%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU704^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:51 AM UTC 2026
% Result : Theorem 3.07s 0.88s
% Output : Refutation 3.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU704^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 % Computer : n009.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 14:12:30 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 Running higher-order theorem proving
% 0.23/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.43 % (4063439)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.48/0.43 % (4063466)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.48/0.43 % (4063466)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
% 0.48/0.43 % (4063466)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=1310455676:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.48/0.43 % (4063459)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3930267517:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.48/0.43 % (4063462)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=2971529589: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)
% 0.48/0.43 % (4063461)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2401625338:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.48/0.43 % (4063463)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2532460391:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.48/0.43 % (4063464)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3326423279:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.48/0.43 % (4063461)Instruction limit reached!
% 0.48/0.43 % (4063461)------------------------------
% 0.48/0.43 % (4063461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (4063461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (4063461)CaDiCaL version: 2.1.3
% 0.48/0.43 % (4063461)Termination reason: Instruction limit
% 0.48/0.43 % (4063461)Termination phase: shuffling
% 0.48/0.43 % (4063461)Time elapsed: 0.002 s
% 0.48/0.43 % (4063461)Peak memory usage: 10 MB
% 0.48/0.43 % (4063461)Instructions burned: 4 (million)
% 0.48/0.43 % (4063460)lrs+10_16_si=on:nwc=1.5:random_seed=2412490921:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.48/0.43 % (4063463)Instruction limit reached!
% 0.48/0.43 % (4063463)------------------------------
% 0.48/0.43 % (4063463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (4063463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (4063463)CaDiCaL version: 2.1.3
% 0.48/0.43 % (4063463)Termination reason: Instruction limit
% 0.48/0.43 % (4063463)Termination phase: Property scanning
% 0.48/0.43 % (4063463)Time elapsed: 0.011 s
% 0.48/0.43 % (4063463)Peak memory usage: 10 MB
% 0.48/0.43 % (4063463)Instructions burned: 25 (million)
% 0.48/0.43 % (4063460)Instruction limit reached!
% 0.48/0.43 % (4063460)------------------------------
% 0.48/0.43 % (4063460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (4063460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (4063460)CaDiCaL version: 2.1.3
% 0.48/0.43 % (4063460)Termination reason: Instruction limit
% 0.48/0.43 % (4063460)Termination phase: shuffling
% 0.48/0.43 % (4063460)Time elapsed: 0.009 s
% 0.48/0.43 % (4063460)Peak memory usage: 10 MB
% 0.48/0.43 % (4063460)Instructions burned: 19 (million)
% 0.48/0.43 % (4063485)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4034949187:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.43 % (4063485)Instruction limit reached!
% 0.48/0.43 % (4063485)------------------------------
% 0.48/0.43 % (4063485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (4063485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (4063485)CaDiCaL version: 2.1.3
% 0.48/0.43 % (4063485)Termination reason: Instruction limit
% 0.48/0.43 % (4063485)Termination phase: shuffling
% 0.48/0.43 % (4063485)Time elapsed: 0.002 s
% 0.48/0.43 % (4063485)Peak memory usage: 10 MB
% 0.48/0.43 % (4063485)Instructions burned: 4 (million)
% 0.48/0.43 % (4063466)Instruction limit reached!
% 0.48/0.43 % (4063466)------------------------------
% 0.48/0.43 % (4063466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.46 % (4063466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.46 % (4063466)CaDiCaL version: 2.1.3
% 0.48/0.46 % (4063466)Termination reason: Instruction limit
% 0.48/0.46 % (4063466)Termination phase: Saturation
% 0.48/0.46 % (4063466)Time elapsed: 0.036 s
% 0.48/0.46 % (4063466)Peak memory usage: 13 MB
% 0.48/0.46 % (4063466)Instructions burned: 158 (million)
% 0.48/0.46 % (4063490)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=73077461:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.48/0.46 % (4063491)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.46 % (4063490)Instruction limit reached!
% 0.48/0.46 % (4063490)------------------------------
% 0.48/0.46 % (4063490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.46 % (4063490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.46 % (4063490)CaDiCaL version: 2.1.3
% 0.48/0.46 % (4063490)Termination reason: Instruction limit
% 0.48/0.46 % (4063490)Termination phase: shuffling
% 0.48/0.46 % (4063490)Time elapsed: 0.003 s
% 0.48/0.46 % (4063490)Peak memory usage: 10 MB
% 0.48/0.46 % (4063490)Instructions burned: 6 (million)
% 0.48/0.46 % (4063464)Instruction limit reached!
% 0.48/0.46 % (4063464)------------------------------
% 0.48/0.46 % (4063464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.46 % (4063464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.46 % (4063464)CaDiCaL version: 2.1.3
% 0.48/0.46 % (4063464)Termination reason: Instruction limit
% 0.48/0.46 % (4063464)Termination phase: Preprocessing 3
% 0.48/0.46 % (4063464)Time elapsed: 0.035 s
% 0.48/0.46 % (4063464)Peak memory usage: 12 MB
% 0.48/0.46 % (4063464)Instructions burned: 75 (million)
% 0.48/0.46 % (4063491)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2538850035:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.46 % (4063500)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
% 0.48/0.46 % (4063500)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.46 % (4063500)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2068954689:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.48/0.46 % (4063491)Instruction limit reached!
% 0.48/0.46 % (4063491)------------------------------
% 0.48/0.46 % (4063491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.46 % (4063491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.46 % (4063491)CaDiCaL version: 2.1.3
% 0.48/0.46 % (4063491)Termination reason: Instruction limit
% 0.48/0.46 % (4063491)Termination phase: shuffling
% 0.48/0.46 % (4063491)Time elapsed: 0.004 s
% 0.48/0.46 % (4063491)Peak memory usage: 10 MB
% 0.48/0.46 % (4063491)Instructions burned: 7 (million)
% 0.48/0.46 % (4063459)Instruction limit reached!
% 0.48/0.46 % (4063459)------------------------------
% 0.48/0.46 % (4063459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.46 % (4063459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.46 % (4063459)CaDiCaL version: 2.1.3
% 0.48/0.46 % (4063459)Termination reason: Instruction limit
% 0.48/0.46 % (4063459)Termination phase: Property scanning
% 0.48/0.46 % (4063459)Time elapsed: 0.043 s
% 0.48/0.46 % (4063459)Peak memory usage: 13 MB
% 0.48/0.46 % (4063459)Instructions burned: 88 (million)
% 0.48/0.46 % (4063497)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1434309714:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.48/0.46 % (4063500)Instruction limit reached!
% 0.48/0.46 % (4063500)------------------------------
% 0.48/0.46 % (4063500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.46 % (4063500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.46 % (4063500)CaDiCaL version: 2.1.3
% 0.48/0.46 % (4063500)Termination reason: Instruction limit
% 1.22/0.49 % (4063500)Termination phase: shuffling
% 1.22/0.49 % (4063500)Time elapsed: 0.007 s
% 1.22/0.49 % (4063500)Peak memory usage: 10 MB
% 1.22/0.49 % (4063500)Instructions burned: 31 (million)
% 1.22/0.49 % (4063497)Instruction limit reached!
% 1.22/0.49 % (4063497)------------------------------
% 1.22/0.49 % (4063497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.49 % (4063497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.49 % (4063497)CaDiCaL version: 2.1.3
% 1.22/0.49 % (4063497)Termination reason: Instruction limit
% 1.22/0.49 % (4063497)Termination phase: shuffling
% 1.22/0.49 % (4063497)Time elapsed: 0.006 s
% 1.22/0.49 % (4063497)Peak memory usage: 10 MB
% 1.22/0.49 % (4063497)Instructions burned: 13 (million)
% 1.22/0.49 % (4063502)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=1633984681:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.22/0.49 % (4063507)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.22/0.49 % (4063504)lrs+10_1_si=on:cs=on:random_seed=2931895644:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.22/0.49 % (4063512)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=237055538:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.22/0.49 % (4063507)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=3582837988:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.22/0.49 % (4063504)Instruction limit reached!
% 1.22/0.49 % (4063504)------------------------------
% 1.22/0.49 % (4063504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.49 % (4063504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.49 % (4063504)CaDiCaL version: 2.1.3
% 1.22/0.49 % (4063504)Termination reason: Instruction limit
% 1.22/0.49 % (4063504)Termination phase: shuffling
% 1.22/0.49 % (4063504)Time elapsed: 0.004 s
% 1.22/0.49 % (4063504)Peak memory usage: 10 MB
% 1.22/0.49 % (4063504)Instructions burned: 8 (million)
% 1.22/0.49 % (4063509)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1586738225:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.22/0.49 % (4063507)Instruction limit reached!
% 1.22/0.49 % (4063507)------------------------------
% 1.22/0.49 % (4063507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.49 % (4063507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.49 % (4063507)CaDiCaL version: 2.1.3
% 1.22/0.49 % (4063507)Termination reason: Instruction limit
% 1.22/0.49 % (4063507)Termination phase: shuffling
% 1.22/0.49 % (4063507)Time elapsed: 0.002 s
% 1.22/0.49 % (4063507)Peak memory usage: 10 MB
% 1.22/0.49 % (4063507)Instructions burned: 3 (million)
% 1.22/0.49 % (4063515)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2910568923:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.22/0.49 % (4063522)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=177103844:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.22/0.49 % (4063509)Instruction limit reached!
% 1.22/0.49 % (4063509)------------------------------
% 1.22/0.49 % (4063509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.49 % (4063509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.49 % (4063509)CaDiCaL version: 2.1.3
% 1.22/0.49 % (4063509)Termination reason: Instruction limit
% 1.22/0.49 % (4063509)Termination phase: SInE selection
% 1.22/0.49 % (4063509)Time elapsed: 0.017 s
% 1.22/0.49 % (4063509)Peak memory usage: 11 MB
% 1.22/0.49 % (4063509)Instructions burned: 39 (million)
% 1.22/0.49 % (4063526)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1303698573:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.22/0.49 % (4063515)Instruction limit reached!
% 1.22/0.49 % (4063515)------------------------------
% 1.22/0.49 % (4063515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.49 % (4063515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.54 % (4063515)CaDiCaL version: 2.1.3
% 1.22/0.54 % (4063515)Termination reason: Instruction limit
% 1.22/0.54 % (4063515)Termination phase: Property scanning
% 1.22/0.54 % (4063515)Time elapsed: 0.012 s
% 1.22/0.54 % (4063515)Peak memory usage: 10 MB
% 1.22/0.54 % (4063515)Instructions burned: 26 (million)
% 1.22/0.54 % (4063522)Instruction limit reached!
% 1.22/0.54 % (4063522)------------------------------
% 1.22/0.54 % (4063522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.54 % (4063522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.54 % (4063522)CaDiCaL version: 2.1.3
% 1.22/0.54 % (4063522)Termination reason: Instruction limit
% 1.22/0.54 % (4063522)Termination phase: shuffling
% 1.22/0.54 % (4063522)Time elapsed: 0.007 s
% 1.22/0.54 % (4063522)Peak memory usage: 10 MB
% 1.22/0.54 % (4063522)Instructions burned: 16 (million)
% 1.22/0.54 % (4063502)Instruction limit reached!
% 1.22/0.54 % (4063502)------------------------------
% 1.22/0.54 % (4063502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.54 % (4063502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.54 % (4063502)CaDiCaL version: 2.1.3
% 1.22/0.54 % (4063502)Termination reason: Instruction limit
% 1.22/0.54 % (4063502)Termination phase: Function definition elimination
% 1.22/0.54 % (4063502)Time elapsed: 0.036 s
% 1.22/0.54 % (4063502)Peak memory usage: 11 MB
% 1.22/0.54 % (4063502)Instructions burned: 87 (million)
% 1.22/0.54 % (4063537)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2123944010:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.22/0.54 % (4063540)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=541924349: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)
% 1.22/0.54 % (4063540)Instruction limit reached!
% 1.22/0.54 % (4063540)------------------------------
% 1.22/0.54 % (4063540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.54 % (4063540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.54 % (4063540)CaDiCaL version: 2.1.3
% 1.22/0.54 % (4063540)Termination reason: Instruction limit
% 1.22/0.54 % (4063540)Termination phase: shuffling
% 1.22/0.54 % (4063540)Time elapsed: 0.003 s
% 1.22/0.54 % (4063540)Peak memory usage: 10 MB
% 1.22/0.54 % (4063540)Instructions burned: 6 (million)
% 1.22/0.54 % (4063537)Instruction limit reached!
% 1.22/0.54 % (4063537)------------------------------
% 1.22/0.54 % (4063537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.54 % (4063537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.54 % (4063537)CaDiCaL version: 2.1.3
% 1.22/0.54 % (4063537)Termination reason: Instruction limit
% 1.22/0.54 % (4063537)Termination phase: shuffling
% 1.22/0.54 % (4063537)Time elapsed: 0.007 s
% 1.22/0.54 % (4063537)Peak memory usage: 10 MB
% 1.22/0.54 % (4063537)Instructions burned: 15 (million)
% 1.22/0.54 % (4063541)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2444292332:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.22/0.54 % (4063542)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2191422839:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.22/0.54 % (4063512)Instruction limit reached!
% 1.22/0.54 % (4063512)------------------------------
% 1.22/0.54 % (4063512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.54 % (4063512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.54 % (4063512)CaDiCaL version: 2.1.3
% 1.22/0.54 % (4063512)Termination reason: Instruction limit
% 1.22/0.54 % (4063512)Termination phase: Saturation
% 1.22/0.54 % (4063512)Time elapsed: 0.061 s
% 1.22/0.54 % (4063512)Peak memory usage: 15 MB
% 1.22/0.54 % (4063512)Instructions burned: 250 (million)
% 1.22/0.54 % (4063542)Instruction limit reached!
% 1.22/0.54 % (4063542)------------------------------
% 1.22/0.54 % (4063542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.54 % (4063542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.54 % (4063542)CaDiCaL version: 2.1.3
% 1.22/0.54 % (4063542)Termination reason: Instruction limit
% 1.22/0.54 % (4063542)Termination phase: shuffling
% 1.22/0.54 % (4063542)Time elapsed: 0.011 s
% 1.22/0.54 % (4063542)Peak memory usage: 10 MB
% 1.83/0.60 % (4063542)Instructions burned: 25 (million)
% 1.83/0.60 % (4063550)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
% 1.83/0.60 % (4063550)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.83/0.60 % (4063541)Instruction limit reached!
