%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU584^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:32:33 AM UTC 2026
% Result : Theorem 5.64s 1.06s
% Output : Refutation 5.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU584^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:53:19 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.89/0.96 % (1091088)Will run a generic schedule for satisfiability detection.
% 3.89/0.96 % (1091093)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2391863847_2999 on theBenchmark for (2999ds/0Mi)
% 3.89/0.96 % (1091094)% WARNING: option uhcvi not known.
% 3.89/0.96 % (1091095)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3433087045:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.89/0.96 % (1091094)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4031482043:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.89/0.96 % (1091096)dis+10_1_sil=32000:sp=arity:random_seed=1741322092:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.89/0.96 % (1091097)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1143126617:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.89/0.96 % (1091098)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3612232106:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.89/0.96 % (1091099)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4145080242:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.89/0.96 % Exception at run slice level
% 3.89/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.89/0.96 % (1091094)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.89/0.96 % (1091097)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.89/0.96 % (1091107)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1318039622:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.89/0.96 % (1091094)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.89/0.96 % Exception at run slice level
% 3.89/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.89/0.96 % (1091109)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3717837821:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.89/0.96 % (1091096)Instruction limit reached!
% 3.89/0.96 % (1091096)------------------------------
% 3.89/0.96 % (1091096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.89/0.96 % (1091096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/0.96 % (1091096)CaDiCaL version: 2.1.3
% 3.89/0.96 % (1091096)Termination reason: Instruction limit
% 3.89/0.96 % (1091096)Termination phase: Saturation
% 3.89/0.96 % (1091096)Time elapsed: 0.049 s
% 3.89/0.96 % (1091096)Peak memory usage: 13 MB
% 3.89/0.96 % (1091096)Instructions burned: 104 (million)
% 3.89/0.96 % (1091097)Instruction limit reached!
% 3.89/0.96 % (1091097)------------------------------
% 3.89/0.96 % (1091097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.89/0.96 % (1091097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/0.96 % (1091097)CaDiCaL version: 2.1.3
% 3.89/0.96 % (1091097)Termination reason: Instruction limit
% 3.89/0.96 % (1091097)Termination phase: Saturation
% 3.89/0.96 % (1091097)Time elapsed: 0.054 s
% 3.89/0.96 % (1091097)Peak memory usage: 13 MB
% 3.89/0.96 % (1091097)Instructions burned: 117 (million)
% 3.89/0.96 % (1091098)Instruction limit reached!
% 3.89/0.96 % (1091098)------------------------------
% 3.89/0.96 % (1091098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.89/0.96 % (1091098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/0.96 % (1091098)CaDiCaL version: 2.1.3
% 3.89/0.96 % (1091098)Termination reason: Instruction limit
% 3.89/0.96 % (1091098)Termination phase: Saturation
% 3.89/0.96 % (1091098)Time elapsed: 0.062 s
% 3.89/0.96 % (1091098)Peak memory usage: 13 MB
% 3.89/0.96 % (1091098)Instructions burned: 135 (million)
% 3.89/0.96 % (1091109)Instruction limit reached!
% 3.89/0.96 % (1091109)------------------------------
% 3.89/0.96 % (1091109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.89/0.96 % (1091109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/0.96 % (1091109)CaDiCaL version: 2.1.3
% 3.89/0.96 % (1091109)Termination reason: Instruction limit
% 3.89/0.96 % (1091109)Termination phase: Saturation
% 3.89/0.96 % (1091109)Time elapsed: 0.032 s
% 3.89/0.96 % (1091109)Peak memory usage: 13 MB
% 3.89/0.96 % (1091109)Instructions burned: 132 (million)
% 3.89/0.96 % (1091111)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3445743041:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.64/1.06 % (1091099)Instruction limit reached!
% 5.64/1.06 % (1091099)------------------------------
% 5.64/1.06 % (1091099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.06 % (1091099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.06 % (1091099)CaDiCaL version: 2.1.3
% 5.64/1.06 % (1091099)Termination reason: Instruction limit
% 5.64/1.06 % (1091099)Termination phase: Saturation
% 5.64/1.06 % (1091099)Time elapsed: 0.069 s
% 5.64/1.06 % (1091099)Peak memory usage: 14 MB
% 5.64/1.06 % (1091099)Instructions burned: 162 (million)
% 5.64/1.06 % (1091112)ott-21_1_sil=16000:fs=off:random_seed=2450216083:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 5.64/1.06 % (1091114)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1646626150:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.64/1.06 % (1091111)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.64/1.06 % (1091113)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1866954139:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 5.64/1.06 % Exception at run slice level
% 5.64/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.06 % (1091111)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.64/1.06 % (1091116)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1079022176:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.64/1.06 % (1091120)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2461294236:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.64/1.06 % Exception at run slice level
% 5.64/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.06 % (1091123)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=73225386:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 5.64/1.06 % (1091123)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.64/1.06 % (1091112)Instruction limit reached!
