg = $true) & (binunionIR = $true) & (emptyE1 = $true) & (subsetTrans = $true) & (exuE2 = $true) & (bs114d = $true) & (ap2apEq1 = $true) & (powersetT_lem = $true) & (emptyInPowerset = $true) & (setadjoinIL = $true) & (binintersectSubset1 = $true) & (dsetconstr__Cong = $true) & (funcGraphProp4 = $true) & (dsetconstrER = $true) & (upairequniteq = $true) & (setukpairinjR11 = $true) & (setunionI = $true) & (kpairiskpair = $true) & (setukpairIL = $true) & (setminusEL = $true) & (subset2powerset = $true) & (app = $true) & (notdallE = $true) & (setextAx = $true) & (emptyinPowerset = $true) & (setukpairinjL1 = $true) & (setadjoinAx = $true) & (dpsetconstrSub = $true) & (nonemptyImpWitness = $true) & (subsetE = $true) & (ex1E2 = $true) & (descr__Cong = $true) & (binintersectI = $true) & (ubforcartprodlem3 = $true) & (binunionT_lem = $true) & (setunionAx = $true) & (dpsetconstrI = $true) & (powersetE = $true) & (omegaIndAx = $true) & (binintersectER = $true) & (notequalI1 = $true) & (ap2apEq2 = $true) & (ex1I = $true) & (emptyset__Cong = $true) & (powersetI1 = $true) & (singletonsswitch = $true) & (setbeta = $true) & ((((in @ sK531 @ (powerset @ sK532))) = $true) & ((((in @ sK531 @ (powerset @ sK533))) != $true) & ($true = ((in @ sK533 @ (powerset @ sK532)))) & ! [X3 : $i] : ((((in @ X3 @ sK531)) != $true) | (((in @ X3 @ sK533)) = $true) | (((in @ X3 @ sK532)) != $true)))) & (kpairp = $true) & (setunionE = $true) & (ubforcartprodlem2 = $true) & (quantDeMorgan3 = $true) & (binintersectSubset4 = $true) & (ifSingleton = $true) & (setextT = $true) & (exuEu = $true) & (setukpairinjL2 = $true) & (subsetI2 = $true) & (exuI1 = $true) & (replAx = $true) & (dpsetconstrEL1 = $true) & (symdiffIneg2 = $true) & (binintersectSubset3 = $true) & (setminusELneg = $true) & (omega__Cong = $true) & (funcinfuncset = $true) & (foundationAx = $true) & (kpairsurjEq = $true) & (symdiffI2 = $true) & (emptysetsubset = $true) & (omega0Ax = $true) & (cartprodpairmemER = $true) & (notdexE = $true) & (quantDeMorgan4 = $true) & (binintersectRsub = $true) & (omegaSAx = $true) & (secondinupair = $true) & (nonemptyI = $true) & (ex1E1 = $true) & (emptysetE = $true) & (lamp = $true) & (binunionLsub = $true) & (kfstsingleton = $true) & (symdiffIneg1 = $true) & (notinsingleton = $true) & (setminusLsub = $true) & (lamProp = $true) & (setminusERneg = $true) & (symdiffE = $true) & (setOfPairsIsBReln = $true) & (upairinpowunion = $true) & (subsetRefl = $true) & (subsetemptysetimpeq = $true) & (funcGraphProp2 = $true) & (singletonsubset = $true) & (ksndsingleton = $true) & (theeq = $true) & (quantDeMorgan2 = $true) & (ifp = $true) & (cartprodpairin = $true) & (eqbreln = $true) & (singletonprop = $true) & (setunionsingleton1 = $true) & (binintersectLsub = $true) & (setadjoinSub2 = $true) & (in__Cong = $true) & (cartprodpairmemEL = $true) & (iftrue = $true) & (setext = $true) & (funcImageSingleton = $true) & (setunionsingleton = $true) & (dpsetconstrEL2 = $true) & (ex1I2 = $true) & (subbreln = $true) & (disjointsetsI1 = $true) & (binintersectSubset2 = $true) & (apProp = $true) & (eqimpsubset1 = $true) & (binunionRsub = $true) & (cartprodsndin = $true) & (binunionIL = $true) & (notsubsetI = $true) & (subsetTI = $true) & (funcextLem = $true) & (sepInPowerset = $true) & (funcGraphProp3 = $true) & (exuI2 = $true) & (complementT_lem = $true) & (uniqinunit = $true) & (kfstpairEq = $true) & (brelnall1 = $true) & (iffalse = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (exuE1 = $true) & (dpsetconstrER = $true) & (subsetE2 = $true) & (ubforcartprodlem1 = $true) & (cartprodpairsurjEq = $true) & (setoftrueEq = $true) & (upairsubunion = $true) & (cartprodfstpairEq = $true) & (beta1 = $true) & (setminusSubset2 = $true) & (cartprodmempaircEq = $true) & (exuI3 = $true) & (eta2 = $true) & (notequalI2 = $true) & (binintersectSubset5 = $true) & (theprop = $true) & (wellorderingAx = $true) & (exu__Cong = $true) & (binintersectEL = $true) & (singletoninpowerset = $true) & (inPowerset = $true) & (setextsub = $true) & (powersetE1 = $true)),
% 1.24/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK531,sK532,sK533]),skolemize(X0,sK531),skolemize(X1,sK532),skolemize(X2,sK533)],[f759])).
% 1.24/0.55 thf(f1527,plain,(
% 1.24/0.55 ((powersetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) & (((subset @ X0 @ X1)) = $true))) & (! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) | (((subset @ X0 @ X1)) != $true)) | (powersetI1 != $true))),
% 1.24/0.55 inference(nnf_transformation,[],[f876])).
% 1.24/0.55 thf(f1528,plain,(
% 1.24/0.55 ((powersetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) & (((subset @ X0 @ X1)) = $true))) & (! [X2 : $i,X3 : $i] : ((((in @ X2 @ (powerset @ X3))) = $true) | (((subset @ X2 @ X3)) != $true)) | (powersetI1 != $true))),
% 1.24/0.55 inference(rectify,[],[f1527])).
% 1.24/0.55 thf(f1529,plain,(
% 1.24/0.55 ((powersetI1 = $true) | ((((in @ sK548 @ (powerset @ sK549))) != $true) & (((subset @ sK548 @ sK549)) = $true))) & (! [X2 : $i,X3 : $i] : ((((in @ X2 @ (powerset @ X3))) = $true) | (((subset @ X2 @ X3)) != $true)) | (powersetI1 != $true))),
% 1.24/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK548,sK549]),skolemize(X0,sK548),skolemize(X1,sK549)],[f1528])).
% 1.24/0.55 thf(f1957,plain,(
% 1.24/0.55 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK191 @ X4 @ X3) @ X3))) | (subsetI2 != $true) | (((subset @ X3 @ X4)) = $true)) )),
% 1.24/0.55 inference(cnf_transformation,[],[f1185])).
% 1.24/0.55 thf(f1958,plain,(
% 1.24/0.55 ( ! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | (((in @ (sK191 @ X4 @ X3) @ X4)) != $true) | (subsetI2 != $true)) )),
% 1.24/0.55 inference(cnf_transformation,[],[f1185])).
% 1.24/0.55 thf(f2033,plain,(
% 1.24/0.55 ( ! [X0 : $i,X1 : $i] : ((powersetE1 != $true) | (((in @ X0 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X1)) = $true)) )),
% 1.24/0.55 inference(cnf_transformation,[],[f1246])).
% 1.24/0.55 thf(f2213,plain,(
% 1.24/0.55 ( ! [X0 : $i,X1 : $i] : ((binintersectSubset4 != $true) | (((binintersect @ X1 @ X0)) = X0) | (((subset @ X0 @ X1)) != $true)) )),
% 1.24/0.55 inference(cnf_transformation,[],[f1379])).