% 1.83/0.60 % (4063541)------------------------------
% 1.83/0.60 % (4063541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (4063541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (4063541)CaDiCaL version: 2.1.3
% 1.83/0.60 % (4063541)Termination reason: Instruction limit
% 1.83/0.60 % (4063541)Termination phase: shuffling
% 1.83/0.60 % (4063541)Time elapsed: 0.015 s
% 1.83/0.60 % (4063541)Peak memory usage: 10 MB
% 1.83/0.60 % (4063541)Instructions burned: 28 (million)
% 1.83/0.60 % (4063548)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3762039030:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.83/0.60 % (4063550)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=2189743870:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.83/0.60 % (4063556)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.83/0.60 % (4063556)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=1581092228:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.83/0.60 % (4063550)Instruction limit reached!
% 1.83/0.60 % (4063550)------------------------------
% 1.83/0.60 % (4063550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (4063550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (4063550)CaDiCaL version: 2.1.3
% 1.83/0.60 % (4063550)Termination reason: Instruction limit
% 1.83/0.60 % (4063550)Termination phase: shuffling
% 1.83/0.60 % (4063550)Time elapsed: 0.007 s
% 1.83/0.60 % (4063550)Peak memory usage: 10 MB
% 1.83/0.60 % (4063550)Instructions burned: 16 (million)
% 1.83/0.60 % (4063556)Instruction limit reached!
% 1.83/0.60 % (4063556)------------------------------
% 1.83/0.60 % (4063556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (4063556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (4063556)CaDiCaL version: 2.1.3
% 1.83/0.60 % (4063556)Termination reason: Instruction limit
% 1.83/0.60 % (4063556)Termination phase: shuffling
% 1.83/0.60 % (4063556)Time elapsed: 0.002 s
% 1.83/0.60 % (4063556)Peak memory usage: 10 MB
% 1.83/0.60 % (4063556)Instructions burned: 8 (million)
% 1.83/0.60 % (4063557)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=4057313600:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.83/0.60 % (4063560)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=993871531:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.83/0.60 % (4063570)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=501329669:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.83/0.60 % (4063560)Instruction limit reached!
% 1.83/0.60 % (4063560)------------------------------
% 1.83/0.60 % (4063560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (4063560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (4063560)CaDiCaL version: 2.1.3
% 1.83/0.60 % (4063560)Termination reason: Instruction limit
% 1.83/0.60 % (4063560)Termination phase: shuffling
% 1.83/0.60 % (4063560)Time elapsed: 0.004 s
% 1.83/0.60 % (4063560)Peak memory usage: 10 MB
% 1.83/0.60 % (4063560)Instructions burned: 8 (million)
% 1.83/0.60 % (4063570)Instruction limit reached!
% 1.83/0.60 % (4063570)------------------------------
% 1.83/0.60 % (4063570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.60 % (4063570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.60 % (4063570)CaDiCaL version: 2.1.3
% 2.19/0.68 % (4063570)Termination reason: Instruction limit
% 2.19/0.68 % (4063570)Termination phase: shuffling
% 2.19/0.68 % (4063570)Time elapsed: 0.005 s
% 2.19/0.68 % (4063570)Peak memory usage: 10 MB
% 2.19/0.68 % (4063570)Instructions burned: 22 (million)
% 2.19/0.68 % (4063569)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3437662054:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.19/0.68 % (4063548)Instruction limit reached!
% 2.19/0.68 % (4063548)------------------------------
% 2.19/0.68 % (4063548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (4063548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (4063548)CaDiCaL version: 2.1.3
% 2.19/0.68 % (4063548)Termination reason: Instruction limit
% 2.19/0.68 % (4063548)Termination phase: Preprocessing 3
% 2.19/0.68 % (4063548)Time elapsed: 0.028 s
% 2.19/0.68 % (4063548)Peak memory usage: 12 MB
% 2.19/0.68 % (4063548)Instructions burned: 60 (million)
% 2.19/0.68 % (4063557)Instruction limit reached!
% 2.19/0.68 % (4063557)------------------------------
% 2.19/0.68 % (4063557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (4063557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (4063557)CaDiCaL version: 2.1.3
% 2.19/0.68 % (4063557)Termination reason: Instruction limit
% 2.19/0.68 % (4063557)Termination phase: shuffling
% 2.19/0.68 % (4063557)Time elapsed: 0.014 s
% 2.19/0.68 % (4063557)Peak memory usage: 10 MB
% 2.19/0.68 % (4063557)Instructions burned: 31 (million)
% 2.19/0.68 % (4063580)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=27426388:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.19/0.68 % (4063569)Instruction limit reached!
% 2.19/0.68 % (4063569)------------------------------
% 2.19/0.68 % (4063569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (4063569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (4063569)CaDiCaL version: 2.1.3
% 2.19/0.68 % (4063569)Termination reason: Instruction limit
% 2.19/0.68 % (4063569)Termination phase: shuffling
% 2.19/0.68 % (4063569)Time elapsed: 0.011 s
% 2.19/0.68 % (4063569)Peak memory usage: 10 MB
% 2.19/0.68 % (4063569)Instructions burned: 24 (million)
% 2.19/0.68 % (4063579)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2449504505:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.19/0.68 % (4063582)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=825672387:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.19/0.68 % (4063583)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2180540007:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.19/0.68 % (4063588)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.19/0.68 % (4063588)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2213823126:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.19/0.68 % (4063588)Instruction limit reached!
% 2.19/0.68 % (4063588)------------------------------
% 2.19/0.68 % (4063588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (4063588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (4063588)CaDiCaL version: 2.1.3
% 2.19/0.68 % (4063588)Termination reason: Instruction limit
% 2.19/0.68 % (4063588)Termination phase: shuffling
% 2.19/0.68 % (4063588)Time elapsed: 0.004 s
% 2.19/0.68 % (4063588)Peak memory usage: 10 MB
% 2.19/0.68 % (4063588)Instructions burned: 9 (million)
% 2.19/0.68 % (4063583)Instruction limit reached!
% 2.19/0.68 % (4063583)------------------------------
% 2.19/0.68 % (4063583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (4063583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (4063583)CaDiCaL version: 2.1.3
% 2.19/0.68 % (4063583)Termination reason: Instruction limit
% 2.19/0.68 % (4063583)Termination phase: Property scanning
% 2.19/0.68 % (4063583)Time elapsed: 0.019 s
% 2.19/0.68 % (4063583)Peak memory usage: 11 MB
% 2.19/0.68 % (4063583)Instructions burned: 44 (million)
% 2.19/0.68 % (4063580)Instruction limit reached!
% 2.19/0.68 % (4063580)------------------------------
% 2.51/0.76 % (4063580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.76 % (4063580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.76 % (4063580)CaDiCaL version: 2.1.3
% 2.51/0.76 % (4063580)Termination reason: Instruction limit
% 2.51/0.76 % (4063580)Termination phase: Saturation
% 2.51/0.76 % (4063580)Time elapsed: 0.033 s
% 2.51/0.76 % (4063580)Peak memory usage: 13 MB
% 2.51/0.76 % (4063580)Instructions burned: 146 (million)
% 2.51/0.76 % (4063613)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.51/0.76 % (4063613)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2060434170:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.51/0.76 % (4063613)Instruction limit reached!
% 2.51/0.76 % (4063613)------------------------------
% 2.51/0.76 % (4063613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.76 % (4063613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.76 % (4063613)CaDiCaL version: 2.1.3
% 2.51/0.76 % (4063613)Termination reason: Instruction limit
% 2.51/0.76 % (4063613)Termination phase: shuffling
% 2.51/0.76 % (4063613)Time elapsed: 0.001 s
% 2.51/0.76 % (4063613)Peak memory usage: 10 MB
% 2.51/0.76 % (4063613)Instructions burned: 6 (million)
% 2.51/0.76 % (4063608)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3094783511:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.51/0.76 % (4063610)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=486901824:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.51/0.76 % (4063623)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2859342027:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.51/0.76 % (4063623)Instruction limit reached!
% 2.51/0.76 % (4063623)------------------------------
% 2.51/0.76 % (4063623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.76 % (4063623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.76 % (4063623)CaDiCaL version: 2.1.3
% 2.51/0.76 % (4063623)Termination reason: Instruction limit
% 2.51/0.76 % (4063623)Termination phase: shuffling
% 2.51/0.76 % (4063623)Time elapsed: 0.005 s
% 2.51/0.76 % (4063623)Peak memory usage: 10 MB
% 2.51/0.76 % (4063623)Instructions burned: 22 (million)
% 2.51/0.76 % (4063526)Instruction limit reached!
% 2.51/0.76 % (4063526)------------------------------
% 2.51/0.76 % (4063526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.76 % (4063526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.76 % (4063526)CaDiCaL version: 2.1.3
% 2.51/0.76 % (4063526)Termination reason: Instruction limit
% 2.51/0.76 % (4063526)Termination phase: Saturation
% 2.51/0.76 % (4063526)Time elapsed: 0.154 s
% 2.51/0.76 % (4063526)Peak memory usage: 15 MB
% 2.51/0.76 % (4063526)Instructions burned: 328 (million)
% 2.51/0.76 % (4063636)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2428692307:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.51/0.76 % (4063636)Instruction limit reached!
% 2.51/0.76 % (4063636)------------------------------
% 2.51/0.76 % (4063636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.51/0.76 % (4063636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/0.76 % (4063636)CaDiCaL version: 2.1.3
% 2.51/0.76 % (4063636)Termination reason: Instruction limit
% 2.51/0.76 % (4063636)Termination phase: shuffling
% 2.51/0.76 % (4063636)Time elapsed: 0.005 s
% 2.51/0.76 % (4063636)Peak memory usage: 10 MB
% 2.51/0.76 % (4063636)Instructions burned: 22 (million)
% 2.51/0.76 % (4063643)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3430976505:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.51/0.76 % (4063639)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=690061388:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 3.07/0.86 % (4063582)Instruction limit reached!
% 3.07/0.86 % (4063582)------------------------------
% 3.07/0.86 % (4063582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.86 % (4063582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.86 % (4063582)CaDiCaL version: 2.1.3
% 3.07/0.86 % (4063582)Termination reason: Instruction limit
% 3.07/0.86 % (4063582)Termination phase: Saturation
% 3.07/0.86 % (4063582)Time elapsed: 0.082 s
% 3.07/0.86 % (4063582)Peak memory usage: 14 MB
% 3.07/0.86 % (4063582)Instructions burned: 194 (million)
% 3.07/0.86 % (4063646)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=4210386786:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.07/0.86 % (4063610)Instruction limit reached!
% 3.07/0.86 % (4063610)------------------------------
% 3.07/0.86 % (4063610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.86 % (4063610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.86 % (4063610)CaDiCaL version: 2.1.3
% 3.07/0.86 % (4063610)Termination reason: Instruction limit
% 3.07/0.86 % (4063610)Termination phase: Saturation
% 3.07/0.86 % (4063610)Time elapsed: 0.073 s
% 3.07/0.86 % (4063610)Peak memory usage: 13 MB
% 3.07/0.86 % (4063610)Instructions burned: 171 (million)
% 3.07/0.86 % (4063608)Instruction limit reached!
% 3.07/0.86 % (4063608)------------------------------
% 3.07/0.86 % (4063608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.86 % (4063608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.86 % (4063608)CaDiCaL version: 2.1.3
% 3.07/0.86 % (4063608)Termination reason: Instruction limit
% 3.07/0.86 % (4063608)Termination phase: Saturation
% 3.07/0.86 % (4063608)Time elapsed: 0.079 s
% 3.07/0.86 % (4063608)Peak memory usage: 14 MB
% 3.07/0.86 % (4063608)Instructions burned: 182 (million)
% 3.07/0.86 % (4063646)Instruction limit reached!
% 3.07/0.86 % (4063646)------------------------------
% 3.07/0.86 % (4063646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.86 % (4063646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.86 % (4063646)CaDiCaL version: 2.1.3
% 3.07/0.86 % (4063646)Termination reason: Instruction limit
% 3.07/0.86 % (4063646)Termination phase: SInE selection
% 3.07/0.86 % (4063646)Time elapsed: 0.020 s
% 3.07/0.86 % (4063646)Peak memory usage: 11 MB
% 3.07/0.86 % (4063646)Instructions burned: 46 (million)
% 3.07/0.86 % (4063648)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=75507609:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.07/0.86 % (4063649)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3119264316:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.07/0.86 % (4063650)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.07/0.86 % (4063650)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1394472617:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.07/0.86 % (4063649)Instruction limit reached!
% 3.07/0.86 % (4063649)------------------------------
% 3.07/0.86 % (4063649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.86 % (4063649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.86 % (4063649)CaDiCaL version: 2.1.3
% 3.07/0.86 % (4063649)Termination reason: Instruction limit
% 3.07/0.86 % (4063649)Termination phase: shuffling
% 3.07/0.86 % (4063649)Time elapsed: 0.010 s
% 3.07/0.86 % (4063649)Peak memory usage: 10 MB
% 3.07/0.86 % (4063649)Instructions burned: 21 (million)
% 3.07/0.86 % (4063462)Instruction limit reached!
% 3.07/0.86 % (4063462)------------------------------
% 3.07/0.86 % (4063462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.86 % (4063462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.86 % (4063462)CaDiCaL version: 2.1.3
% 3.07/0.86 % (4063462)Termination reason: Instruction limit
% 3.07/0.86 % (4063462)Termination phase: Saturation
% 3.07/0.87 % (4063462)Time elapsed: 0.337 s
% 3.07/0.87 % (4063462)Peak memory usage: 20 MB
% 3.07/0.87 % (4063462)Instructions burned: 635 (million)
% 3.07/0.87 % (4063654)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1973146625:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.07/0.87 % (4063654)Instruction limit reached!
% 3.07/0.87 % (4063654)------------------------------
% 3.07/0.87 % (4063654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063654)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063654)Termination reason: Instruction limit
% 3.07/0.87 % (4063654)Termination phase: shuffling
% 3.07/0.87 % (4063654)Time elapsed: 0.006 s
% 3.07/0.87 % (4063654)Peak memory usage: 10 MB
% 3.07/0.87 % (4063654)Instructions burned: 13 (million)
% 3.07/0.87 % (4063655)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=27596877:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.07/0.87 % (4063657)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=307520702:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.07/0.87 % (4063655)Instruction limit reached!
% 3.07/0.87 % (4063655)------------------------------
% 3.07/0.87 % (4063655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063655)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063655)Termination reason: Instruction limit
% 3.07/0.87 % (4063655)Termination phase: SInE selection
% 3.07/0.87 % (4063655)Time elapsed: 0.028 s
% 3.07/0.87 % (4063655)Peak memory usage: 11 MB
% 3.07/0.87 % (4063655)Instructions burned: 68 (million)
% 3.07/0.87 % (4063657)Instruction limit reached!