% 5.64/1.06 % (1091112)------------------------------
% 5.64/1.06 % (1091112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.06 % (1091112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.06 % (1091112)CaDiCaL version: 2.1.3
% 5.64/1.06 % (1091112)Termination reason: Instruction limit
% 5.64/1.06 % (1091112)Termination phase: Saturation
% 5.64/1.06 % (1091112)Time elapsed: 0.086 s
% 5.64/1.06 % (1091112)Peak memory usage: 13 MB
% 5.64/1.06 % (1091112)Instructions burned: 181 (million)
% 5.64/1.06 % (1091125)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=782337708:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 5.64/1.06 % (1091125)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.64/1.06 % (1091123)Instruction limit reached!
% 5.64/1.06 % (1091123)------------------------------
% 5.64/1.06 % (1091123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.06 % (1091123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.06 % (1091123)CaDiCaL version: 2.1.3
% 5.64/1.06 % (1091123)Termination reason: Instruction limit
% 5.64/1.06 % (1091123)Termination phase: Saturation
% 5.64/1.06 % (1091123)Time elapsed: 0.154 s
% 5.64/1.06 % (1091123)Peak memory usage: 15 MB
% 5.64/1.06 % (1091123)Instructions burned: 697 (million)
% 5.64/1.06 % (1091127)fmb+10_1_sil=64000:random_seed=3153444140:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 5.64/1.06 % (1091127)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.64/1.06 % Exception at run slice level
% 5.64/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.06 % (1091129)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=295534246:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 5.64/1.06 % Exception at run slice level
% 5.64/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.06 % (1091131)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2190352490:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 5.64/1.06 % (1091111)Instruction limit reached!
% 5.64/1.06 % (1091111)------------------------------
% 5.64/1.06 % (1091111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.06 % (1091111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.06 % (1091111)CaDiCaL version: 2.1.3
% 5.64/1.06 % (1091111)Termination reason: Instruction limit
% 5.64/1.06 % (1091111)Termination phase: Saturation
% 5.64/1.06 % (1091111)Time elapsed: 0.259 s
% 5.64/1.06 % (1091111)Peak memory usage: 14 MB
% 5.64/1.06 % (1091111)Instructions burned: 684 (million)
% 5.64/1.06 % Exception at run slice level
% 5.64/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.06 % (1091133)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2874572766:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 5.64/1.06 % (1091113)Instruction limit reached!
% 5.64/1.06 % (1091113)------------------------------
% 5.64/1.06 % (1091113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.06 % (1091113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.06 % (1091113)CaDiCaL version: 2.1.3
% 5.64/1.06 % (1091113)Termination reason: Instruction limit
% 5.64/1.06 % (1091113)Termination phase: Saturation
% 5.64/1.06 % (1091113)Time elapsed: 0.260 s
% 5.64/1.06 % (1091113)Peak memory usage: 14 MB
% 5.64/1.06 % (1091113)Instructions burned: 477 (million)
% 5.64/1.06 % (1091133)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.64/1.06 % (1091134)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1831666974:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 5.64/1.06 % (1091136)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2270631411:i=6324_2996 on theBenchmark for (2996ds/6324Mi)
% 5.64/1.06 % (1091134)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.64/1.06 % (1091134)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.64/1.06 % Exception at run slice level
% 5.64/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.06 % (1091139)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2980553440:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 5.64/1.06 % Exception at run slice level
% 5.64/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.06 % (1091141)ott-2_1_sil=16000:newcnf=on:random_seed=1364958059:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 5.64/1.06 % (1091141)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.64/1.06 % (1091125)Instruction limit reached!
% 5.64/1.06 % (1091125)------------------------------
% 5.64/1.06 % (1091125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.06 % (1091125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.06 % (1091125)CaDiCaL version: 2.1.3
% 5.64/1.06 % (1091125)Termination reason: Instruction limit
% 5.64/1.06 % (1091125)Termination phase: Saturation
% 5.64/1.06 % (1091125)Time elapsed: 0.431 s
% 5.64/1.06 % (1091125)Peak memory usage: 17 MB
% 5.64/1.06 % (1091125)Instructions burned: 879 (million)
% 5.64/1.06 % (1091143)ott+10_1_sil=32000:tgt=ground:random_seed=3085810010:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 5.64/1.06 % (1091116)Instruction limit reached!
% 5.64/1.06 % (1091116)------------------------------
% 5.64/1.06 % (1091116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.06 % (1091116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.06 % (1091116)CaDiCaL version: 2.1.3
% 5.64/1.06 % (1091116)Termination reason: Instruction limit
% 5.64/1.06 % (1091116)Termination phase: Saturation
% 5.64/1.06 % (1091116)Time elapsed: 0.567 s
% 5.64/1.06 % (1091116)Peak memory usage: 18 MB
% 5.64/1.06 % (1091116)Instructions burned: 1181 (million)
% 5.64/1.06 % (1091145)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1266601633:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 5.64/1.06 % Exception at run slice level
% 5.64/1.06 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.64/1.06 % (1091147)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1937766516:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 5.64/1.06 % (1091147)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.64/1.06 % (1091141) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1091088-1091141"...