% 1.24/0.55 thf(f2320,plain,(
% 1.24/0.55 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((binintersectEL != $true) | (((in @ X0 @ X1)) = $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) != $true)) )),
% 1.24/0.55 inference(cnf_transformation,[],[f1438])).
% 1.24/0.55 thf(f2417,plain,(
% 1.24/0.55 (powersetE1 = $true)),
% 1.24/0.55 inference(cnf_transformation,[],[f1511])).
% 1.24/0.55 thf(f2421,plain,(
% 1.24/0.55 (binintersectEL = $true)),
% 1.24/0.55 inference(cnf_transformation,[],[f1511])).
% 1.24/0.55 thf(f2516,plain,(
% 1.24/0.55 (subsetI2 = $true)),
% 1.24/0.55 inference(cnf_transformation,[],[f1511])).
% 1.24/0.55 thf(f2521,plain,(
% 1.24/0.55 (binintersectSubset4 = $true)),
% 1.24/0.55 inference(cnf_transformation,[],[f1511])).
% 1.24/0.55 thf(f2526,plain,(
% 1.24/0.55 ( ! [X3 : $i] : ((((in @ X3 @ sK533)) = $true) | (((in @ X3 @ sK532)) != $true) | (((in @ X3 @ sK531)) != $true)) )),
% 1.24/0.55 inference(cnf_transformation,[],[f1511])).
% 1.24/0.55 thf(f2528,plain,(
% 1.24/0.55 (((in @ sK531 @ (powerset @ sK533))) != $true)),
% 1.24/0.55 inference(cnf_transformation,[],[f1511])).
% 1.24/0.55 thf(f2529,plain,(
% 1.24/0.55 (((in @ sK531 @ (powerset @ sK532))) = $true)),
% 1.24/0.55 inference(cnf_transformation,[],[f1511])).
% 1.24/0.55 thf(f2532,plain,(
% 1.24/0.55 (powersetI1 = $true)),
% 1.24/0.55 inference(cnf_transformation,[],[f1511])).
% 1.24/0.55 thf(f2675,plain,(
% 1.24/0.55 ( ! [X2 : $i,X3 : $i] : ((((subset @ X2 @ X3)) != $true) | (powersetI1 != $true) | (((in @ X2 @ (powerset @ X3))) = $true)) )),
% 1.24/0.55 inference(cnf_transformation,[],[f1529])).
% 1.24/0.55 thf(f3137,definition,(
% 1.24/0.55 spl728_3 <=> (subsetI2 = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_3])],[avatar_definition])).
% 1.24/0.55 thf(f4101,definition,(
% 1.24/0.55 spl728_221 <=> (((in @ sK531 @ (powerset @ sK532))) = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_221])],[avatar_definition])).
% 1.24/0.55 thf(f4103,plain,(
% 1.24/0.55 (((in @ sK531 @ (powerset @ sK532))) = $true) | ~spl728_221),
% 1.24/0.55 inference(avatar_component_clause,[],[f4101])).
% 1.24/0.55 thf(f4104,plain,(
% 1.24/0.55 spl728_221),
% 1.24/0.55 inference(avatar_split_clause,[],[f2529,f4101])).
% 1.24/0.55 thf(f4568,definition,(
% 1.24/0.55 spl728_324 <=> (powersetE1 = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_324])],[avatar_definition])).
% 1.24/0.55 thf(f4571,plain,(
% 1.24/0.55 spl728_324),
% 1.24/0.55 inference(avatar_split_clause,[],[f2417,f4568])).
% 1.24/0.55 thf(f4767,definition,(
% 1.24/0.55 spl728_368 <=> (binintersectSubset4 = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_368])],[avatar_definition])).
% 1.24/0.55 thf(f5244,plain,(
% 1.24/0.55 spl728_368),
% 1.24/0.55 inference(avatar_split_clause,[],[f2521,f4767])).