% 3.07/0.87 % (4063657)------------------------------
% 3.07/0.87 % (4063657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063657)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063657)Termination reason: Instruction limit
% 3.07/0.87 % (4063657)Termination phase: Property scanning
% 3.07/0.87 % (4063657)Time elapsed: 0.023 s
% 3.07/0.87 % (4063657)Peak memory usage: 11 MB
% 3.07/0.87 % (4063657)Instructions burned: 53 (million)
% 3.07/0.87 % (4063650)Instruction limit reached!
% 3.07/0.87 % (4063650)------------------------------
% 3.07/0.87 % (4063650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063650)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063650)Termination reason: Instruction limit
% 3.07/0.87 % (4063650)Termination phase: Saturation
% 3.07/0.87 % (4063650)Time elapsed: 0.087 s
% 3.07/0.87 % (4063650)Peak memory usage: 14 MB
% 3.07/0.87 % (4063650)Instructions burned: 202 (million)
% 3.07/0.87 % (4063660)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3332270319:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.07/0.87 % (4063661)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1409085458:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.07/0.87 % (4063639)Instruction limit reached!
% 3.07/0.87 % (4063639)------------------------------
% 3.07/0.87 % (4063639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063639)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063639)Termination reason: Instruction limit
% 3.07/0.87 % (4063639)Termination phase: Saturation
% 3.07/0.87 % (4063639)Time elapsed: 0.154 s
% 3.07/0.87 % (4063639)Peak memory usage: 14 MB
% 3.07/0.87 % (4063639)Instructions burned: 317 (million)
% 3.07/0.87 % (4063660)Instruction limit reached!
% 3.07/0.87 % (4063660)------------------------------
% 3.07/0.87 % (4063660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063660)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063660)Termination reason: Instruction limit
% 3.07/0.87 % (4063660)Termination phase: shuffling
% 3.07/0.87 % (4063660)Time elapsed: 0.014 s
% 3.07/0.87 % (4063660)Peak memory usage: 10 MB
% 3.07/0.87 % (4063660)Instructions burned: 31 (million)
% 3.07/0.87 % (4063662)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=974121557:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.07/0.87 % (4063665)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1973030942:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 3.07/0.87 % (4063666)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.07/0.87 % (4063662)Instruction limit reached!
% 3.07/0.87 % (4063662)------------------------------
% 3.07/0.87 % (4063662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063662)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063662)Termination reason: Instruction limit
% 3.07/0.87 % (4063662)Termination phase: Property scanning
% 3.07/0.87 % (4063662)Time elapsed: 0.015 s
% 3.07/0.87 % (4063662)Peak memory usage: 10 MB
% 3.07/0.87 % (4063662)Instructions burned: 34 (million)
% 3.07/0.87 % (4063666)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1185877013:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 3.07/0.87 % (4063670)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1884769254:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 3.07/0.87 % (4063665)Instruction limit reached!
% 3.07/0.87 % (4063665)------------------------------
% 3.07/0.87 % (4063665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063665)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063665)Termination reason: Instruction limit
% 3.07/0.87 % (4063665)Termination phase: Property scanning
% 3.07/0.87 % (4063665)Time elapsed: 0.029 s
% 3.07/0.87 % (4063665)Peak memory usage: 11 MB
% 3.07/0.87 % (4063665)Instructions burned: 67 (million)
% 3.07/0.87 % (4063661)Instruction limit reached!
% 3.07/0.87 % (4063661)------------------------------
% 3.07/0.87 % (4063661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063661)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063661)Termination reason: Instruction limit
% 3.07/0.87 % (4063661)Termination phase: Saturation
% 3.07/0.87 % (4063661)Time elapsed: 0.057 s
% 3.07/0.87 % (4063661)Peak memory usage: 13 MB
% 3.07/0.87 % (4063661)Instructions burned: 138 (million)
% 3.07/0.87 % (4063672)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1513864265:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 3.07/0.87 % (4063673)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1065443859:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 3.07/0.87 % (4063643)Instruction limit reached!
% 3.07/0.87 % (4063643)------------------------------
% 3.07/0.87 % (4063643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063643)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063643)Termination reason: Instruction limit
% 3.07/0.87 % (4063643)Termination phase: Saturation
% 3.07/0.87 % (4063643)Time elapsed: 0.241 s
% 3.07/0.87 % (4063643)Peak memory usage: 22 MB
% 3.07/0.87 % (4063643)Instructions burned: 854 (million)
% 3.07/0.87 % (4063676)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4272891877:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 3.07/0.87 % (4063666)Instruction limit reached!
% 3.07/0.87 % (4063666)------------------------------
% 3.07/0.87 % (4063666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.87 % (4063666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.87 % (4063666)CaDiCaL version: 2.1.3
% 3.07/0.87 % (4063666)Termination reason: Instruction limit
% 3.07/0.87 % (4063666)Termination phase: Saturation
% 3.07/0.87 % (4063666)Time elapsed: 0.077 s
% 3.07/0.87 % (4063666)Peak memory usage: 13 MB
% 3.07/0.87 % (4063666)Instructions burned: 181 (million)
% 3.07/0.87 % (4063648) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4063439-4063648"...
% 3.07/0.88 % (4063672)Instruction limit reached!
% 3.07/0.88 % (4063672)------------------------------
% 3.07/0.88 % (4063672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.88 % (4063672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.88 % (4063672)CaDiCaL version: 2.1.3
% 3.07/0.88 % (4063672)Termination reason: Instruction limit
% 3.07/0.88 % (4063672)Termination phase: Twee Goal Transformation
% 3.07/0.88 % (4063672)Time elapsed: 0.041 s
% 3.07/0.88 % (4063672)Peak memory usage: 12 MB
% 3.07/0.88 % (4063672)Instructions burned: 98 (million)
% 3.07/0.88 % (4063648)...printing done.
% 3.07/0.88 % (4063648)Refutation found. Thanks to Tanya!
% 3.07/0.88 % SZS status Theorem for theBenchmark
% 3.07/0.88 % SZS output start Proof for theBenchmark
% 3.07/0.88 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.07/0.88 thf(func_def_0, type, in: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 3.07/0.88 thf(func_def_3, type, setextAx: $o).
% 3.07/0.88 thf(func_def_5, type, emptysetAx: $o).
% 3.07/0.88 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_7, type, setadjoinAx: $o).
% 3.07/0.88 thf(func_def_8, type, powerset: ($i > $i)).
% 3.07/0.88 thf(func_def_9, type, powersetAx: $o).
% 3.07/0.88 thf(func_def_10, type, setunion: ($i > $i)).
% 3.07/0.88 thf(func_def_11, type, setunionAx: $o).
% 3.07/0.88 thf(func_def_13, type, omega0Ax: $o).
% 3.07/0.88 thf(func_def_14, type, omegaSAx: $o).
% 3.07/0.88 thf(func_def_15, type, omegaIndAx: $o).
% 3.07/0.88 thf(func_def_16, type, replAx: $o).
% 3.07/0.88 thf(func_def_17, type, foundationAx: $o).
% 3.07/0.88 thf(func_def_18, type, wellorderingAx: $o).
% 3.07/0.88 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 3.07/0.88 thf(func_def_20, type, descrp: $o).
% 3.07/0.88 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_22, type, dsetconstrI: $o).
% 3.07/0.88 thf(func_def_23, type, dsetconstrEL: $o).
% 3.07/0.88 thf(func_def_24, type, dsetconstrER: $o).
% 3.07/0.88 thf(func_def_25, type, exuE1: $o).
% 3.07/0.88 thf(func_def_26, type, prop2set: ($o > $i)).
% 3.07/0.88 thf(func_def_27, type, prop2setE: $o).
% 3.07/0.88 thf(func_def_28, type, emptysetE: $o).
% 3.07/0.88 thf(func_def_29, type, emptysetimpfalse: $o).
% 3.07/0.88 thf(func_def_30, type, notinemptyset: $o).
% 3.07/0.88 thf(func_def_31, type, exuE3e: $o).
% 3.07/0.88 thf(func_def_32, type, setext: $o).
% 3.07/0.88 thf(func_def_33, type, emptyI: $o).
% 3.07/0.88 thf(func_def_34, type, noeltsimpempty: $o).
% 3.07/0.88 thf(func_def_35, type, setbeta: $o).
% 3.07/0.88 thf(func_def_36, type, nonempty: ($i > $o)).
% 3.07/0.88 thf(func_def_37, type, nonemptyE1: $o).
% 3.07/0.88 thf(func_def_38, type, nonemptyI: $o).
% 3.07/0.88 thf(func_def_39, type, nonemptyI1: $o).
% 3.07/0.88 thf(func_def_40, type, setadjoinIL: $o).
% 3.07/0.88 thf(func_def_41, type, emptyinunitempty: $o).
% 3.07/0.88 thf(func_def_42, type, setadjoinIR: $o).
% 3.07/0.88 thf(func_def_43, type, setadjoinE: $o).
% 3.07/0.88 thf(func_def_44, type, setadjoinOr: $o).
% 3.07/0.88 thf(func_def_45, type, setoftrueEq: $o).
% 3.07/0.88 thf(func_def_46, type, powersetI: $o).
% 3.07/0.88 thf(func_def_47, type, emptyinPowerset: $o).
% 3.07/0.88 thf(func_def_48, type, emptyInPowerset: $o).
% 3.07/0.88 thf(func_def_49, type, powersetE: $o).
% 3.07/0.88 thf(func_def_50, type, setunionI: $o).
% 3.07/0.88 thf(func_def_51, type, setunionE: $o).
% 3.07/0.88 thf(func_def_52, type, subPowSU: $o).
% 3.07/0.88 thf(func_def_53, type, exuE2: $o).
% 3.07/0.88 thf(func_def_54, type, nonemptyImpWitness: $o).
% 3.07/0.88 thf(func_def_55, type, uniqinunit: $o).
% 3.07/0.88 thf(func_def_56, type, notinsingleton: $o).
% 3.07/0.88 thf(func_def_57, type, eqinunit: $o).
% 3.07/0.88 thf(func_def_58, type, singletonsswitch: $o).
% 3.07/0.88 thf(func_def_59, type, upairsetE: $o).
% 3.07/0.88 thf(func_def_60, type, upairsetIL: $o).
% 3.07/0.88 thf(func_def_61, type, upairsetIR: $o).
% 3.07/0.88 thf(func_def_62, type, emptyE1: $o).
% 3.07/0.88 thf(func_def_63, type, vacuousDall: $o).
% 3.07/0.88 thf(func_def_64, type, quantDeMorgan1: $o).
% 3.07/0.88 thf(func_def_65, type, quantDeMorgan2: $o).
% 3.07/0.88 thf(func_def_66, type, quantDeMorgan3: $o).
% 3.07/0.88 thf(func_def_67, type, quantDeMorgan4: $o).
% 3.07/0.88 thf(func_def_68, type, prop2setI: $o).
% 3.07/0.88 thf(func_def_69, type, set2prop: ($i > $o)).
% 3.07/0.88 thf(func_def_70, type, prop2set2propI: $o).
% 3.07/0.88 thf(func_def_71, type, notdexE: $o).
% 3.07/0.88 thf(func_def_72, type, notdallE: $o).
% 3.07/0.88 thf(func_def_73, type, exuI1: $o).
% 3.07/0.88 thf(func_def_74, type, exuI3: $o).
% 3.07/0.88 thf(func_def_75, type, exuI2: $o).
% 3.07/0.88 thf(func_def_76, type, inCongP: $o).
% 3.07/0.88 thf(func_def_77, type, in__Cong: $o).
% 3.07/0.88 thf(func_def_78, type, exuE3u: $o).
% 3.07/0.88 thf(func_def_79, type, exu__Cong: $o).
% 3.07/0.88 thf(func_def_80, type, emptyset__Cong: $o).
% 3.07/0.88 thf(func_def_81, type, setadjoin__Cong: $o).
% 3.07/0.88 thf(func_def_82, type, powerset__Cong: $o).
% 3.07/0.88 thf(func_def_83, type, setunion__Cong: $o).
% 3.07/0.88 thf(func_def_84, type, omega__Cong: $o).
% 3.07/0.88 thf(func_def_85, type, exuEu: $o).
% 3.07/0.88 thf(func_def_86, type, descr__Cong: $o).
% 3.07/0.88 thf(func_def_87, type, dsetconstr__Cong: $o).
% 3.07/0.88 thf(func_def_88, type, subset: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_91, type, subsetI1: $o).
% 3.07/0.88 thf(func_def_92, type, eqimpsubset2: $o).
% 3.07/0.88 thf(func_def_93, type, eqimpsubset1: $o).
% 3.07/0.88 thf(func_def_94, type, subsetI2: $o).
% 3.07/0.88 thf(func_def_95, type, emptysetsubset: $o).
% 3.07/0.88 thf(func_def_96, type, subsetE: $o).
% 3.07/0.88 thf(func_def_97, type, subsetE2: $o).
% 3.07/0.88 thf(func_def_98, type, notsubsetI: $o).
% 3.07/0.88 thf(func_def_99, type, notequalI1: $o).
% 3.07/0.88 thf(func_def_100, type, notequalI2: $o).
% 3.07/0.88 thf(func_def_101, type, subsetRefl: $o).
% 3.07/0.88 thf(func_def_102, type, subsetTrans: $o).
% 3.07/0.88 thf(func_def_103, type, setadjoinSub: $o).
% 3.07/0.88 thf(func_def_104, type, setadjoinSub2: $o).
% 3.07/0.88 thf(func_def_105, type, subset2powerset: $o).
% 3.07/0.88 thf(func_def_106, type, setextsub: $o).
% 3.07/0.88 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 3.07/0.88 thf(func_def_108, type, powersetI1: $o).
% 3.07/0.88 thf(func_def_109, type, powersetE1: $o).
% 3.07/0.88 thf(func_def_110, type, inPowerset: $o).
% 3.07/0.88 thf(func_def_111, type, powersetsubset: $o).
% 3.07/0.88 thf(func_def_112, type, sepInPowerset: $o).
% 3.07/0.88 thf(func_def_113, type, sepSubset: $o).
% 3.07/0.88 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_115, type, binunionIL: $o).
% 3.07/0.88 thf(func_def_116, type, upairset2IR: $o).
% 3.07/0.88 thf(func_def_117, type, binunionIR: $o).
% 3.07/0.88 thf(func_def_118, type, binunionEcases: $o).
% 3.07/0.88 thf(func_def_119, type, binunionE: $o).
% 3.07/0.88 thf(func_def_120, type, binunionLsub: $o).
% 3.07/0.88 thf(func_def_121, type, binunionRsub: $o).