% 5.64/1.06 % (1091141)...printing done.
% 5.64/1.06 % (1091141)Refutation found. Thanks to Tanya!
% 5.64/1.06 % SZS status Theorem for theBenchmark
% 5.64/1.06 % SZS output start Proof for theBenchmark
% 5.64/1.06 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 5.64/1.06 thf(func_def_0, type, in: ($i > $i > $o)).
% 5.64/1.06 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 5.64/1.06 thf(func_def_3, type, setextAx: $o).
% 5.64/1.06 thf(func_def_5, type, emptysetAx: $o).
% 5.64/1.06 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_7, type, setadjoinAx: $o).
% 5.64/1.06 thf(func_def_8, type, powerset: ($i > $i)).
% 5.64/1.06 thf(func_def_9, type, powersetAx: $o).
% 5.64/1.06 thf(func_def_10, type, setunion: ($i > $i)).
% 5.64/1.06 thf(func_def_11, type, setunionAx: $o).
% 5.64/1.06 thf(func_def_13, type, omega0Ax: $o).
% 5.64/1.06 thf(func_def_14, type, omegaSAx: $o).
% 5.64/1.06 thf(func_def_15, type, omegaIndAx: $o).
% 5.64/1.06 thf(func_def_16, type, replAx: $o).
% 5.64/1.06 thf(func_def_17, type, foundationAx: $o).
% 5.64/1.06 thf(func_def_18, type, wellorderingAx: $o).
% 5.64/1.06 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_20, type, descrp: $o).
% 5.64/1.06 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 5.64/1.06 thf(func_def_22, type, dsetconstrI: $o).
% 5.64/1.06 thf(func_def_23, type, dsetconstrEL: $o).
% 5.64/1.06 thf(func_def_24, type, dsetconstrER: $o).
% 5.64/1.06 thf(func_def_25, type, exuE1: $o).
% 5.64/1.06 thf(func_def_26, type, prop2set: ($o > $i)).
% 5.64/1.06 thf(func_def_27, type, prop2setE: $o).
% 5.64/1.06 thf(func_def_28, type, emptysetE: $o).
% 5.64/1.06 thf(func_def_29, type, emptysetimpfalse: $o).
% 5.64/1.06 thf(func_def_30, type, notinemptyset: $o).
% 5.64/1.06 thf(func_def_31, type, exuE3e: $o).
% 5.64/1.06 thf(func_def_32, type, setext: $o).
% 5.64/1.06 thf(func_def_33, type, emptyI: $o).
% 5.64/1.06 thf(func_def_34, type, noeltsimpempty: $o).
% 5.64/1.06 thf(func_def_35, type, setbeta: $o).
% 5.64/1.06 thf(func_def_36, type, nonempty: ($i > $o)).
% 5.64/1.06 thf(func_def_37, type, nonemptyE1: $o).
% 5.64/1.06 thf(func_def_38, type, nonemptyI: $o).
% 5.64/1.06 thf(func_def_39, type, nonemptyI1: $o).
% 5.64/1.06 thf(func_def_40, type, setadjoinIL: $o).
% 5.64/1.06 thf(func_def_41, type, emptyinunitempty: $o).
% 5.64/1.06 thf(func_def_42, type, setadjoinIR: $o).
% 5.64/1.06 thf(func_def_43, type, setadjoinE: $o).
% 5.64/1.06 thf(func_def_44, type, setadjoinOr: $o).
% 5.64/1.06 thf(func_def_45, type, setoftrueEq: $o).
% 5.64/1.06 thf(func_def_46, type, powersetI: $o).
% 5.64/1.06 thf(func_def_47, type, emptyinPowerset: $o).
% 5.64/1.06 thf(func_def_48, type, emptyInPowerset: $o).
% 5.64/1.06 thf(func_def_49, type, powersetE: $o).
% 5.64/1.06 thf(func_def_50, type, setunionI: $o).
% 5.64/1.06 thf(func_def_51, type, setunionE: $o).
% 5.64/1.06 thf(func_def_52, type, subPowSU: $o).
% 5.64/1.06 thf(func_def_53, type, exuE2: $o).
% 5.64/1.06 thf(func_def_54, type, nonemptyImpWitness: $o).
% 5.64/1.06 thf(func_def_55, type, uniqinunit: $o).
% 5.64/1.06 thf(func_def_56, type, notinsingleton: $o).
% 5.64/1.06 thf(func_def_57, type, eqinunit: $o).
% 5.64/1.06 thf(func_def_58, type, singletonsswitch: $o).
% 5.64/1.06 thf(func_def_59, type, upairsetE: $o).
% 5.64/1.06 thf(func_def_60, type, upairsetIL: $o).
% 5.64/1.06 thf(func_def_61, type, upairsetIR: $o).
% 5.64/1.06 thf(func_def_62, type, emptyE1: $o).
% 5.64/1.06 thf(func_def_63, type, vacuousDall: $o).