% 1.24/0.55 thf(f5386,definition,(
% 1.24/0.55 spl728_503 <=> ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) | (((in @ X1 @ (powerset @ X0))) = $true))),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_503])],[avatar_definition])).
% 1.24/0.55 thf(f5387,plain,(
% 1.24/0.55 ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) | (((subset @ X1 @ X0)) != $true)) ) | ~spl728_503),
% 1.24/0.55 inference(avatar_component_clause,[],[f5386])).
% 1.24/0.55 thf(f5399,plain,(
% 1.24/0.55 spl728_3),
% 1.24/0.55 inference(avatar_split_clause,[],[f2516,f3137])).
% 1.24/0.55 thf(f5485,definition,(
% 1.24/0.55 spl728_523 <=> (((in @ sK531 @ (powerset @ sK533))) = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_523])],[avatar_definition])).
% 1.24/0.55 thf(f5487,plain,(
% 1.24/0.55 (((in @ sK531 @ (powerset @ sK533))) != $true) | spl728_523),
% 1.24/0.55 inference(avatar_component_clause,[],[f5485])).
% 1.24/0.55 thf(f5488,plain,(
% 1.24/0.55 ~spl728_523),
% 1.24/0.55 inference(avatar_split_clause,[],[f2528,f5485])).
% 1.24/0.55 thf(f5490,definition,(
% 1.24/0.55 spl728_524 <=> ! [X4 : $i,X3 : $i] : ((((subset @ X3 @ X4)) = $true) | (((in @ (sK191 @ X4 @ X3) @ X4)) != $true))),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_524])],[avatar_definition])).
% 1.24/0.55 thf(f5491,plain,(
% 1.24/0.55 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK191 @ X4 @ X3) @ X4)) != $true) | (((subset @ X3 @ X4)) = $true)) ) | ~spl728_524),
% 1.24/0.55 inference(avatar_component_clause,[],[f5490])).
% 1.24/0.55 thf(f5492,plain,(
% 1.24/0.55 ~spl728_3 | spl728_524),
% 1.24/0.55 inference(avatar_split_clause,[],[f1958,f5490,f3137])).
% 1.24/0.55 thf(f5518,definition,(
% 1.24/0.55 spl728_530 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) != $true))),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_530])],[avatar_definition])).
% 1.24/0.55 thf(f5519,plain,(
% 1.24/0.55 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2))) != $true) | (((in @ X0 @ X1)) = $true)) ) | ~spl728_530),
% 1.24/0.55 inference(avatar_component_clause,[],[f5518])).
% 1.24/0.55 thf(f5521,definition,(
% 1.24/0.55 spl728_531 <=> (binintersectEL = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_531])],[avatar_definition])).
% 1.24/0.55 thf(f5524,plain,(
% 1.24/0.55 spl728_530 | ~spl728_531),
% 1.24/0.55 inference(avatar_split_clause,[],[f2320,f5521,f5518])).
% 1.24/0.55 thf(f5923,definition,(
% 1.24/0.55 spl728_619 <=> (powersetI1 = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_619])],[avatar_definition])).
% 1.24/0.55 thf(f6092,definition,(
% 1.24/0.55 spl728_655 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) != $true) | (((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) = $true))),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_655])],[avatar_definition])).
% 1.24/0.55 thf(f6093,plain,(
% 1.24/0.55 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) = $true) | (((subset @ X0 @ X2)) != $true) | (((in @ X1 @ X0)) != $true)) ) | ~spl728_655),
% 1.24/0.55 inference(avatar_component_clause,[],[f6092])).
% 1.24/0.55 thf(f6811,definition,(
% 1.24/0.55 spl728_805 <=> ! [X0 : $i,X1 : $i] : ((((binintersect @ X1 @ X0)) = X0) | (((subset @ X0 @ X1)) != $true))),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_805])],[avatar_definition])).