% 3.07/0.88 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_123, type, binintersectI: $o).
% 3.07/0.88 thf(func_def_124, type, binintersectSubset5: $o).
% 3.07/0.88 thf(func_def_125, type, binintersectEL: $o).
% 3.07/0.88 thf(func_def_126, type, binintersectLsub: $o).
% 3.07/0.88 thf(func_def_127, type, binintersectSubset2: $o).
% 3.07/0.88 thf(func_def_128, type, binintersectSubset3: $o).
% 3.07/0.88 thf(func_def_129, type, binintersectER: $o).
% 3.07/0.88 thf(func_def_130, type, disjointsetsI1: $o).
% 3.07/0.88 thf(func_def_131, type, binintersectRsub: $o).
% 3.07/0.88 thf(func_def_132, type, binintersectSubset4: $o).
% 3.07/0.88 thf(func_def_133, type, binintersectSubset1: $o).
% 3.07/0.88 thf(func_def_134, type, bs114d: $o).
% 3.07/0.88 thf(func_def_135, type, regular: ($i > $o)).
% 3.07/0.88 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_137, type, setminusI: $o).
% 3.07/0.88 thf(func_def_138, type, setminusEL: $o).
% 3.07/0.88 thf(func_def_139, type, setminusER: $o).
% 3.07/0.88 thf(func_def_140, type, setminusSubset2: $o).
% 3.07/0.88 thf(func_def_141, type, setminusERneg: $o).
% 3.07/0.88 thf(func_def_142, type, setminusELneg: $o).
% 3.07/0.88 thf(func_def_143, type, setminusILneg: $o).
% 3.07/0.88 thf(func_def_144, type, setminusIRneg: $o).
% 3.07/0.88 thf(func_def_145, type, setminusLsub: $o).
% 3.07/0.88 thf(func_def_146, type, setminusSubset1: $o).
% 3.07/0.88 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_148, type, symdiffE: $o).
% 3.07/0.88 thf(func_def_149, type, symdiffI1: $o).
% 3.07/0.88 thf(func_def_150, type, symdiffI2: $o).
% 3.07/0.88 thf(func_def_151, type, symdiffIneg1: $o).
% 3.07/0.88 thf(func_def_152, type, symdiffIneg2: $o).
% 3.07/0.88 thf(func_def_153, type, iskpair: ($i > $o)).
% 3.07/0.88 thf(func_def_154, type, secondinupair: $o).
% 3.07/0.88 thf(func_def_155, type, setukpairIL: $o).
% 3.07/0.88 thf(func_def_156, type, setukpairIR: $o).
% 3.07/0.88 thf(func_def_157, type, kpairiskpair: $o).
% 3.07/0.88 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_159, type, kpairp: $o).
% 3.07/0.88 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_161, type, singletonsubset: $o).
% 3.07/0.88 thf(func_def_162, type, singletoninpowerset: $o).
% 3.07/0.88 thf(func_def_163, type, singletoninpowunion: $o).
% 3.07/0.88 thf(func_def_164, type, upairset2E: $o).
% 3.07/0.88 thf(func_def_165, type, upairsubunion: $o).
% 3.07/0.88 thf(func_def_166, type, upairinpowunion: $o).
% 3.07/0.88 thf(func_def_167, type, ubforcartprodlem1: $o).
% 3.07/0.88 thf(func_def_168, type, ubforcartprodlem2: $o).
% 3.07/0.88 thf(func_def_169, type, ubforcartprodlem3: $o).
% 3.07/0.88 thf(func_def_170, type, cartprodpairin: $o).
% 3.07/0.88 thf(func_def_171, type, cartprodmempair1: $o).
% 3.07/0.88 thf(func_def_172, type, cartprodmempair: $o).
% 3.07/0.88 thf(func_def_173, type, setunionE2: $o).
% 3.07/0.88 thf(func_def_174, type, setunionsingleton1: $o).
% 3.07/0.88 thf(func_def_175, type, setunionsingleton2: $o).
% 3.07/0.88 thf(func_def_176, type, setunionsingleton: $o).
% 3.07/0.88 thf(func_def_177, type, singleton: ($i > $o)).
% 3.07/0.88 thf(func_def_178, type, singletonprop: $o).
% 3.07/0.88 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 3.07/0.88 thf(func_def_180, type, ex1E1: $o).
% 3.07/0.88 thf(func_def_181, type, ex1I: $o).
% 3.07/0.88 thf(func_def_182, type, ex1I2: $o).
% 3.07/0.88 thf(func_def_183, type, singletonsuniq: $o).
% 3.07/0.88 thf(func_def_184, type, atmost1p: ($i > $o)).
% 3.07/0.88 thf(func_def_185, type, atleast2p: ($i > $o)).
% 3.07/0.88 thf(func_def_186, type, atmost2p: ($i > $o)).
% 3.07/0.88 thf(func_def_187, type, upairsetp: ($i > $o)).
% 3.07/0.88 thf(func_def_188, type, setukpairinjL1: $o).
% 3.07/0.88 thf(func_def_189, type, kfstsingleton: $o).
% 3.07/0.88 thf(func_def_190, type, theprop: $o).
% 3.07/0.88 thf(func_def_191, type, kfst: ($i > $i)).
% 3.07/0.88 thf(func_def_192, type, kfstpairEq: $o).
% 3.07/0.88 thf(func_def_193, type, cartprodfstin: $o).
% 3.07/0.88 thf(func_def_194, type, setukpairinjL2: $o).
% 3.07/0.88 thf(func_def_195, type, setukpairinjL: $o).
% 3.07/0.88 thf(func_def_196, type, setukpairinjR11: $o).
% 3.07/0.88 thf(func_def_197, type, setukpairinjR12: $o).
% 3.07/0.88 thf(func_def_198, type, setukpairinjR1: $o).
% 3.07/0.88 thf(func_def_199, type, upairequniteq: $o).
% 3.07/0.88 thf(func_def_200, type, setukpairinjR2: $o).
% 3.07/0.88 thf(func_def_201, type, setukpairinjR: $o).
% 3.07/0.88 thf(func_def_202, type, ksndsingleton: $o).
% 3.07/0.88 thf(func_def_203, type, ksnd: ($i > $i)).
% 3.07/0.88 thf(func_def_204, type, ksndpairEq: $o).
% 3.07/0.88 thf(func_def_205, type, kpairsurjEq: $o).
% 3.07/0.88 thf(func_def_206, type, cartprodsndin: $o).
% 3.07/0.88 thf(func_def_207, type, cartprodpairmemEL: $o).
% 3.07/0.88 thf(func_def_208, type, cartprodpairmemER: $o).
% 3.07/0.88 thf(func_def_209, type, cartprodmempaircEq: $o).
% 3.07/0.88 thf(func_def_210, type, cartprodfstpairEq: $o).
% 3.07/0.88 thf(func_def_211, type, cartprodsndpairEq: $o).
% 3.07/0.88 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 3.07/0.88 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 3.07/0.88 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 3.07/0.88 thf(func_def_215, type, dpsetconstrI: $o).
% 3.07/0.88 thf(func_def_216, type, dpsetconstrSub: $o).
% 3.07/0.88 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 3.07/0.88 thf(func_def_218, type, dpsetconstrERa: $o).
% 3.07/0.88 thf(func_def_219, type, dpsetconstrEL1: $o).
% 3.07/0.88 thf(func_def_220, type, dpsetconstrEL2: $o).
% 3.07/0.88 thf(func_def_221, type, dpsetconstrER: $o).
% 3.07/0.88 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 3.07/0.88 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_224, type, funcImageSingleton: $o).
% 3.07/0.88 thf(func_def_225, type, apProp: $o).
% 3.07/0.88 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_227, type, app: $o).
% 3.07/0.88 thf(func_def_228, type, infuncsetfunc: $o).
% 3.07/0.88 thf(func_def_229, type, ap2p: $o).
% 3.07/0.88 thf(func_def_230, type, funcinfuncset: $o).
% 3.07/0.88 thf(func_def_231, type, lamProp: $o).
% 3.07/0.88 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 3.07/0.88 thf(func_def_233, type, lamp: $o).
% 3.07/0.88 thf(func_def_234, type, lam2p: $o).
% 3.07/0.88 thf(func_def_235, type, brelnall1: $o).
% 3.07/0.88 thf(func_def_236, type, brelnall2: $o).
% 3.07/0.88 thf(func_def_237, type, ex1E2: $o).
% 3.07/0.88 thf(func_def_238, type, funcGraphProp1: $o).
% 3.07/0.88 thf(func_def_239, type, funcGraphProp3: $o).
% 3.07/0.88 thf(func_def_240, type, funcGraphProp2: $o).
% 3.07/0.88 thf(func_def_241, type, funcextLem: $o).
% 3.07/0.88 thf(func_def_242, type, funcGraphProp4: $o).
% 3.07/0.88 thf(func_def_243, type, subbreln: $o).
% 3.07/0.88 thf(func_def_244, type, eqbreln: $o).
% 3.07/0.88 thf(func_def_245, type, funcext: $o).
% 3.07/0.88 thf(func_def_246, type, funcext2: $o).
% 3.07/0.88 thf(func_def_247, type, ap2apEq1: $o).
% 3.07/0.88 thf(func_def_248, type, ap2apEq2: $o).
% 3.07/0.88 thf(func_def_249, type, beta1: $o).
% 3.07/0.88 thf(func_def_250, type, eta1: $o).
% 3.07/0.88 thf(func_def_251, type, lam2lamEq: $o).
% 3.07/0.88 thf(func_def_252, type, beta2: $o).
% 3.07/0.88 thf(func_def_253, type, eta2: $o).
% 3.07/0.88 thf(func_def_254, type, iffalseProp1: $o).
% 3.07/0.88 thf(func_def_255, type, iffalseProp2: $o).
% 3.07/0.88 thf(func_def_256, type, iftrueProp1: $o).
% 3.07/0.88 thf(func_def_257, type, iftrueProp2: $o).
% 3.07/0.88 thf(func_def_260, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.07/0.88 thf(func_def_261, type, vAND: ($o > $o > $o)).
% 3.07/0.88 thf(func_def_262, type, db0: !>[X0: $tType]:(X0)).
% 3.07/0.88 thf(func_def_263, type, db1: !>[X0: $tType]:(X0)).
% 3.07/0.88 thf(func_def_264, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.07/0.88 thf(func_def_265, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.07/0.88 thf(func_def_266, type, vOR: ($o > $o > $o)).
% 3.07/0.88 thf(func_def_267, type, vNOT: ($o > $o)).
% 3.07/0.88 thf(func_def_268, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.07/0.88 thf(func_def_269, type, vIMP: ($o > $o > $o)).
% 3.07/0.88 thf(func_def_270, type, db2: !>[X0: $tType]:(X0)).
% 3.07/0.88 thf(func_def_271, type, sP0: $o).
% 3.07/0.88 thf(func_def_272, type, sP1: $o).
% 3.07/0.88 thf(func_def_273, type, sP2: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_274, type, sP3: ($i > $o)).
% 3.07/0.88 thf(func_def_275, type, sP4: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_276, type, sP5: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_277, type, sP6: $o).
% 3.07/0.88 thf(func_def_278, type, sP7: ($i > $i > $i > $o > $o)).
% 3.07/0.88 thf(func_def_279, type, sP8: $o).
% 3.07/0.88 thf(func_def_280, type, sP9: ($i > $i > $i > $i > $o)).
% 3.07/0.88 thf(func_def_281, type, sP10: $o).
% 3.07/0.88 thf(func_def_283, type, sK12: ($i > $i)).
% 3.07/0.88 thf(func_def_294, type, sK23: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_295, type, sK24: ($i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_296, type, sK25: ($i > $o)).
% 3.07/0.88 thf(func_def_300, type, sK29: ($i > $o)).
% 3.07/0.88 thf(func_def_311, type, sK40: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_313, type, sK42: ($i > $o)).
% 3.07/0.88 thf(func_def_316, type, sK45: ($i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_317, type, sK46: ($i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_320, type, sK49: (($i > $o) > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_321, type, sK50: (($i > $o) > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_322, type, sK51: ($i > $o)).
% 3.07/0.88 thf(func_def_323, type, sK52: ($i > $o)).
% 3.07/0.88 thf(func_def_324, type, sK53: $o).
% 3.07/0.88 thf(func_def_326, type, sK55: ($i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_327, type, sK56: ($i > $o)).
% 3.07/0.88 thf(func_def_338, type, sK67: ($i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_339, type, sK68: ($i > $o)).
% 3.07/0.88 thf(func_def_346, type, sK75: ($i > $i)).
% 3.07/0.88 thf(func_def_348, type, sK77: ($i > ($i > $i) > $i > $i)).
% 3.07/0.88 thf(func_def_352, type, sK81: ($i > $i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_353, type, sK82: ($i > $o)).
% 3.07/0.88 thf(func_def_358, type, sK87: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_360, type, sK89: ($i > $i)).
% 3.07/0.88 thf(func_def_361, type, sK90: ($i > $i)).
% 3.07/0.88 thf(func_def_362, type, sK91: ($i > ($i > $i > $o) > $i)).
% 3.07/0.88 thf(func_def_363, type, sK92: ($i > ($i > $i > $o) > $i)).
% 3.07/0.88 thf(func_def_364, type, sK93: ($i > $i > ($i > $i > $o) > $i)).
% 3.07/0.88 thf(func_def_392, type, sK121: ($i > $i)).
% 3.07/0.88 thf(func_def_394, type, sK123: ($i > ($i > $i) > $i > $i)).
% 3.07/0.88 thf(func_def_401, type, sK130: ($i > $o)).
% 3.07/0.88 thf(func_def_406, type, sK135: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_411, type, sK140: (($i > $o) > $i > $i)).
% 3.07/0.88 thf(func_def_413, type, sK142: ($i > $o)).
% 3.07/0.88 thf(func_def_426, type, sK155: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_434, type, sK163: $o).
% 3.07/0.88 thf(func_def_435, type, sK164: (($i > $o) > $i)).
% 3.07/0.88 thf(func_def_436, type, sK165: ($i > $o)).
% 3.07/0.88 thf(func_def_465, type, sK194: (($i > $i) > $i > $i > $i)).
% 3.07/0.88 thf(func_def_468, type, sK197: ($i > $i)).
% 3.07/0.88 thf(func_def_488, type, sK217: ($i > $i)).
% 3.07/0.88 thf(func_def_490, type, sK219: ($i > $i)).
% 3.07/0.88 thf(func_def_495, type, sK224: ($i > $o)).
% 3.07/0.88 thf(func_def_499, type, sK228: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_506, type, sK235: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_510, type, sK239: $o).