% 5.64/1.06 thf(func_def_64, type, quantDeMorgan1: $o).
% 5.64/1.06 thf(func_def_65, type, quantDeMorgan2: $o).
% 5.64/1.06 thf(func_def_66, type, quantDeMorgan3: $o).
% 5.64/1.06 thf(func_def_67, type, quantDeMorgan4: $o).
% 5.64/1.06 thf(func_def_68, type, prop2setI: $o).
% 5.64/1.06 thf(func_def_69, type, set2prop: ($i > $o)).
% 5.64/1.06 thf(func_def_70, type, prop2set2propI: $o).
% 5.64/1.06 thf(func_def_71, type, notdexE: $o).
% 5.64/1.06 thf(func_def_72, type, notdallE: $o).
% 5.64/1.06 thf(func_def_73, type, exuI1: $o).
% 5.64/1.06 thf(func_def_74, type, exuI3: $o).
% 5.64/1.06 thf(func_def_75, type, exuI2: $o).
% 5.64/1.06 thf(func_def_76, type, inCongP: $o).
% 5.64/1.06 thf(func_def_77, type, in__Cong: $o).
% 5.64/1.06 thf(func_def_78, type, exuE3u: $o).
% 5.64/1.06 thf(func_def_79, type, exu__Cong: $o).
% 5.64/1.06 thf(func_def_80, type, emptyset__Cong: $o).
% 5.64/1.06 thf(func_def_81, type, setadjoin__Cong: $o).
% 5.64/1.06 thf(func_def_82, type, powerset__Cong: $o).
% 5.64/1.06 thf(func_def_83, type, setunion__Cong: $o).
% 5.64/1.06 thf(func_def_84, type, omega__Cong: $o).
% 5.64/1.06 thf(func_def_85, type, exuEu: $o).
% 5.64/1.06 thf(func_def_86, type, descr__Cong: $o).
% 5.64/1.06 thf(func_def_87, type, dsetconstr__Cong: $o).
% 5.64/1.06 thf(func_def_88, type, subset: ($i > $i > $o)).
% 5.64/1.06 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 5.64/1.06 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 5.64/1.06 thf(func_def_91, type, subsetI1: $o).
% 5.64/1.06 thf(func_def_92, type, eqimpsubset2: $o).
% 5.64/1.06 thf(func_def_93, type, eqimpsubset1: $o).
% 5.64/1.06 thf(func_def_94, type, subsetI2: $o).
% 5.64/1.06 thf(func_def_95, type, emptysetsubset: $o).
% 5.64/1.06 thf(func_def_96, type, subsetE: $o).
% 5.64/1.06 thf(func_def_97, type, subsetE2: $o).
% 5.64/1.06 thf(func_def_98, type, notsubsetI: $o).
% 5.64/1.06 thf(func_def_99, type, notequalI1: $o).
% 5.64/1.06 thf(func_def_100, type, notequalI2: $o).
% 5.64/1.06 thf(func_def_101, type, subsetRefl: $o).
% 5.64/1.06 thf(func_def_102, type, subsetTrans: $o).
% 5.64/1.06 thf(func_def_103, type, setadjoinSub: $o).
% 5.64/1.06 thf(func_def_104, type, setadjoinSub2: $o).
% 5.64/1.06 thf(func_def_105, type, subset2powerset: $o).
% 5.64/1.06 thf(func_def_106, type, setextsub: $o).
% 5.64/1.06 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 5.64/1.06 thf(func_def_108, type, powersetI1: $o).
% 5.64/1.06 thf(func_def_109, type, powersetE1: $o).
% 5.64/1.06 thf(func_def_110, type, inPowerset: $o).
% 5.64/1.06 thf(func_def_111, type, powersetsubset: $o).
% 5.64/1.06 thf(func_def_112, type, sepInPowerset: $o).
% 5.64/1.06 thf(func_def_113, type, sepSubset: $o).
% 5.64/1.06 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_115, type, binunionIL: $o).
% 5.64/1.06 thf(func_def_116, type, upairset2IR: $o).
% 5.64/1.06 thf(func_def_117, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.64/1.06 thf(func_def_118, type, vAND: ($o > $o > $o)).
% 5.64/1.06 thf(func_def_119, type, db1: !>[X0: $tType]:(X0)).
% 5.64/1.06 thf(func_def_120, type, db0: !>[X0: $tType]:(X0)).
% 5.64/1.06 thf(func_def_121, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.64/1.06 thf(func_def_122, type, vIMP: ($o > $o > $o)).
% 5.64/1.06 thf(func_def_123, type, db2: !>[X0: $tType]:(X0)).
% 5.64/1.06 thf(func_def_124, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.64/1.06 thf(func_def_125, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.64/1.06 thf(func_def_126, type, vIFF: ($o > $o > $o)).
% 5.64/1.06 thf(func_def_127, type, vNOT: ($o > $o)).
% 5.64/1.06 thf(func_def_128, type, vOR: ($o > $o > $o)).