% 1.24/0.55 thf(f6812,plain,(
% 1.24/0.55 ( ! [X0 : $i,X1 : $i] : ((((binintersect @ X1 @ X0)) = X0) | (((subset @ X0 @ X1)) != $true)) ) | ~spl728_805),
% 1.24/0.55 inference(avatar_component_clause,[],[f6811])).
% 1.24/0.55 thf(f6813,plain,(
% 1.24/0.55 spl728_805 | ~spl728_368),
% 1.24/0.55 inference(avatar_split_clause,[],[f2213,f4767,f6811])).
% 1.24/0.55 thf(f7336,definition,(
% 1.24/0.55 spl728_912 <=> ! [X4 : $i,X3 : $i] : (($true = ((in @ (sK191 @ X4 @ X3) @ X3))) | (((subset @ X3 @ X4)) = $true))),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_912])],[avatar_definition])).
% 1.24/0.55 thf(f7337,plain,(
% 1.24/0.55 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK191 @ X4 @ X3) @ X3))) | (((subset @ X3 @ X4)) = $true)) ) | ~spl728_912),
% 1.24/0.55 inference(avatar_component_clause,[],[f7336])).
% 1.24/0.55 thf(f7338,plain,(
% 1.24/0.55 ~spl728_3 | spl728_912),
% 1.24/0.55 inference(avatar_split_clause,[],[f1957,f7336,f3137])).
% 1.24/0.55 thf(f7463,plain,(
% 1.24/0.55 spl728_503 | ~spl728_619),
% 1.24/0.55 inference(avatar_split_clause,[],[f2675,f5923,f5386])).
% 1.24/0.55 thf(f7536,plain,(
% 1.24/0.55 spl728_531),
% 1.24/0.55 inference(avatar_split_clause,[],[f2421,f5521])).
% 1.24/0.55 thf(f7775,definition,(
% 1.24/0.55 spl728_1001 <=> ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X1)) = $true))),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_1001])],[avatar_definition])).
% 1.24/0.55 thf(f7776,plain,(
% 1.24/0.55 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | (((subset @ X0 @ X1)) = $true)) ) | ~spl728_1001),
% 1.24/0.55 inference(avatar_component_clause,[],[f7775])).
% 1.24/0.55 thf(f7777,plain,(
% 1.24/0.55 spl728_1001 | ~spl728_324),
% 1.24/0.55 inference(avatar_split_clause,[],[f2033,f4568,f7775])).
% 1.24/0.55 thf(f8193,plain,(
% 1.24/0.55 spl728_619),
% 1.24/0.55 inference(avatar_split_clause,[],[f2532,f5923])).
% 1.24/0.55 thf(f9043,plain,(
% 1.24/0.55 ($true != $true) | (((subset @ sK531 @ sK533)) != $true) | (~spl728_503 | spl728_523)),
% 1.24/0.55 inference(superposition,[],[f5487,f5387])).
% 1.24/0.55 thf(f9053,plain,(
% 1.24/0.55 (((subset @ sK531 @ sK533)) != $true) | (~spl728_503 | spl728_523)),
% 1.24/0.55 inference(trivial_inequality_removal,[],[f9043])).
% 1.24/0.55 thf(f9056,definition,(
% 1.24/0.55 spl728_1167 <=> (((subset @ sK531 @ sK533)) = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_1167])],[avatar_definition])).
% 1.24/0.55 thf(f9058,plain,(
% 1.24/0.55 (((subset @ sK531 @ sK533)) != $true) | spl728_1167),
% 1.24/0.55 inference(avatar_component_clause,[],[f9056])).
% 1.24/0.55 thf(f9059,plain,(
% 1.24/0.55 ~spl728_1167 | ~spl728_503 | spl728_523),
% 1.24/0.55 inference(avatar_split_clause,[],[f9053,f5485,f5386,f9056])).