% 3.07/0.88 thf(func_def_511, type, sK240: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_512, type, sK241: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_513, type, sK242: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_514, type, sK243: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_515, type, sK244: ($i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_516, type, sK245: ($i > $i)).
% 3.07/0.88 thf(func_def_517, type, sK246: ($i > $i)).
% 3.07/0.88 thf(func_def_518, type, sK247: ($i > $i)).
% 3.07/0.88 thf(func_def_519, type, sK248: ($i > $i)).
% 3.07/0.88 thf(func_def_520, type, sK249: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_521, type, sK250: ($i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_522, type, sK251: ($i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_523, type, sK252: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_524, type, sK253: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_526, type, sK255: ($i > $i)).
% 3.07/0.88 thf(func_def_527, type, sK256: ($i > $i)).
% 3.07/0.88 thf(func_def_528, type, sK257: ($i > $i)).
% 3.07/0.88 thf(func_def_529, type, sK258: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_534, type, sK263: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_539, type, sK268: ($i > $i)).
% 3.07/0.88 thf(func_def_543, type, sK272: (($i > $o) > $i > $i)).
% 3.07/0.88 thf(func_def_545, type, sK274: ($i > $o)).
% 3.07/0.88 thf(func_def_554, type, sK283: ($i > $i)).
% 3.07/0.88 thf(func_def_556, type, sK285: (($i > $i) > $i > $i > $i)).
% 3.07/0.88 thf(func_def_557, type, sK286: ($i > $o)).
% 3.07/0.88 thf(func_def_558, type, sK287: ($i > $i)).
% 3.07/0.88 thf(func_def_559, type, sK288: (($i > $o) > $i)).
% 3.07/0.88 thf(func_def_561, type, sK290: ($i > $o)).
% 3.07/0.88 thf(func_def_564, type, sK293: ($i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_565, type, sK294: ($i > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_576, type, sK305: (($i > $o) > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_577, type, sK306: (($i > $o) > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_581, type, sK310: ($i > $o)).
% 3.07/0.88 thf(func_def_587, type, sK316: ($i > $o)).
% 3.07/0.88 thf(func_def_589, type, sK318: (($i > $o) > $i > $i)).
% 3.07/0.88 thf(func_def_592, type, sK321: $o).
% 3.07/0.88 thf(func_def_596, type, sK325: (($i > $o) > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_597, type, sK326: (($i > $o) > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_601, type, sK330: ($i > $o)).
% 3.07/0.88 thf(func_def_605, type, sK334: ($i > $o)).
% 3.07/0.88 thf(func_def_608, type, sK337: ($i > $o)).
% 3.07/0.88 thf(func_def_613, type, sK342: ($i > $i > ($i > $i) > $i)).
% 3.07/0.88 thf(func_def_614, type, sK343: ($i > $i)).
% 3.07/0.88 thf(func_def_619, type, sK348: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_628, type, sK357: (($i > $o) > $i > $i)).
% 3.07/0.88 thf(func_def_630, type, sK359: ($i > $o)).
% 3.07/0.88 thf(func_def_647, type, sK376: (($i > $o) > $i)).
% 3.07/0.88 thf(func_def_648, type, sK377: (($i > $o) > $i)).
% 3.07/0.88 thf(func_def_649, type, sK378: ($i > $o)).
% 3.07/0.88 thf(func_def_653, type, sK382: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_656, type, sK385: (($i > $o) > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_657, type, sK386: (($i > $o) > ($i > $o) > $i)).
% 3.07/0.88 thf(func_def_658, type, sK387: ($i > $o)).
% 3.07/0.88 thf(func_def_659, type, sK388: ($i > $o)).
% 3.07/0.88 thf(func_def_666, type, sK395: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_668, type, sK397: ($i > $o)).
% 3.07/0.88 thf(func_def_679, type, sK408: $o).
% 3.07/0.88 thf(func_def_692, type, sK421: $o).
% 3.07/0.88 thf(func_def_693, type, sK422: ($i > $i)).
% 3.07/0.88 thf(func_def_695, type, sK424: ($i > $i)).
% 3.07/0.88 thf(func_def_725, type, sK454: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_729, type, sK458: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_732, type, sK461: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_740, type, sK469: ($i > $o)).
% 3.07/0.88 thf(func_def_746, type, sK475: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_755, type, sK484: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_758, type, sK487: ($i > $i)).
% 3.07/0.88 thf(func_def_762, type, sK491: $o).
% 3.07/0.88 thf(func_def_771, type, sK500: (($i > $o) > $i > $i)).
% 3.07/0.88 thf(func_def_773, type, sK502: ($i > $o)).
% 3.07/0.88 thf(func_def_775, type, sK504: $o).
% 3.07/0.88 thf(func_def_788, type, sK517: $o).
% 3.07/0.88 thf(func_def_801, type, sK530: ($i > $o)).
% 3.07/0.88 thf(func_def_814, type, sK543: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_815, type, sK544: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_816, type, sK545: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_817, type, sK546: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_818, type, sK547: ($i > $o)).
% 3.07/0.88 thf(func_def_831, type, sK560: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_835, type, sK564: (($i > $o) > $i)).
% 3.07/0.88 thf(func_def_836, type, sK565: ($i > $o)).
% 3.07/0.88 thf(func_def_837, type, sK566: ($i > $i)).
% 3.07/0.88 thf(func_def_840, type, sK569: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_841, type, sK570: ($i > $i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_866, type, sK595: $o).
% 3.07/0.88 thf(func_def_874, type, sK603: ($o > $i > $i > $i)).
% 3.07/0.88 thf(func_def_877, type, sK606: $o).
% 3.07/0.88 thf(func_def_880, type, sK609: ($i > $o)).
% 3.07/0.88 thf(func_def_881, type, sK610: ($i > $o)).
% 3.07/0.88 thf(func_def_882, type, sK611: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 3.07/0.88 thf(func_def_883, type, sK612: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 3.07/0.88 thf(func_def_890, type, sK619: ($i > $o)).
% 3.07/0.88 thf(func_def_904, type, sK633: ($i > $o)).
% 3.07/0.88 thf(func_def_907, type, sK636: ($i > $i)).
% 3.07/0.88 thf(func_def_909, type, sK638: ($i > ($i > $i) > $i > $i)).
% 3.07/0.88 thf(func_def_911, type, sK640: $o).
% 3.07/0.88 thf(func_def_915, type, sK644: ($i > $o)).
% 3.07/0.88 thf(func_def_932, type, sK661: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_933, type, sK662: ($i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_934, type, sK663: ($i > $i > $i > $i)).
% 3.07/0.88 thf(func_def_939, type, sK668: ($i > $o)).
% 3.07/0.88 thf(func_def_941, type, sK670: (($i > $o) > $i > $i)).
% 3.07/0.88 thf(func_def_945, type, sK674: ($i > $i > $o)).
% 3.07/0.88 thf(func_def_951, type, sK680: $o).
% 3.07/0.88 thf(func_def_957, type, sK686: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_958, type, sK687: ($i > $i > $i)).
% 3.07/0.88 thf(func_def_960, type, sK689: ($i > $o)).
% 3.07/0.88 thf(f157,axiom,(
% 3.07/0.88 (! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))) = singletonprop)),
% 3.07/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop)).
% 3.07/0.88 thf(f226,conjecture,(
% 3.07/0.88 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 => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 3.07/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton)).
% 3.07/0.88 thf(f227,negated_conjecture,(
% 3.07/0.88 ~(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 => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 3.07/0.88 inference(negated_conjecture,[status(cth)],[f226])).
% 3.07/0.88 thf(f251,plain,(
% 3.07/0.88 (! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((in @ X4 @ X0) & (X1 @ X4)) => (singleton @ (dsetconstr @ X0 @ (^[X5 : $i] : ((X1 @ X5))))))) = singletonprop)),
% 3.07/0.88 inference(rectify,[],[f157])).
% 3.07/0.88 thf(f252,plain,(
% 3.07/0.88 (singletonprop = $true) <=> ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((X1 @ X2)) = $true) => ((((X1 @ X3)) = $true) => (X2 = X3))))) => (? [X4 : $i] : ((((in @ X4 @ X0)) = $true) & (((X1 @ X4)) = $true)) => (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true)))),
% 3.07/0.88 inference(fool_elimination,[],[f251])).
% 3.07/0.88 thf(f329,plain,(
% 3.07/0.88 ~(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 => ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (singleton @ (dsetconstr @ X2 @ (^[X4 : $i] : (((X4 = X3) & ~X0) | ((X1 = X4) & X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 3.07/0.88 inference(rectify,[],[f227])).
% 3.07/0.88 thf(f330,plain,(
% 3.07/0.88 ~((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) => ! [X1 : $i,X2 : $i,X0 : $o] : ((((in @ X1 @ X2)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X2)) = $true) => (((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0))))))) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 3.07/0.88 inference(fool_elimination,[],[f329])).
% 3.07/0.88 thf(f765,plain,(
% 3.07/0.88 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0))))))) != $true)) & (((in @ X1 @ X2)) = $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)),
% 3.07/0.88 inference(ennf_transformation,[],[f330])).
% 3.07/0.88 thf(f766,plain,(
% 3.07/0.88 (setukpairIL = $true) & (setminusSubset1 = $true) & (uniqinunit = $true) & (upairset2E = $true) & (subsetE = $true) & (setadjoin__Cong = $true) & (cartprodpairin = $true) & (funcextLem = $true) & (binintersectSubset1 = $true) & (emptyinPowerset = $true) & (kfstpairEq = $true) & (eqinunit = $true) & (setbeta = $true) & (subsetI2 = $true) & (singletonsubset = $true) & (eqimpsubset2 = $true) & (ap2p = $true) & (lam2p = $true) & (lam2lamEq = $true) & (setunionAx = $true) & (setukpairinjL2 = $true) & (setunionsingleton1 = $true) & (exuE3u = $true) & (singletonsuniq = $true) & (cartprodmempair1 = $true) & (inPowerset = $true) & (symdiffI2 = $true) & (singletoninpowerset = $true) & (notequalI2 = $true) & (setukpairinjR2 = $true) & (setadjoinOr = $true) & (ap2apEq2 = $true) & (notdexE = $true) & (subbreln = $true) & (exuI3 = $true) & (exuI2 = $true) & (subPowSU = $true) & (binintersectER = $true) & (singletoninpowunion = $true) & (powersetI = $true) & (emptysetE = $true) & (emptysetAx = $true) & (setukpairinjR = $true) & (sepSubset = $true) & (binintersectSubset4 = $true) & (symdiffE = $true) & (cartprodmempair = $true) & (ex1I = $true) & (setextsub = $true) & (setoftrueEq = $true) & (bs114d = $true) & (kpairsurjEq = $true) & (notinsingleton = $true) & (setunionI = $true) & (setukpairinjL1 = $true) & (setext = $true) & (cartprodmempaircEq = $true) & (app = $true) & (setunionE = $true) & (binintersectRsub = $true) & (powerset__Cong = $true) & (binunionE = $true) & (funcImageSingleton = $true) & (notequalI1 = $true) & (infuncsetfunc = $true) & (exuEu = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (setextAx = $true) & (binunionEcases = $true) & (upairsetIL = $true) & (setunionE2 = $true) & (descrp = $true) & (setminusERneg = $true) & (ex1I2 = $true) & (iffalseProp1 = $true) & (setminusILneg = $true) & (cartprodpairmemEL = $true) & (prop2set2propI = $true) & (setminusLsub = $true) & (notsubsetI = $true) & (lamProp = $true) & (upairsetIR = $true) & (emptyI = $true) & (ex1E1 = $true) & (emptyInPowerset = $true) & (symdiffI1 = $true) & (vacuousDall = $true) & (sepInPowerset = $true) & (nonemptyI = $true) & (apProp = $true) & (binintersectSubset2 = $true) & (powersetE = $true) & (dpsetconstrSub = $true) & (dsetconstr__Cong = $true) & (beta1 = $true) & (subsetI1 = $true) & (setminusER = $true) & (setunionsingleton2 = $true) & (subset2powerset = $true) & (quantDeMorgan1 = $true) & (powersetsubset = $true) & (brelnall1 = $true) & (funcext = $true) & (nonemptyI1 = $true) & (secondinupair = $true) & (setunion__Cong = $true) & (exu__Cong = $true) & (eta2 = $true) & (binintersectLsub = $true) & (cartprodpairmemER = $true) & (setadjoinSub = $true) & (wellorderingAx = $true) & (setminusIRneg = $true) & (upairsubunion = $true) & (kpairiskpair = $true) & (dsetconstrI = $true) & (ksndpairEq = $true) & (singletonprop = $true) & (setminusEL = $true) & (dpsetconstrEL1 = $true) & (emptyE1 = $true) & (setukpairinjL = $true) & (kfstsingleton = $true) & (ubforcartprodlem2 = $true) & (notinemptyset = $true) & (omega__Cong = $true) & (subsetTrans = $true) & (setadjoinIR = $true) & (funcext2 = $true) & (powersetI1 = $true) & (setOfPairsIsBReln = $true) & (exuE2 = $true) & (dpsetconstrI = $true) & (symdiffIneg2 = $true) & (setminusSubset2 = $true) & (ubforcartprodlem3 = $true) & (iftrueProp1 = $true) & (upairset2IR = $true) & (binintersectSubset3 = $true) & (nonemptyImpWitness = $true) & (prop2setI = $true) & (descr__Cong = $true) & (cartprodsndpairEq = $true) & (setukpairinjR11 = $true) & (binunionIR = $true) & (exuE3e = $true) & (cartprodfstpairEq = $true) & (funcGraphProp4 = $true) & (setminusI = $true) & (foundationAx = $true) & (cartprodfstin = $true) & (upairsetE = $true) & (dpsetconstrEL2 = $true) & (ap2apEq1 = $true) & (funcGraphProp2 = $true) & (powersetE1 = $true) & (binunionRsub = $true) & (funcinfuncset = $true) & (powersetAx = $true) & (subsetE2 = $true) & (eqimpsubset1 = $true) & (theprop = $true) & (setminusELneg = $true) & (eta1 = $true) & (dpsetconstrERa = $true) & (exuE1 = $true) & ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0))))))) != $true)) & (((in @ X1 @ X2)) = $true)) & (brelnall2 = $true) & (subsetRefl = $true) & (beta2 = $true) & (eqbreln = $true) & (setadjoinSub2 = $true) & (setunionsingleton = $true) & (emptysetimpfalse = $true) & (disjointsetsI1 = $true) & (kpairp = $true) & (ubforcartprodlem1 = $true) & (setadjoinE = $true) & (binintersectI = $true) & (funcGraphProp3 = $true) & (notdallE = $true) & (binunionLsub = $true) & (omegaSAx = $true) & (singletonsswitch = $true) & (subsetemptysetimpeq = $true) & (iffalseProp2 = $true) & (replAx = $true) & (emptyinunitempty = $true) & (dpsetconstrER = $true) & (emptysetsubset = $true) & (exuI1 = $true) & (dsetconstrER = $true) & (prop2setE = $true) & (setadjoinAx = $true) & (ksndsingleton = $true) & (setukpairinjR1 = $true) & (iftrueProp2 = $true) & (ex1E2 = $true) & (binunionIL = $true) & (noeltsimpempty = $true) & (symdiffIneg1 = $true) & (setukpairinjR12 = $true) & (setukpairIR = $true) & (quantDeMorgan3 = $true) & (binintersectSubset5 = $true) & (cartprodsndin = $true) & (funcGraphProp1 = $true) & (omegaIndAx = $true) & (upairequniteq = $true) & (in__Cong = $true) & (quantDeMorgan2 = $true) & (upairinpowunion = $true) & (binintersectEL = $true) & (dsetconstrEL = $true) & (omega0Ax = $true) & (emptyset__Cong = $true) & (cartprodpairsurjEq = $true) & (quantDeMorgan4 = $true) & (lamp = $true) & (setadjoinIL = $true)),
% 3.07/0.88 inference(flattening,[],[f765])).