% 5.64/1.06 thf(func_def_129, type, db4: !>[X0: $tType]:(X0)).
% 5.64/1.06 thf(func_def_130, type, db3: !>[X0: $tType]:(X0)).
% 5.64/1.06 thf(func_def_133, type, db5: !>[X0: $tType]:(X0)).
% 5.64/1.06 thf(func_def_137, type, sK3: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_138, type, sK4: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_139, type, sK5: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 5.64/1.06 thf(func_def_140, type, sK6: ($i > $i > ($i > $o) > ($i > $o) > $i)).
% 5.64/1.06 thf(func_def_141, type, sK7: (($i > $o) > ($i > $o) > $i)).
% 5.64/1.06 thf(func_def_142, type, sK8: (($i > $o) > ($i > $o) > $i)).
% 5.64/1.06 thf(func_def_143, type, sK9: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_144, type, sK10: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_145, type, sK11: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_146, type, sK12: (($i > $o) > ($i > $o) > $i)).
% 5.64/1.06 thf(func_def_147, type, sK13: (($i > $o) > ($i > $o) > $i)).
% 5.64/1.06 thf(func_def_148, type, sK14: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_149, type, sK15: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_150, type, sK16: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_151, type, sK17: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_152, type, sK18: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_153, type, sK19: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_154, type, sK20: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_155, type, sK21: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_156, type, sK22: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_157, type, sK23: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_158, type, sK24: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_159, type, sK25: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_160, type, sK26: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_161, type, sK27: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_162, type, sK28: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_163, type, sK29: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_164, type, sK30: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_165, type, sK31: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_166, type, sK32: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_167, type, sK33: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_168, type, sK34: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_169, type, sK35: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_170, type, sK36: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_171, type, sK37: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_172, type, sK38: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_173, type, sK39: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_174, type, sK40: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_175, type, sK41: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_176, type, sK42: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_177, type, sK43: ($i > $i)).
% 5.64/1.06 thf(func_def_178, type, sK44: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_179, type, sK45: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_180, type, sK46: ($i > $o > $i > $i)).
% 5.64/1.06 thf(func_def_181, type, sK47: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_182, type, sK48: ($i > $i)).
% 5.64/1.06 thf(func_def_183, type, sK49: ($i > $i)).
% 5.64/1.06 thf(func_def_184, type, sK50: ($i > $i)).
% 5.64/1.06 thf(func_def_185, type, sK51: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_186, type, sK52: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_187, type, sK53: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_188, type, sK54: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_189, type, sK55: (($i > $o) > $i)).
% 5.64/1.06 thf(func_def_190, type, sK56: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_191, type, sK57: (($i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_192, type, sK58: ($i > $i)).
% 5.64/1.06 thf(func_def_193, type, sK59: ($i > $i > $i > $i)).
% 5.64/1.06 thf(func_def_194, type, sK60: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_195, type, sK61: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_196, type, sK62: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_197, type, sK63: ($i > $i)).
% 5.64/1.06 thf(func_def_198, type, sK64: ($i > ($i > $i > $o) > $i)).
% 5.64/1.06 thf(func_def_199, type, sK65: ($i > ($i > $i > $o) > $i)).
% 5.64/1.06 thf(func_def_200, type, sK66: ($i > $i > ($i > $i > $o) > $i)).
% 5.64/1.06 thf(func_def_201, type, sK67: ($i > ($i > $i > $o) > $i > $i)).
% 5.64/1.06 thf(func_def_202, type, sK68: ($i > $i > ($i > $i > $o) > $i)).
% 5.64/1.06 thf(func_def_203, type, sK69: ($i > $i > ($i > $i > $o) > $i)).
% 5.64/1.06 thf(func_def_204, type, sK70: ($i > $i)).
% 5.64/1.06 thf(func_def_205, type, sK71: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_206, type, sK72: ($i > $i > $i)).
% 5.64/1.06 thf(func_def_207, type, sK73: ($i > $i > $i)).
% 5.64/1.06 thf(f41,axiom,(
% 5.64/1.06 (setunionI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))),
% 5.64/1.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI)).
% 5.64/1.06 thf(f71,axiom,(
% 5.64/1.06 (setadjoin__Cong = ! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => (((setadjoin @ X0 @ X2)) = ((setadjoin @ X1 @ X3))))))),
% 5.64/1.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong)).
% 5.64/1.06 thf(f101,axiom,(
% 5.64/1.06 (binunion = (^[X0 : $i, X1 : $i] : ((setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))))),
% 5.64/1.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunion)).
% 5.64/1.06 thf(f103,axiom,(
% 5.64/1.06 (upairset2IR = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 5.64/1.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR)).
% 5.64/1.06 thf(f104,conjecture,(
% 5.64/1.06 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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 5.64/1.06 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR)).
% 5.64/1.06 thf(f105,negated_conjecture,(
% 5.64/1.06 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 5.64/1.06 inference(negated_conjecture,[status(cth)],[f104])).