% 1.24/0.55 thf(f9115,plain,(
% 1.24/0.55 ($true != $true) | (((subset @ sK531 @ sK532)) = $true) | (~spl728_221 | ~spl728_1001)),
% 1.24/0.55 inference(superposition,[],[f7776,f4103])).
% 1.24/0.55 thf(f9135,plain,(
% 1.24/0.55 (((subset @ sK531 @ sK532)) = $true) | (~spl728_221 | ~spl728_1001)),
% 1.24/0.55 inference(trivial_inequality_removal,[],[f9115])).
% 1.24/0.55 thf(f9144,definition,(
% 1.24/0.55 spl728_1173 <=> (((subset @ sK531 @ sK532)) = $true)),
% 1.24/0.55 introduced(definition,[new_symbols(definition,[spl728_1173])],[avatar_definition])).
% 1.24/0.55 thf(f9146,plain,(
% 1.24/0.55 (((subset @ sK531 @ sK532)) = $true) | ~spl728_1173),
% 1.24/0.55 inference(avatar_component_clause,[],[f9144])).
% 1.24/0.55 thf(f9147,plain,(
% 1.24/0.55 spl728_1173 | ~spl728_221 | ~spl728_1001),
% 1.24/0.55 inference(avatar_split_clause,[],[f9135,f7775,f4101,f9144])).
% 1.24/0.55 thf(f9254,plain,(
% 1.24/0.55 ( ! [X0 : $i] : ((((subset @ X0 @ sK533)) = $true) | ($true != ((in @ (sK191 @ sK533 @ X0) @ sK532))) | ($true != $true) | (((in @ (sK191 @ sK533 @ X0) @ sK531)) != $true)) ) | ~spl728_524),
% 1.24/0.55 inference(superposition,[],[f5491,f2526])).
% 1.24/0.55 thf(f9255,plain,(
% 1.24/0.55 ( ! [X0 : $i] : (($true != ((in @ (sK191 @ sK533 @ X0) @ sK532))) | (((subset @ X0 @ sK533)) = $true) | (((in @ (sK191 @ sK533 @ X0) @ sK531)) != $true)) ) | ~spl728_524),
% 1.24/0.55 inference(trivial_inequality_removal,[],[f9254])).
% 1.24/0.55 thf(f9263,plain,(
% 1.24/0.55 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) != $true) | (((in @ X1 @ X2)) = $true) | (((in @ X1 @ X0)) != $true)) ) | (~spl728_530 | ~spl728_805)),
% 1.24/0.55 inference(superposition,[],[f5519,f6812])).
% 1.24/0.55 thf(f9278,plain,(
% 1.24/0.55 spl728_655 | ~spl728_530 | ~spl728_805),
% 1.24/0.55 inference(avatar_split_clause,[],[f9263,f6811,f5518,f6092])).
% 1.24/0.55 thf(f9686,plain,(
% 1.24/0.55 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((in @ (sK191 @ sK533 @ X0) @ sK531)) != $true) | ($true != ((in @ (sK191 @ sK533 @ X0) @ X1))) | (((subset @ X1 @ sK532)) != $true) | (((subset @ X0 @ sK533)) = $true)) ) | (~spl728_524 | ~spl728_655)),
% 1.24/0.55 inference(superposition,[],[f9255,f6093])).
% 1.24/0.55 thf(f9715,plain,(
% 1.24/0.55 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK191 @ sK533 @ X0) @ X1))) | (((in @ (sK191 @ sK533 @ X0) @ sK531)) != $true) | (((subset @ X0 @ sK533)) = $true) | (((subset @ X1 @ sK532)) != $true)) ) | (~spl728_524 | ~spl728_655)),
% 1.24/0.55 inference(trivial_inequality_removal,[],[f9686])).