% 3.07/0.88 thf(f881,plain,(
% 3.07/0.88 (singletonprop = $true) <=> ! [X0 : $i,X1 : ($i > $o)] : (((((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true) | ! [X4 : $i] : ((((X1 @ X4)) != $true) | (((in @ X4 @ X0)) != $true))) | ? [X2 : $i] : (? [X3 : $i] : ((((X2 != X3) & (((X1 @ X3)) = $true)) & (((X1 @ X2)) = $true)) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ X0)) = $true)))),
% 3.07/0.88 inference(ennf_transformation,[],[f252])).
% 3.07/0.88 thf(f882,plain,(
% 3.07/0.88 (singletonprop = $true) <=> ! [X1 : ($i > $o),X0 : $i] : (! [X4 : $i] : ((((X1 @ X4)) != $true) | (((in @ X4 @ X0)) != $true)) | (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true) | ? [X2 : $i] : (? [X3 : $i] : ((X2 != X3) & (((X1 @ X2)) = $true) & (((X1 @ X3)) = $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ X0)) = $true)))),
% 3.07/0.88 inference(flattening,[],[f881])).
% 3.07/0.88 thf(f947,definition,(
% 3.07/0.88 (sP0 = $true) <=> ! [X1 : ($i > $o),X0 : $i] : (! [X4 : $i] : ((((X1 @ X4)) != $true) | (((in @ X4 @ X0)) != $true)) | (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true) | ? [X2 : $i] : (? [X3 : $i] : ((X2 != X3) & (((X1 @ X2)) = $true) & (((X1 @ X3)) = $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ X0)) = $true)))),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.07/0.88 thf(f948,plain,(
% 3.07/0.88 (singletonprop = $true) <=> (sP0 = $true)),
% 3.07/0.88 inference(definition_folding,[],[f882,f947])).
% 3.07/0.88 thf(f995,plain,(
% 3.07/0.88 ((sP0 = $true) | ? [X1 : ($i > $o),X0 : $i] : (? [X4 : $i] : ((((X1 @ X4)) = $true) & (((in @ X4 @ X0)) = $true)) & (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) != $true) & ! [X2 : $i] : (! [X3 : $i] : ((X2 = X3) | (((X1 @ X2)) != $true) | (((X1 @ X3)) != $true) | (((in @ X3 @ X0)) != $true)) | (((in @ X2 @ X0)) != $true)))) & (! [X1 : ($i > $o),X0 : $i] : (! [X4 : $i] : ((((X1 @ X4)) != $true) | (((in @ X4 @ X0)) != $true)) | (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true) | ? [X2 : $i] : (? [X3 : $i] : ((X2 != X3) & (((X1 @ X2)) = $true) & (((X1 @ X3)) = $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ X0)) = $true))) | (sP0 != $true))),
% 3.07/0.88 inference(nnf_transformation,[],[f947])).
% 3.07/0.88 thf(f996,plain,(
% 3.07/0.88 ((sP0 = $true) | ? [X0 : ($i > $o),X1 : $i] : (? [X2 : $i] : ((((X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true)) & (((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) & ! [X3 : $i] : (! [X4 : $i] : ((X3 = X4) | (((X0 @ X3)) != $true) | ($true != ((X0 @ X4))) | (((in @ X4 @ X1)) != $true)) | (((in @ X3 @ X1)) != $true)))) & (! [X5 : ($i > $o),X6 : $i] : (! [X7 : $i] : ((((X5 @ X7)) != $true) | (((in @ X7 @ X6)) != $true)) | (((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) = $true) | ? [X8 : $i] : (? [X9 : $i] : ((X8 != X9) & (((X5 @ X8)) = $true) & (((X5 @ X9)) = $true) & (((in @ X9 @ X6)) = $true)) & (((in @ X8 @ X6)) = $true))) | (sP0 != $true))),
% 3.07/0.88 inference(rectify,[],[f995])).
% 3.07/0.88 thf(f997,plain,(
% 3.07/0.88 ((sP0 = $true) | (((((sK42 @ sK44)) = $true) & (((in @ sK44 @ sK43)) = $true)) & (((singleton @ (dsetconstr @ sK43 @ (^[Y0 : $i]: (sK42 @ Y0))))) != $true) & ! [X3 : $i] : (! [X4 : $i] : ((X3 = X4) | (((sK42 @ X3)) != $true) | (((sK42 @ X4)) != $true) | (((in @ X4 @ sK43)) != $true)) | (((in @ X3 @ sK43)) != $true)))) & (! [X5 : ($i > $o),X6 : $i] : (! [X7 : $i] : ((((X5 @ X7)) != $true) | (((in @ X7 @ X6)) != $true)) | (((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) = $true) | (((((sK45 @ X6 @ X5)) != ((sK46 @ X6 @ X5))) & (((X5 @ (sK45 @ X6 @ X5))) = $true) & (((X5 @ (sK46 @ X6 @ X5))) = $true) & (((in @ (sK46 @ X6 @ X5) @ X6)) = $true)) & (((in @ (sK45 @ X6 @ X5) @ X6)) = $true))) | (sP0 != $true))),
% 3.07/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK42,sK43,sK44,vAPP,vAPP]),skolemize(X0,sK42),skolemize(X1,sK43),skolemize(X2,sK44),skolemize(X3,sK12 @ X2),skolemize(X3,sK12 @ X2)],[f996])).
% 3.07/0.88 thf(f998,plain,(
% 3.07/0.88 ((singletonprop = $true) | (sP0 != $true)) & ((sP0 = $true) | (singletonprop != $true))),
% 3.07/0.88 inference(nnf_transformation,[],[f948])).
% 3.07/0.88 thf(f1268,plain,(
% 3.07/0.88 (setukpairIL = $true) & (setminusSubset1 = $true) & (uniqinunit = $true) & (upairset2E = $true) & (subsetE = $true) & (setadjoin__Cong = $true) & (cartprodpairin = $true) & (funcextLem = $true) & (binintersectSubset1 = $true) & (emptyinPowerset = $true) & (kfstpairEq = $true) & (eqinunit = $true) & (setbeta = $true) & (subsetI2 = $true) & (singletonsubset = $true) & (eqimpsubset2 = $true) & (ap2p = $true) & (lam2p = $true) & (lam2lamEq = $true) & (setunionAx = $true) & (setukpairinjL2 = $true) & (setunionsingleton1 = $true) & (exuE3u = $true) & (singletonsuniq = $true) & (cartprodmempair1 = $true) & (inPowerset = $true) & (symdiffI2 = $true) & (singletoninpowerset = $true) & (notequalI2 = $true) & (setukpairinjR2 = $true) & (setadjoinOr = $true) & (ap2apEq2 = $true) & (notdexE = $true) & (subbreln = $true) & (exuI3 = $true) & (exuI2 = $true) & (subPowSU = $true) & (binintersectER = $true) & (singletoninpowunion = $true) & (powersetI = $true) & (emptysetE = $true) & (emptysetAx = $true) & (setukpairinjR = $true) & (sepSubset = $true) & (binintersectSubset4 = $true) & (symdiffE = $true) & (cartprodmempair = $true) & (ex1I = $true) & (setextsub = $true) & (setoftrueEq = $true) & (bs114d = $true) & (kpairsurjEq = $true) & (notinsingleton = $true) & (setunionI = $true) & (setukpairinjL1 = $true) & (setext = $true) & (cartprodmempaircEq = $true) & (app = $true) & (setunionE = $true) & (binintersectRsub = $true) & (powerset__Cong = $true) & (binunionE = $true) & (funcImageSingleton = $true) & (notequalI1 = $true) & (infuncsetfunc = $true) & (exuEu = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (setextAx = $true) & (binunionEcases = $true) & (upairsetIL = $true) & (setunionE2 = $true) & (descrp = $true) & (setminusERneg = $true) & (ex1I2 = $true) & (iffalseProp1 = $true) & (setminusILneg = $true) & (cartprodpairmemEL = $true) & (prop2set2propI = $true) & (setminusLsub = $true) & (notsubsetI = $true) & (lamProp = $true) & (upairsetIR = $true) & (emptyI = $true) & (ex1E1 = $true) & (emptyInPowerset = $true) & (symdiffI1 = $true) & (vacuousDall = $true) & (sepInPowerset = $true) & (nonemptyI = $true) & (apProp = $true) & (binintersectSubset2 = $true) & (powersetE = $true) & (dpsetconstrSub = $true) & (dsetconstr__Cong = $true) & (beta1 = $true) & (subsetI1 = $true) & (setminusER = $true) & (setunionsingleton2 = $true) & (subset2powerset = $true) & (quantDeMorgan1 = $true) & (powersetsubset = $true) & (brelnall1 = $true) & (funcext = $true) & (nonemptyI1 = $true) & (secondinupair = $true) & (setunion__Cong = $true) & (exu__Cong = $true) & (eta2 = $true) & (binintersectLsub = $true) & (cartprodpairmemER = $true) & (setadjoinSub = $true) & (wellorderingAx = $true) & (setminusIRneg = $true) & (upairsubunion = $true) & (kpairiskpair = $true) & (dsetconstrI = $true) & (ksndpairEq = $true) & (singletonprop = $true) & (setminusEL = $true) & (dpsetconstrEL1 = $true) & (emptyE1 = $true) & (setukpairinjL = $true) & (kfstsingleton = $true) & (ubforcartprodlem2 = $true) & (notinemptyset = $true) & (omega__Cong = $true) & (subsetTrans = $true) & (setadjoinIR = $true) & (funcext2 = $true) & (powersetI1 = $true) & (setOfPairsIsBReln = $true) & (exuE2 = $true) & (dpsetconstrI = $true) & (symdiffIneg2 = $true) & (setminusSubset2 = $true) & (ubforcartprodlem3 = $true) & (iftrueProp1 = $true) & (upairset2IR = $true) & (binintersectSubset3 = $true) & (nonemptyImpWitness = $true) & (prop2setI = $true) & (descr__Cong = $true) & (cartprodsndpairEq = $true) & (setukpairinjR11 = $true) & (binunionIR = $true) & (exuE3e = $true) & (cartprodfstpairEq = $true) & (funcGraphProp4 = $true) & (setminusI = $true) & (foundationAx = $true) & (cartprodfstin = $true) & (upairsetE = $true) & (dpsetconstrEL2 = $true) & (ap2apEq1 = $true) & (funcGraphProp2 = $true) & (powersetE1 = $true) & (binunionRsub = $true) & (funcinfuncset = $true) & (powersetAx = $true) & (subsetE2 = $true) & (eqimpsubset1 = $true) & (theprop = $true) & (setminusELneg = $true) & (eta1 = $true) & (dpsetconstrERa = $true) & (exuE1 = $true) & (((((in @ sK324 @ sK323)) = $true) & (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) != $true)) & (((in @ sK322 @ sK323)) = $true)) & (brelnall2 = $true) & (subsetRefl = $true) & (beta2 = $true) & (eqbreln = $true) & (setadjoinSub2 = $true) & (setunionsingleton = $true) & (emptysetimpfalse = $true) & (disjointsetsI1 = $true) & (kpairp = $true) & (ubforcartprodlem1 = $true) & (setadjoinE = $true) & (binintersectI = $true) & (funcGraphProp3 = $true) & (notdallE = $true) & (binunionLsub = $true) & (omegaSAx = $true) & (singletonsswitch = $true) & (subsetemptysetimpeq = $true) & (iffalseProp2 = $true) & (replAx = $true) & (emptyinunitempty = $true) & (dpsetconstrER = $true) & (emptysetsubset = $true) & (exuI1 = $true) & (dsetconstrER = $true) & (prop2setE = $true) & (setadjoinAx = $true) & (ksndsingleton = $true) & (setukpairinjR1 = $true) & (iftrueProp2 = $true) & (ex1E2 = $true) & (binunionIL = $true) & (noeltsimpempty = $true) & (symdiffIneg1 = $true) & (setukpairinjR12 = $true) & (setukpairIR = $true) & (quantDeMorgan3 = $true) & (binintersectSubset5 = $true) & (cartprodsndin = $true) & (funcGraphProp1 = $true) & (omegaIndAx = $true) & (upairequniteq = $true) & (in__Cong = $true) & (quantDeMorgan2 = $true) & (upairinpowunion = $true) & (binintersectEL = $true) & (dsetconstrEL = $true) & (omega0Ax = $true) & (emptyset__Cong = $true) & (cartprodpairsurjEq = $true) & (quantDeMorgan4 = $true) & (lamp = $true) & (setadjoinIL = $true)),
% 3.07/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK321,sK322,sK323,sK324]),skolemize(X0,sK321),skolemize(X1,sK322),skolemize(X2,sK323),skolemize(X3,sK324)],[f766])).
% 3.07/0.88 thf(f1680,plain,(
% 3.07/0.88 ( ! [X6 : $i,X7 : $i,X5 : ($i > $o)] : ((((X5 @ X7)) != $true) | (((in @ X7 @ X6)) != $true) | (((X5 @ (sK46 @ X6 @ X5))) = $true) | (((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) = $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(cnf_transformation,[],[f997])).