% 5.64/1.06 thf(f181,plain,(
% 5.64/1.06 (setunionI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))),
% 5.64/1.06 inference(rectify,[],[f41])).
% 5.64/1.06 thf(f182,plain,(
% 5.64/1.06 (setunionI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2))))))))))))),
% 5.64/1.06 inference(fool_elimination,[],[f181])).
% 5.64/1.06 thf(f240,plain,(
% 5.64/1.06 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))))))),
% 5.64/1.06 inference(fool_elimination,[],[f71])).
% 5.64/1.06 thf(f296,plain,(
% 5.64/1.06 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 5.64/1.06 inference(fool_elimination,[],[f101])).
% 5.64/1.06 thf(f299,plain,(
% 5.64/1.06 (upairset2IR = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 5.64/1.06 inference(rectify,[],[f103])).
% 5.64/1.06 thf(f300,plain,(
% 5.64/1.06 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 5.64/1.06 inference(fool_elimination,[],[f299])).
% 5.64/1.06 thf(f301,plain,(
% 5.64/1.06 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 5.64/1.06 inference(rectify,[],[f105])).
% 5.64/1.06 thf(f302,plain,(
% 5.64/1.06 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ (binunion @ X0 @ X1))) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 5.64/1.06 inference(fool_elimination,[],[f301])).
% 5.64/1.06 thf(f303,plain,(
% 5.64/1.06 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (binunion @ X0 @ X1))) != $true) & (((in @ X2 @ X1)) = $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)),
% 5.64/1.06 inference(ennf_transformation,[],[f302])).
% 5.64/1.06 thf(f304,plain,(
% 5.64/1.06 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (binunion @ X0 @ X1))) != $true) & (((in @ X2 @ X1)) = $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 = $true)),
% 5.64/1.06 inference(flattening,[],[f303])).
% 5.64/1.06 thf(f305,plain,(
% 5.64/1.06 (($true != ((in @ sK2 @ (binunion @ sK0 @ sK1)))) & ($true = ((in @ sK2 @ sK1)))) & (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)),
% 5.64/1.06 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f304])).
% 5.64/1.06 thf(f346,plain,(
% 5.64/1.06 (setunionI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2))))))))))))),
% 5.64/1.06 inference(cnf_transformation,[],[f182])).
% 5.64/1.06 thf(f376,plain,(
% 5.64/1.06 (setadjoin__Cong = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))))))),
% 5.64/1.06 inference(cnf_transformation,[],[f240])).
% 5.64/1.06 thf(f406,plain,(
% 5.64/1.06 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 5.64/1.06 inference(cnf_transformation,[],[f296])).
% 5.64/1.06 thf(f408,plain,(
% 5.64/1.06 (upairset2IR = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 5.64/1.06 inference(cnf_transformation,[],[f300])).
% 5.64/1.06 thf(f447,plain,(
% 5.64/1.06 (setunionI = $true)),
% 5.64/1.06 inference(cnf_transformation,[],[f305])).
% 5.64/1.06 thf(f477,plain,(
% 5.64/1.06 (setadjoin__Cong = $true)),
% 5.64/1.06 inference(cnf_transformation,[],[f305])).
% 5.64/1.06 thf(f508,plain,(
% 5.64/1.06 (upairset2IR = $true)),
% 5.64/1.06 inference(cnf_transformation,[],[f305])).
% 5.64/1.06 thf(f509,plain,(
% 5.64/1.06 ($true = ((in @ sK2 @ sK1)))),
% 5.64/1.06 inference(cnf_transformation,[],[f305])).
% 5.64/1.06 thf(f510,plain,(
% 5.64/1.06 ($true != ((in @ sK2 @ (binunion @ sK0 @ sK1))))),
% 5.64/1.06 inference(cnf_transformation,[],[f305])).
% 5.64/1.06 thf(f512,definition,(
% 5.64/1.06 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 5.64/1.06 introduced(theory,[fool_exhaustiveness_axiom])).
% 5.64/1.06 thf(f551,plain,(
% 5.64/1.06 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2))))))))))))),
% 5.64/1.06 inference(definition_unfolding,[],[f346,f447])).
% 5.64/1.06 thf(f581,plain,(
% 5.64/1.06 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))))))),
% 5.64/1.06 inference(definition_unfolding,[],[f376,f477])).
% 5.64/1.06 thf(f612,plain,(
% 5.64/1.06 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 5.64/1.06 inference(definition_unfolding,[],[f408,f508])).
% 5.64/1.06 thf(f613,plain,(
% 5.64/1.06 ($true != ((in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ sK0 @ sK1))))),
% 5.64/1.06 inference(definition_unfolding,[],[f510,f406])).
% 5.64/1.06 thf(f614,plain,(
% 5.64/1.06 ($true != ((in @ sK2 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))))))),
% 5.64/1.06 inference(beta-eta_normalization,[],[f613])).
% 5.64/1.06 thf(f615,plain,(
% 5.64/1.06 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))) @ X1)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f612])).