% 1.24/0.55 thf(f10059,plain,(
% 1.24/0.55 ( ! [X0 : $i] : ((((in @ (sK191 @ sK533 @ X0) @ sK531)) != $true) | (((subset @ X0 @ sK533)) = $true) | (((subset @ X0 @ sK533)) = $true) | (((subset @ X0 @ sK532)) != $true) | ($true != $true)) ) | (~spl728_524 | ~spl728_655 | ~spl728_912)),
% 1.24/0.55 inference(superposition,[],[f9715,f7337])).
% 1.24/0.55 thf(f10072,plain,(
% 1.24/0.55 ( ! [X0 : $i] : ((((in @ (sK191 @ sK533 @ X0) @ sK531)) != $true) | ($true != $true) | (((subset @ X0 @ sK533)) = $true) | (((subset @ X0 @ sK532)) != $true)) ) | (~spl728_524 | ~spl728_655 | ~spl728_912)),
% 1.24/0.55 inference(duplicate_literal_removal,[],[f10059])).
% 1.24/0.55 thf(f10073,plain,(
% 1.24/0.55 ( ! [X0 : $i] : ((((in @ (sK191 @ sK533 @ X0) @ sK531)) != $true) | (((subset @ X0 @ sK532)) != $true) | (((subset @ X0 @ sK533)) = $true)) ) | (~spl728_524 | ~spl728_655 | ~spl728_912)),
% 1.24/0.55 inference(trivial_inequality_removal,[],[f10072])).
% 1.24/0.55 thf(f10083,plain,(
% 1.24/0.55 (((subset @ sK531 @ sK533)) = $true) | (((subset @ sK531 @ sK533)) = $true) | ($true != $true) | (((subset @ sK531 @ sK532)) != $true) | (~spl728_524 | ~spl728_655 | ~spl728_912)),
% 1.24/0.55 inference(superposition,[],[f10073,f7337])).
% 1.24/0.55 thf(f10086,plain,(
% 1.24/0.55 (((subset @ sK531 @ sK532)) != $true) | ($true != $true) | (((subset @ sK531 @ sK533)) = $true) | (~spl728_524 | ~spl728_655 | ~spl728_912)),
% 1.24/0.55 inference(duplicate_literal_removal,[],[f10083])).
% 1.24/0.55 thf(f10087,plain,(
% 1.24/0.55 (((subset @ sK531 @ sK533)) = $true) | (((subset @ sK531 @ sK532)) != $true) | (~spl728_524 | ~spl728_655 | ~spl728_912)),
% 1.24/0.55 inference(trivial_inequality_removal,[],[f10086])).
% 1.24/0.55 thf(f10088,plain,(
% 1.24/0.55 (((subset @ sK531 @ sK532)) != $true) | (~spl728_524 | ~spl728_655 | ~spl728_912 | spl728_1167)),
% 1.24/0.55 inference(forward_subsumption_resolution,[],[f10087,f9058])).
% 1.24/0.55 thf(f10089,plain,(
% 1.24/0.55 $false | (~spl728_524 | ~spl728_655 | ~spl728_912 | spl728_1167 | ~spl728_1173)),
% 1.24/0.55 inference(forward_subsumption_resolution,[],[f10088,f9146])).
% 1.24/0.55 thf(f10090,plain,(
% 1.24/0.55 ~spl728_524 | ~spl728_655 | ~spl728_912 | spl728_1167 | ~spl728_1173),
% 1.24/0.55 inference(avatar_contradiction_clause,[],[f10089])).
% 1.24/0.55 cnf(s141, plain, spl728_221, inference(sat_conversion,[],[f4104])).
% 1.24/0.55 cnf(s227, plain, spl728_324, inference(sat_conversion,[],[f4571])).
% 1.24/0.55 cnf(s360, plain, spl728_368, inference(sat_conversion,[],[f5244])).
% 1.24/0.55 cnf(s392, plain, spl728_3, inference(sat_conversion,[],[f5399])).
% 1.24/0.55 cnf(s411, plain, ~spl728_523, inference(sat_conversion,[],[f5488])).