% 3.07/0.88 thf(f1681,plain,(
% 3.07/0.88 ( ! [X6 : $i,X7 : $i,X5 : ($i > $o)] : ((((X5 @ (sK45 @ X6 @ X5))) = $true) | (((in @ X7 @ X6)) != $true) | (sP0 != $true) | (((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) = $true) | (((X5 @ X7)) != $true)) )),
% 3.07/0.88 inference(cnf_transformation,[],[f997])).
% 3.07/0.88 thf(f1682,plain,(
% 3.07/0.88 ( ! [X6 : $i,X7 : $i,X5 : ($i > $o)] : ((((sK45 @ X6 @ X5)) != ((sK46 @ X6 @ X5))) | (((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) = $true) | (sP0 != $true) | (((in @ X7 @ X6)) != $true) | (((X5 @ X7)) != $true)) )),
% 3.07/0.88 inference(cnf_transformation,[],[f997])).
% 3.07/0.88 thf(f1687,plain,(
% 3.07/0.88 (sP0 = $true) | (singletonprop != $true)),
% 3.07/0.88 inference(cnf_transformation,[],[f998])).
% 3.07/0.88 thf(f2106,plain,(
% 3.07/0.88 (((in @ sK322 @ sK323)) = $true)),
% 3.07/0.88 inference(cnf_transformation,[],[f1268])).
% 3.07/0.88 thf(f2107,plain,(
% 3.07/0.88 (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) != $true)),
% 3.07/0.88 inference(cnf_transformation,[],[f1268])).
% 3.07/0.88 thf(f2108,plain,(
% 3.07/0.88 (((in @ sK324 @ sK323)) = $true)),
% 3.07/0.88 inference(cnf_transformation,[],[f1268])).
% 3.07/0.88 thf(f2157,plain,(
% 3.07/0.88 (singletonprop = $true)),
% 3.07/0.88 inference(cnf_transformation,[],[f1268])).
% 3.07/0.88 thf(f2814,plain,(
% 3.07/0.88 ( ! [X6 : $i,X7 : $i,X5 : ($i > $o)] : (($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((in @ X7 @ X6)) != $true) | (((X5 @ (sK46 @ X6 @ X5))) = $true) | (((X5 @ X7)) != $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(beta-eta_normalization,[],[f1680])).
% 3.07/0.88 thf(f2828,plain,(
% 3.07/0.88 ( ! [X6 : $i,X7 : $i,X5 : ($i > $o)] : (($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((in @ X7 @ X6)) != $true) | (sP0 != $true) | (((X5 @ (sK45 @ X6 @ X5))) = $true) | (((X5 @ X7)) != $true)) )),
% 3.07/0.88 inference(beta-eta_normalization,[],[f1681])).
% 3.07/0.88 thf(f2900,plain,(
% 3.07/0.88 ( ! [X6 : $i,X7 : $i,X5 : ($i > $o)] : ((((sK45 @ X6 @ X5)) != ((sK46 @ X6 @ X5))) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (sP0 != $true) | (((in @ X7 @ X6)) != $true) | (((X5 @ X7)) != $true)) )),
% 3.07/0.88 inference(beta-eta_normalization,[],[f1682])).
% 3.07/0.88 thf(f2929,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (($true != $true) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true) | ((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | ((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ X0)) != $true)) )),
% 3.07/0.88 inference(constrained_superposition,[],[f2107,f2828])).
% 3.07/0.88 thf(f2930,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sP0 != $true) | ($true != $true) | ((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | ((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ X0)) != $true)) )),
% 3.07/0.88 inference(constrained_superposition,[],[f2107,f2814])).
% 3.07/0.88 thf(f2932,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ X0)) != $true) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true) | ((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true)) )),
% 3.07/0.88 inference(trivial_inequality_removal,[],[f2930])).
% 3.07/0.88 thf(f2933,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((sK321 & (sK322 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | ((~ sK321) & (sK324 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))))) = $true) | (sP0 != $true) | ((((sK321 & (sK322 = X0)) | ((~ sK321) & (sK324 = X0)))) != $true) | (((in @ X0 @ sK323)) != $true)) )),
% 3.07/0.88 inference(beta-eta_normalization,[],[f2932])).
% 3.07/0.88 thf(f2934,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((sK321 & (sK322 = X0)) | ((~ sK321) & (sK324 = X0)))) != $true) | (((in @ X0 @ sK323)) != $true) | ((((~ sK321) & (sK324 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (sP0 != $true) | (((sK321 & (sK322 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(or_proxy_clausification,[],[f2933])).
% 3.07/0.88 thf(f2935,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (((sK321 & (sK322 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (sP0 != $true) | ((((~ sK321) & (sK324 = X0))) = $false) | ((((~ sK321) & (sK324 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(or_proxy_clausification,[],[f2934])).
% 3.07/0.88 thf(f2936,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | ((((~ sK321) & (sK324 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | ($false = ((sK321 & (sK322 = X0)))) | (((sK321 & (sK322 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(or_proxy_clausification,[],[f2934])).
% 3.07/0.88 thf(f2938,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((~ sK321)) = $true) | ($false = ((sK321 & (sK322 = X0)))) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true) | (((sK321 & (sK322 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f2936])).
% 3.07/0.88 thf(f2939,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((sK321 & (sK322 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (sP0 != $true) | ($false = ((sK321 & (sK322 = X0)))) | (((in @ X0 @ sK323)) != $true) | (sK321 = $false)) )),
% 3.07/0.88 inference(not_proxy_clausification,[],[f2938])).
% 3.07/0.88 thf(f2940,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sP0 != $true) | (((sK322 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sK321 = $false) | ($false = ((sK321 & (sK322 = X0))))) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f2939])).
% 3.07/0.88 thf(f2945,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (($false = ((sK321 & (sK322 = X0)))) | (sK321 = $false) | (sK322 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f2940])).
% 3.07/0.88 thf(f2946,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sP0 != $true) | (sK322 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sK321 = $false) | ($false = ((sK322 = X0))) | (sK321 = $false)) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f2945])).
% 3.07/0.88 thf(f2947,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sK321 = $false) | (sP0 != $true) | (sK322 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sK321 = $false) | (sK322 != X0)) )),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f2946])).
% 3.07/0.88 thf(f2948,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sK322 != X0) | (sP0 != $true) | (sK322 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sK321 = $false)) )),
% 3.07/0.88 inference(duplicate_literal_removal,[],[f2947])).
% 3.07/0.88 thf(f2956,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sP0 != $true) | (sK321 = $true) | ((((~ sK321) & (sK324 = X0))) = $false) | (((in @ X0 @ sK323)) != $true) | ((((~ sK321) & (sK324 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f2935])).
% 3.07/0.88 thf(f2957,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sP0 != $true) | (((in @ X0 @ sK323)) != $true) | ($false = ((sK324 = X0))) | (sK321 = $true) | ((((~ sK321) & (sK324 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | ($false = ((~ sK321)))) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f2956])).
% 3.07/0.88 thf(f2958,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK324 != X0) | (sP0 != $true) | ((((~ sK321) & (sK324 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (sK321 = $true) | (((in @ X0 @ sK323)) != $true) | ($false = ((~ sK321)))) )),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f2957])).
% 3.07/0.88 thf(f2959,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((sK324 = (sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | ($false = ((~ sK321))) | (sK324 != X0) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true) | (sK321 = $true)) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f2958])).
% 3.07/0.88 thf(f2964,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK324 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true) | (sK324 != X0) | ($false = ((~ sK321))) | (sK321 = $true)) )),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f2959])).
% 3.07/0.88 thf(f2965,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK321 = $true) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true) | (sK324 != X0) | (sK321 = $true) | (sK324 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) )),
% 3.07/0.88 inference(not_proxy_clausification,[],[f2964])).
% 3.07/0.88 thf(f2966,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK324 != X0) | (sK324 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sK321 = $true) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true)) )),
% 3.07/0.88 inference(duplicate_literal_removal,[],[f2965])).
% 3.07/0.88 thf(f2999,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ X0)) != $true) | ((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(trivial_inequality_removal,[],[f2929])).
% 3.07/0.88 thf(f3000,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | ((~ sK321) & (sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))))) = $true) | ((((sK321 & (sK322 = X0)) | ((~ sK321) & (sK324 = X0)))) != $true) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(beta-eta_normalization,[],[f2999])).
% 3.07/0.88 thf(f3001,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((sK321 & (sK322 = X0)) | ((~ sK321) & (sK324 = X0)))) != $true) | (((in @ X0 @ sK323)) != $true) | (((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | ((((~ sK321) & (sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(or_proxy_clausification,[],[f3000])).
% 3.07/0.88 thf(f3002,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((~ sK321) & (sK324 = X0))) = $false) | (((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true) | ((((~ sK321) & (sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(or_proxy_clausification,[],[f3001])).
% 3.07/0.88 thf(f3003,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((~ sK321) & (sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | ($false = ((sK321 & (sK322 = X0)))) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true) | (((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(or_proxy_clausification,[],[f3001])).
% 3.07/0.88 thf(f3005,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (((~ sK321)) = $true) | (sP0 != $true) | ($false = ((sK321 & (sK322 = X0))))) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f3003])).
% 3.07/0.88 thf(f3006,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (((~ sK321)) = $true) | (sP0 != $true) | (((sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | ($false = ((sK321 & (sK322 = X0))))) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f3005])).
% 3.07/0.88 thf(f3012,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (($false = ((sK321 & (sK322 = X0)))) | (((sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true) | (sK321 = $false)) )),
% 3.07/0.88 inference(not_proxy_clausification,[],[f3006])).
% 3.07/0.88 thf(f3013,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sK321 = $false) | (((sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | ($false = ((sK322 = X0))) | (sK321 = $false) | (sP0 != $true)) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f3012])).
% 3.07/0.88 thf(f3014,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sP0 != $true) | (sK321 = $false) | (sK321 = $false) | ($false = ((sK322 = X0))) | (((in @ X0 @ sK323)) != $true) | (sK322 = ((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) )),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f3013])).
% 3.07/0.88 thf(f3015,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK321 = $false) | (sK321 = $false) | (sK322 != X0) | (sK322 = ((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true)) )),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f3014])).
% 3.07/0.88 thf(f3016,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK322 = ((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sP0 != $true) | (sK321 = $false) | (((in @ X0 @ sK323)) != $true) | (sK322 != X0)) )),
% 3.07/0.88 inference(duplicate_literal_removal,[],[f3015])).
% 3.07/0.88 thf(f3025,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (($false = ((~ sK321))) | ($false = ((sK324 = X0))) | (((in @ X0 @ sK323)) != $true) | ((((~ sK321) & (sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (sP0 != $true) | (((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f3002])).
% 3.07/0.88 thf(f3026,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sP0 != $true) | (sK321 = $true) | ($false = ((sK324 = X0))) | (((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (((in @ X0 @ sK323)) != $true) | ((((~ sK321) & (sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(not_proxy_clausification,[],[f3025])).
% 3.07/0.88 thf(f3027,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (((((~ sK321) & (sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (sK321 = $true) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true) | (sK324 != X0) | (((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true)) )),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f3026])).
% 3.07/0.88 thf(f3028,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((sK321 & (sK322 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) = $true) | (((in @ X0 @ sK323)) != $true) | (sK324 != X0) | (((sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sK321 = $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f3027])).
% 3.07/0.88 thf(f3036,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((sK324 = (sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sP0 != $true) | (sK324 != X0) | (sK321 = $true) | (((in @ X0 @ sK323)) != $true) | (sK321 = $true)) )),
% 3.07/0.88 inference(and_proxy_clausification,[],[f3028])).
% 3.07/0.88 thf(f3037,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))) = sK324) | (sK324 != X0) | (sK321 = $true) | (sK321 = $true) | (sP0 != $true)) )),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f3036])).
% 3.07/0.88 thf(f3038,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))) = sK324) | (sK324 != X0) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true) | (sK321 = $true)) )),
% 3.07/0.88 inference(duplicate_literal_removal,[],[f3037])).
% 3.07/0.88 thf(f3067,definition,(
% 3.07/0.88 spl692_1 <=> (sK322 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_1])],[avatar_definition])).
% 3.07/0.88 thf(f3069,plain,(
% 3.07/0.88 (sK322 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | ~spl692_1),
% 3.07/0.88 inference(avatar_component_clause,[],[f3067])).
% 3.07/0.88 thf(f3071,definition,(
% 3.07/0.88 spl692_2 <=> ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sK322 != X0))),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_2])],[avatar_definition])).
% 3.07/0.88 thf(f3072,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sK322 != X0)) ) | ~spl692_2),
% 3.07/0.88 inference(avatar_component_clause,[],[f3071])).
% 3.07/0.88 thf(f3074,definition,(
% 3.07/0.88 spl692_3 <=> (sP0 = $true)),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_3])],[avatar_definition])).
% 3.07/0.88 thf(f3075,plain,(
% 3.07/0.88 (sP0 = $true) | ~spl692_3),
% 3.07/0.88 inference(avatar_component_clause,[],[f3074])).
% 3.07/0.88 thf(f3076,plain,(
% 3.07/0.88 (sP0 != $true) | spl692_3),
% 3.07/0.88 inference(avatar_component_clause,[],[f3074])).
% 3.07/0.88 thf(f3078,definition,(
% 3.07/0.88 spl692_4 <=> (sK321 = $false)),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_4])],[avatar_definition])).
% 3.07/0.88 thf(f3079,plain,(
% 3.07/0.88 (sK321 != $false) | spl692_4),
% 3.07/0.88 inference(avatar_component_clause,[],[f3078])).
% 3.07/0.88 thf(f3080,plain,(
% 3.07/0.88 (sK321 = $false) | ~spl692_4),
% 3.07/0.88 inference(avatar_component_clause,[],[f3078])).
% 3.07/0.88 thf(f3081,plain,(
% 3.07/0.88 spl692_1 | spl692_2 | ~spl692_3 | spl692_4),
% 3.07/0.88 inference(avatar_split_clause,[],[f2948,f3078,f3074,f3071,f3067])).
% 3.07/0.88 thf(f3083,definition,(
% 3.07/0.88 spl692_5 <=> (sK324 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_5])],[avatar_definition])).
% 3.07/0.88 thf(f3085,plain,(
% 3.07/0.88 (sK324 = ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | ~spl692_5),
% 3.07/0.88 inference(avatar_component_clause,[],[f3083])).
% 3.07/0.88 thf(f3088,definition,(
% 3.07/0.88 spl692_6 <=> (sK321 = $true)),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_6])],[avatar_definition])).
% 3.07/0.88 thf(f3090,plain,(
% 3.07/0.88 (sK321 = $true) | ~spl692_6),
% 3.07/0.88 inference(avatar_component_clause,[],[f3088])).