% 5.64/1.06 thf(f616,plain,(
% 5.64/1.06 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)))))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f615])).
% 5.64/1.06 thf(f617,plain,(
% 5.64/1.06 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)))) @ X2)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f616])).
% 5.64/1.06 thf(f618,plain,(
% 5.64/1.06 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f617])).
% 5.64/1.06 thf(f878,plain,(
% 5.64/1.06 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y1 @ Y3) = (setadjoin @ Y0 @ Y2))))))))))) @ X1)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f581])).
% 5.64/1.06 thf(f879,plain,(
% 5.64/1.06 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y2 = Y1) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ X1 @ Y1))))))))))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f878])).
% 5.64/1.06 thf(f880,plain,(
% 5.64/1.06 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((Y0 = X1) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y2 = Y1) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ X1 @ Y1))))))))) @ X2)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f879])).
% 5.64/1.06 thf(f881,plain,(
% 5.64/1.06 ( ! [X2 : $i,X1 : $i] : (($true = (((X2 = X1) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ X2 @ Y1) = (setadjoin @ X1 @ Y0))))))))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f880])).
% 5.64/1.06 thf(f882,plain,(
% 5.64/1.06 ( ! [X2 : $i,X1 : $i] : (($false = ((X2 = X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ X2 @ Y1) = (setadjoin @ X1 @ Y0)))))))))) )),
% 5.64/1.06 inference(imp_proxy_clausification,[],[f881])).
% 5.64/1.06 thf(f883,plain,(
% 5.64/1.06 ( ! [X2 : $i,X1 : $i] : ((X1 != X2) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ X2 @ Y1) = (setadjoin @ X1 @ Y0)))))))))) )),
% 5.64/1.06 inference(equality_proxy_clausification,[],[f882])).
% 5.64/1.06 thf(f884,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((X1 != X2) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ X2 @ Y1) = (setadjoin @ X1 @ Y0)))))) @ X3)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f883])).
% 5.64/1.06 thf(f885,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((X1 != X2) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((Y0 = X3) => ((setadjoin @ X2 @ Y0) = (setadjoin @ X1 @ X3)))))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f884])).
% 5.64/1.06 thf(f886,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((X1 != X2) | ($true = (((^[Y0 : $i]: ((Y0 = X3) => ((setadjoin @ X2 @ Y0) = (setadjoin @ X1 @ X3)))) @ X4)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f885])).
% 5.64/1.06 thf(f887,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((X1 != X2) | ($true = (((X4 = X3) => ((setadjoin @ X2 @ X4) = (setadjoin @ X1 @ X3)))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f886])).
% 5.64/1.06 thf(f888,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((X1 != X2) | ($false = ((X4 = X3))) | ($true = (((setadjoin @ X2 @ X4) = (setadjoin @ X1 @ X3))))) )),
% 5.64/1.06 inference(imp_proxy_clausification,[],[f887])).
% 5.64/1.06 thf(f889,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((X1 != X2) | (X3 != X4) | ($true = (((setadjoin @ X2 @ X4) = (setadjoin @ X1 @ X3))))) )),
% 5.64/1.06 inference(equality_proxy_clausification,[],[f888])).
% 5.64/1.06 thf(f890,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((setadjoin @ X1 @ X3)) = ((setadjoin @ X2 @ X4))) | (X3 != X4) | (X1 != X2)) )),
% 5.64/1.06 inference(equality_proxy_clausification,[],[f889])).
% 5.64/1.06 thf(f1362,plain,(
% 5.64/1.06 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2))))))))) @ X1)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f551])).
% 5.64/1.06 thf(f1363,plain,(
% 5.64/1.06 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ X1 @ Y1) => (in @ Y0 @ (setunion @ Y1))))))))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f1362])).
% 5.64/1.06 thf(f1364,plain,(
% 5.64/1.06 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ X1 @ Y1) => (in @ Y0 @ (setunion @ Y1))))))) @ X2)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f1363])).
% 5.64/1.06 thf(f1365,plain,(
% 5.64/1.06 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => ((in @ X1 @ Y0) => (in @ X2 @ (setunion @ Y0))))))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f1364])).
% 5.64/1.06 thf(f1366,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X2 @ X1) => ((in @ X1 @ Y0) => (in @ X2 @ (setunion @ Y0))))) @ X3)))) )),
% 5.64/1.06 inference(pi_proxy_clausification,[],[f1365])).
% 5.64/1.06 thf(f1367,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X2 @ X1) => ((in @ X1 @ X3) => (in @ X2 @ (setunion @ X3))))))) )),
% 5.64/1.06 inference(beta-eta_normalization,[],[f1366])).
% 5.64/1.06 thf(f1368,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $false) | ($true = (((in @ X1 @ X3) => (in @ X2 @ (setunion @ X3)))))) )),
% 5.64/1.06 inference(imp_proxy_clausification,[],[f1367])).