% 1.24/0.55 cnf(s412, plain, ~spl728_3 | spl728_524, inference(sat_conversion,[],[f5492])).
% 1.24/0.55 cnf(s418, plain, spl728_530 | ~spl728_531, inference(sat_conversion,[],[f5524])).
% 1.24/0.55 cnf(s723, plain, ~spl728_368 | spl728_805, inference(sat_conversion,[],[f6813])).
% 1.24/0.55 cnf(s858, plain, ~spl728_3 | spl728_912, inference(sat_conversion,[],[f7338])).
% 1.24/0.55 cnf(s893, plain, spl728_503 | ~spl728_619, inference(sat_conversion,[],[f7463])).
% 1.24/0.55 cnf(s916, plain, spl728_531, inference(sat_conversion,[],[f7536])).
% 1.24/0.55 cnf(s982, plain, ~spl728_324 | spl728_1001, inference(sat_conversion,[],[f7777])).
% 1.24/0.55 cnf(s1089, plain, spl728_619, inference(sat_conversion,[],[f8193])).
% 1.24/0.55 cnf(s1187, plain, ~spl728_503 | spl728_523 | ~spl728_1167, inference(sat_conversion,[],[f9059])).
% 1.24/0.55 cnf(s1192, plain, ~spl728_221 | ~spl728_1001 | spl728_1173, inference(sat_conversion,[],[f9147])).
% 1.24/0.55 cnf(s1199, plain, ~spl728_530 | spl728_655 | ~spl728_805, inference(sat_conversion,[],[f9278])).
% 1.24/0.55 cnf(s1210, plain, ~spl728_524 | ~spl728_655 | ~spl728_912 | spl728_1167 | ~spl728_1173, inference(sat_conversion,[],[f10090])).
% 1.24/0.55 cnf(s1227, plain, spl728_503, inference(rat,[],[s893,s1089])).
% 1.24/0.55 cnf(s1326, plain, spl728_530, inference(rat,[],[s418,s916])).
% 1.24/0.55 cnf(s1328, plain, ~spl728_1167, inference(rat,[],[s1187,s1227,s411])).
% 1.24/0.55 cnf(s1335, plain, spl728_912, inference(rat,[],[s858,s392])).
% 1.24/0.55 cnf(s1336, plain, spl728_524, inference(rat,[],[s412,s392])).
% 1.24/0.55 cnf(s1347, plain, spl728_805, inference(rat,[],[s723,s360])).
% 1.24/0.55 cnf(s1349, plain, spl728_655, inference(rat,[],[s1199,s1326,s1347])).
% 1.24/0.55 cnf(s1350, plain, ~spl728_1173, inference(rat,[],[s1210,s1336,s1328,s1335,s1349])).
% 1.24/0.55 cnf(s1418, plain, spl728_1001, inference(rat,[],[s982,s227])).
% 1.24/0.55 cnf(s1419, plain, ~spl728_221, inference(rat,[],[s1192,s1350,s1418])).
% 1.24/0.55 cnf(s1467, plain, $false, inference(rat,[],[s141,s1419])).
% 1.24/0.55 thf(f10091,plain,(
% 1.24/0.55 $false),
% 1.24/0.55 inference(avatar_sat_refutation,[],[s1467])).
% 1.24/0.55 % SZS output end Proof for theBenchmark
% 1.24/0.55 % (783124)------------------------------
% 1.24/0.55 % (783124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.55 % (783124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.55 % (783124)CaDiCaL version: 2.1.3
% 1.24/0.55 % (783124)Termination reason: Refutation
% 1.24/0.55 % (783124)Time elapsed: 0.206 s
% 1.24/0.55 % (783124)Peak memory usage: 20 MB
% 1.24/0.55 % (783124)Instructions burned: 428 (million)
% 1.24/0.55 % (783116)Success in time 0.256 s
% 1.24/0.55 % Vampire exiting
%------------------------------------------------------------------------------