% 3.07/0.88 thf(f3092,definition,(
% 3.07/0.88 spl692_7 <=> ! [X0 : $i] : ((sK324 != X0) | (((in @ X0 @ sK323)) != $true))),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_7])],[avatar_definition])).
% 3.07/0.88 thf(f3093,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sK324 != X0)) ) | ~spl692_7),
% 3.07/0.88 inference(avatar_component_clause,[],[f3092])).
% 3.07/0.88 thf(f3094,plain,(
% 3.07/0.88 spl692_6 | spl692_7 | spl692_5 | ~spl692_3),
% 3.07/0.88 inference(avatar_split_clause,[],[f2966,f3074,f3083,f3092,f3088])).
% 3.07/0.88 thf(f3102,definition,(
% 3.07/0.88 spl692_8 <=> (sK322 = ((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_8])],[avatar_definition])).
% 3.07/0.88 thf(f3104,plain,(
% 3.07/0.88 (sK322 = ((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | ~spl692_8),
% 3.07/0.88 inference(avatar_component_clause,[],[f3102])).
% 3.07/0.88 thf(f3105,plain,(
% 3.07/0.88 spl692_2 | spl692_8 | ~spl692_3 | spl692_4),
% 3.07/0.88 inference(avatar_split_clause,[],[f3016,f3078,f3074,f3102,f3071])).
% 3.07/0.88 thf(f3107,definition,(
% 3.07/0.88 spl692_9 <=> (((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))) = sK324)),
% 3.07/0.88 introduced(definition,[new_symbols(definition,[spl692_9])],[avatar_definition])).
% 3.07/0.88 thf(f3109,plain,(
% 3.07/0.88 (((sK45 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))) = sK324) | ~spl692_9),
% 3.07/0.88 inference(avatar_component_clause,[],[f3107])).
% 3.07/0.88 thf(f3111,plain,(
% 3.07/0.88 spl692_7 | ~spl692_3 | spl692_6 | spl692_9),
% 3.07/0.88 inference(avatar_split_clause,[],[f3038,f3107,f3088,f3074,f3092])).
% 3.07/0.88 thf(f3150,plain,(
% 3.07/0.88 ($false = $true) | (~spl692_4 | ~spl692_6)),
% 3.07/0.88 inference(forward_demodulation,[],[f3090,f3080])).
% 3.07/0.88 thf(f3151,plain,(
% 3.07/0.88 $false | (~spl692_4 | ~spl692_6)),
% 3.07/0.88 inference(trivial_inequality_removal,[],[f3150])).
% 3.07/0.88 thf(f3152,plain,(
% 3.07/0.88 ~spl692_4 | ~spl692_6),
% 3.07/0.88 inference(avatar_contradiction_clause,[],[f3151])).
% 3.07/0.88 thf(f3154,plain,(
% 3.07/0.88 ($true != $true) | (singletonprop != $true) | spl692_3),
% 3.07/0.88 inference(constrained_superposition,[],[f3076,f1687])).
% 3.07/0.88 thf(f3157,plain,(
% 3.07/0.88 (singletonprop != $true) | spl692_3),
% 3.07/0.88 inference(trivial_inequality_removal,[],[f3154])).
% 3.07/0.88 thf(f3158,plain,(
% 3.07/0.88 $false | spl692_3),
% 3.07/0.88 inference(forward_subsumption_resolution,[],[f3157,f2157])).
% 3.07/0.88 thf(f3159,plain,(
% 3.07/0.88 spl692_3),
% 3.07/0.88 inference(avatar_contradiction_clause,[],[f3158])).
% 3.07/0.88 thf(f3697,plain,(
% 3.07/0.88 (sK324 != sK324) | ($true != $true) | ~spl692_7),
% 3.07/0.88 inference(constrained_superposition,[],[f3093,f2108])).
% 3.07/0.88 thf(f3731,plain,(
% 3.07/0.88 $false | ~spl692_7),
% 3.07/0.88 inference(trivial_inequality_removal,[],[f3697])).
% 3.07/0.88 thf(f3732,plain,(
% 3.07/0.88 ~spl692_7),
% 3.07/0.88 inference(avatar_contradiction_clause,[],[f3731])).
% 3.07/0.88 thf(f4278,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sP0 != $true) | ((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ X0)) != $true) | (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sK324 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (((in @ X0 @ sK323)) != $true)) ) | ~spl692_9),
% 3.07/0.88 inference(constrained_superposition,[],[f2900,f3109])).
% 3.07/0.88 thf(f4287,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sK324 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sP0 != $true) | ((((sK321 & (sK322 = X0)) | ((~ sK321) & (sK324 = X0)))) != $true) | (((in @ X0 @ sK323)) != $true)) ) | ~spl692_9),
% 3.07/0.88 inference(beta-eta_normalization,[],[f4278])).
% 3.07/0.88 thf(f4288,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sP0 != $true) | (((in @ X0 @ sK323)) != $true) | (sK324 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | ((((~ sK321) & (sK324 = X0))) = $false)) ) | ~spl692_9),
% 3.07/0.88 inference(or_proxy_clausification,[],[f4287])).
% 3.07/0.88 thf(f4292,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | ($false = ((~ sK321))) | (sK324 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | ($false = ((sK324 = X0))) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true)) ) | ~spl692_9),
% 3.07/0.88 inference(and_proxy_clausification,[],[f4288])).
% 3.07/0.88 thf(f4293,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK321 = $true) | (sP0 != $true) | (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sK324 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (((in @ X0 @ sK323)) != $true) | ($false = ((sK324 = X0)))) ) | ~spl692_9),
% 3.07/0.88 inference(not_proxy_clausification,[],[f4292])).
% 3.07/0.88 thf(f4294,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sK324 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true) | (sK321 = $true) | (sK324 != X0)) ) | ~spl692_9),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f4293])).
% 3.07/0.88 thf(f4295,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK321 = $true) | (((in @ X0 @ sK323)) != $true) | (sK324 != X0) | (sP0 != $true) | (sK324 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))))))) ) | ~spl692_9),
% 3.07/0.88 inference(forward_subsumption_resolution,[],[f4294,f2107])).
% 3.07/0.88 thf(f4296,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK324 != X0) | (sK321 = $true) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true)) ) | (~spl692_5 | ~spl692_9)),
% 3.07/0.88 inference(forward_subsumption_resolution,[],[f4295,f3085])).
% 3.07/0.88 thf(f4297,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK324 != X0) | (((in @ X0 @ sK323)) != $true) | (sK321 = $true)) ) | (~spl692_3 | ~spl692_5 | ~spl692_9)),
% 3.07/0.88 inference(forward_subsumption_resolution,[],[f4296,f3075])).
% 3.07/0.88 thf(f4298,plain,(
% 3.07/0.88 ( ! [X0 : $i] : (($false = $true) | (sK324 != X0) | (((in @ X0 @ sK323)) != $true)) ) | (~spl692_3 | ~spl692_4 | ~spl692_5 | ~spl692_9)),
% 3.07/0.88 inference(forward_demodulation,[],[f4297,f3080])).
% 3.07/0.88 thf(f4299,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK324 != X0) | (((in @ X0 @ sK323)) != $true)) ) | (~spl692_3 | ~spl692_4 | ~spl692_5 | ~spl692_9)),
% 3.07/0.88 inference(trivial_inequality_removal,[],[f4298])).
% 3.07/0.88 thf(f4300,plain,(
% 3.07/0.88 spl692_7 | ~spl692_3 | ~spl692_4 | ~spl692_5 | ~spl692_9),
% 3.07/0.88 inference(avatar_split_clause,[],[f4299,f3107,f3083,f3078,f3074,f3092])).
% 3.07/0.88 thf(f4612,plain,(
% 3.07/0.88 (sK322 != sK322) | ($true != $true) | ~spl692_2),
% 3.07/0.88 inference(constrained_superposition,[],[f3072,f2106])).
% 3.07/0.88 thf(f4678,plain,(
% 3.07/0.88 $false | ~spl692_2),
% 3.07/0.88 inference(trivial_inequality_removal,[],[f4612])).
% 3.07/0.88 thf(f4679,plain,(
% 3.07/0.88 ~spl692_2),
% 3.07/0.88 inference(avatar_contradiction_clause,[],[f4678])).
% 3.07/0.88 thf(f4955,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | ((((^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0)))) @ X0)) != $true) | (sP0 != $true) | (sK322 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true)) ) | ~spl692_8),
% 3.07/0.88 inference(constrained_superposition,[],[f2900,f3104])).
% 3.07/0.88 thf(f4956,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sK322 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | ((((sK321 & (sK322 = X0)) | ((~ sK321) & (sK324 = X0)))) != $true) | (sP0 != $true) | (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true)) ) | ~spl692_8),
% 3.07/0.88 inference(beta-eta_normalization,[],[f4955])).
% 3.07/0.88 thf(f4958,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true) | (sK322 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | ($false = ((sK321 & (sK322 = X0))))) ) | ~spl692_8),
% 3.07/0.88 inference(or_proxy_clausification,[],[f4956])).
% 3.07/0.88 thf(f4959,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sP0 != $true) | (sK322 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sK321 = $false) | ($false = ((sK322 = X0))) | (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true)) ) | ~spl692_8),
% 3.07/0.88 inference(and_proxy_clausification,[],[f4958])).
% 3.07/0.88 thf(f4960,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK322 != ((sK46 @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) | (sK322 != X0) | (((in @ X0 @ sK323)) != $true) | (sK321 = $false) | (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sP0 != $true)) ) | ~spl692_8),
% 3.07/0.88 inference(equality_proxy_clausification,[],[f4959])).
% 3.07/0.88 thf(f4972,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK322 != X0) | (((singleton @ (dsetconstr @ sK323 @ (^[Y0 : $i]: ((sK321 & (sK322 = Y0)) | ((~ sK321) & (sK324 = Y0))))))) = $true) | (sK321 = $false) | (sP0 != $true) | (((in @ X0 @ sK323)) != $true)) ) | (~spl692_1 | ~spl692_8)),
% 3.07/0.88 inference(forward_subsumption_resolution,[],[f4960,f3069])).
% 3.07/0.88 thf(f4973,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sK321 = $false) | (sK322 != X0) | (((in @ X0 @ sK323)) != $true) | (sP0 != $true)) ) | (~spl692_1 | ~spl692_8)),
% 3.07/0.88 inference(forward_subsumption_resolution,[],[f4972,f2107])).
% 3.07/0.88 thf(f4974,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((sP0 != $true) | (((in @ X0 @ sK323)) != $true) | (sK322 != X0)) ) | (~spl692_1 | spl692_4 | ~spl692_8)),
% 3.07/0.88 inference(forward_subsumption_resolution,[],[f4973,f3079])).
% 3.07/0.88 thf(f4975,plain,(
% 3.07/0.88 ( ! [X0 : $i] : ((((in @ X0 @ sK323)) != $true) | (sK322 != X0)) ) | (~spl692_1 | ~spl692_3 | spl692_4 | ~spl692_8)),
% 3.07/0.88 inference(forward_subsumption_resolution,[],[f4974,f3075])).
% 3.07/0.88 thf(f4976,plain,(
% 3.07/0.88 spl692_2 | ~spl692_1 | ~spl692_3 | spl692_4 | ~spl692_8),
% 3.07/0.88 inference(avatar_split_clause,[],[f4975,f3102,f3078,f3074,f3067,f3071])).
% 3.07/0.88 cnf(s1, plain, spl692_1 | spl692_2 | ~spl692_3 | spl692_4, inference(sat_conversion,[],[f3081])).
% 3.07/0.88 cnf(s3, plain, ~spl692_3 | spl692_5 | spl692_6 | spl692_7, inference(sat_conversion,[],[f3094])).
% 3.07/0.88 cnf(s5, plain, spl692_2 | ~spl692_3 | spl692_4 | spl692_8, inference(sat_conversion,[],[f3105])).
% 3.07/0.88 cnf(s7, plain, ~spl692_3 | spl692_6 | spl692_7 | spl692_9, inference(sat_conversion,[],[f3111])).
% 3.07/0.88 cnf(s17, plain, ~spl692_4 | ~spl692_6, inference(sat_conversion,[],[f3152])).
% 3.07/0.88 cnf(s18, plain, spl692_3, inference(sat_conversion,[],[f3159])).
% 3.07/0.88 cnf(s24, plain, ~spl692_7, inference(sat_conversion,[],[f3732])).
% 3.07/0.88 cnf(s48, plain, ~spl692_3 | ~spl692_4 | ~spl692_5 | spl692_7 | ~spl692_9, inference(sat_conversion,[],[f4300])).
% 3.07/0.88 cnf(s54, plain, ~spl692_2, inference(sat_conversion,[],[f4679])).
% 3.07/0.88 cnf(s75, plain, ~spl692_1 | spl692_2 | ~spl692_3 | spl692_4 | ~spl692_8, inference(sat_conversion,[],[f4976])).
% 3.07/0.88 cnf(s77, plain, spl692_6 | spl692_9, inference(rat,[],[s7,s24,s18])).
% 3.07/0.88 cnf(s79, plain, spl692_4 | spl692_8, inference(rat,[],[s5,s18,s54])).
% 3.07/0.88 cnf(s81, plain, spl692_5 | spl692_6, inference(rat,[],[s3,s24,s18])).
% 3.07/0.88 cnf(s83, plain, spl692_1 | spl692_4, inference(rat,[],[s1,s18,s54])).
% 3.07/0.88 cnf(s84, plain, ~spl692_4, inference(rat,[],[s48,s81,s77,s17,s18,s24])).
% 3.07/0.88 cnf(s89, plain, spl692_8, inference(rat,[],[s79,s84])).
% 3.07/0.88 cnf(s90, plain, spl692_1, inference(rat,[],[s83,s84])).
% 3.07/0.88 cnf(s91, plain, $false, inference(rat,[],[s75,s84,s18,s54,s90,s89])).
% 3.07/0.88 thf(f4977,plain,(
% 3.07/0.88 $false),
% 3.07/0.88 inference(avatar_sat_refutation,[],[s91])).
% 3.07/0.88 % SZS output end Proof for theBenchmark
% 3.07/0.88 % (4063648)------------------------------
% 3.07/0.88 % (4063648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.07/0.88 % (4063648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/0.88 % (4063648)CaDiCaL version: 2.1.3
% 3.07/0.88 % (4063648)Termination reason: Refutation
% 3.07/0.88 % (4063648)Time elapsed: 0.221 s
% 3.07/0.88 % (4063648)Peak memory usage: 18 MB
% 3.07/0.88 % (4063648)Instructions burned: 448 (million)
% 3.07/0.88 % (4063439)Success in time 0.585 s
% 3.07/0.88 % Vampire exiting
%------------------------------------------------------------------------------