% 5.64/1.06 thf(f1369,plain,(
% 5.64/1.06 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $false) | (((in @ X1 @ X3)) = $false) | ($true = ((in @ X2 @ (setunion @ X3))))) )),
% 5.64/1.06 inference(imp_proxy_clausification,[],[f1368])).
% 5.64/1.06 thf(f1810,definition,(
% 5.64/1.06 spl74_1 <=> ! [X3 : $o] : (($false = X3) | ($true = X3))),
% 5.64/1.06 introduced(definition,[new_symbols(definition,[spl74_1])],[avatar_definition])).
% 5.64/1.06 thf(f1811,plain,(
% 5.64/1.06 ( ! [X3 : $o] : (($true = X3) | ($false = X3)) ) | ~spl74_1),
% 5.64/1.06 inference(avatar_component_clause,[],[f1810])).
% 5.64/1.06 thf(f1828,plain,(
% 5.64/1.06 spl74_1),
% 5.64/1.06 inference(avatar_split_clause,[],[f512,f1810])).
% 5.64/1.06 thf(f2532,plain,(
% 5.64/1.06 ($true != $true) | ($false = ((in @ sK2 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)))))) | ~spl74_1),
% 5.64/1.06 inference(constrained_superposition,[],[f614,f1811])).
% 5.64/1.06 thf(f2533,plain,(
% 5.64/1.06 ($false = ((in @ sK2 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)))))) | ~spl74_1),
% 5.64/1.06 inference(trivial_inequality_removal,[],[f2532])).
% 5.64/1.06 thf(f2539,plain,(
% 5.64/1.06 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ sK2 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ X0 @ X1)))))) | (emptyset != X1) | (sK1 != X0)) ) | ~spl74_1),
% 5.64/1.06 inference(constrained_superposition,[],[f2533,f890])).
% 5.64/1.06 thf(f5377,plain,(
% 5.64/1.06 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = $true) | (emptyset != X1) | (sK1 != X0) | ($false = ((in @ sK2 @ X2))) | ($false = ((in @ X2 @ (setadjoin @ sK0 @ (setadjoin @ X0 @ X1)))))) ) | ~spl74_1),
% 5.64/1.06 inference(constrained_superposition,[],[f2539,f1369])).
% 5.64/1.06 thf(f5385,plain,(
% 5.64/1.06 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((in @ X2 @ (setadjoin @ sK0 @ (setadjoin @ X0 @ X1))))) | (sK1 != X0) | ($false = ((in @ sK2 @ X2))) | (emptyset != X1)) ) | ~spl74_1),
% 5.64/1.06 inference(trivial_inequality_removal,[],[f5377])).
% 5.64/1.06 thf(f5526,plain,(
% 5.64/1.06 ( ! [X0 : $i] : (($false = $true) | (sK1 != X0) | ($false = ((in @ sK2 @ X0))) | (emptyset != emptyset)) ) | ~spl74_1),
% 5.64/1.06 inference(constrained_superposition,[],[f618,f5385])).
% 5.64/1.06 thf(f5545,plain,(
% 5.64/1.06 ( ! [X0 : $i] : (($false = ((in @ sK2 @ X0))) | (sK1 != X0)) ) | ~spl74_1),
% 5.64/1.06 inference(trivial_inequality_removal,[],[f5526])).
% 5.64/1.06 thf(f5629,plain,(
% 5.64/1.06 ($false = $true) | (sK1 != sK1) | ~spl74_1),
% 5.64/1.06 inference(constrained_superposition,[],[f5545,f509])).
% 5.64/1.06 thf(f5673,plain,(
% 5.64/1.06 $false | ~spl74_1),
% 5.64/1.06 inference(trivial_inequality_removal,[],[f5629])).
% 5.64/1.06 thf(f5674,plain,(
% 5.64/1.06 ~spl74_1),
% 5.64/1.06 inference(avatar_contradiction_clause,[],[f5673])).
% 5.64/1.06 cnf(s5, plain, spl74_1, inference(sat_conversion,[],[f1828])).
% 5.64/1.06 cnf(s21, plain, ~spl74_1, inference(sat_conversion,[],[f5674])).
% 5.64/1.06 cnf(s24, plain, $false, inference(rat,[],[s5,s21])).
% 5.64/1.06 thf(f5693,plain,(
% 5.64/1.06 $false),
% 5.64/1.06 inference(avatar_sat_refutation,[],[s24])).
% 5.64/1.06 % SZS output end Proof for theBenchmark
% 5.64/1.06 % (1091141)------------------------------
% 5.64/1.06 % (1091141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.64/1.06 % (1091141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.06 % (1091141)CaDiCaL version: 2.1.3
% 5.64/1.06 % (1091141)Termination reason: Refutation
% 5.64/1.06 % (1091141)Time elapsed: 0.349 s
% 5.64/1.06 % (1091141)Peak memory usage: 16 MB
% 5.64/1.06 % (1091141)Instructions burned: 733 (million)
% 5.64/1.06 % (1091088)Success in time 0.826 s
% 5.64/1.06 % Vampire exiting
%------------------------------------------------------------------------------