%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU814^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:33:31 AM UTC 2026
% Result : Theorem 86.38s 12.47s
% Output : Refutation 86.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU814^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.18 % Computer : n018.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 14:35:56 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 Running first-order model finding
% 0.11/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.61/1.51 % (167568)Will run a generic schedule for satisfiability detection.
% 8.61/1.51 % (167575)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2973892581:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 8.61/1.51 % (167574)% WARNING: option uhcvi not known.
% 8.61/1.51 % (167574)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2694214140:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 8.61/1.51 % (167573)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=6966704_2999 on theBenchmark for (2999ds/0Mi)
% 8.61/1.51 % (167576)dis+10_1_sil=32000:sp=arity:random_seed=1568104400:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 8.61/1.51 % (167577)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4037874121:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 8.61/1.51 % (167578)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=767114978:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 8.61/1.51 % (167579)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=358017375:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 8.61/1.51 % (167574)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.61/1.51 % (167574)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.61/1.51 % (167577)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.61/1.51 % (167576)Instruction limit reached!
% 8.61/1.51 % (167576)------------------------------
% 8.61/1.51 % (167576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.51 % (167576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.51 % (167576)CaDiCaL version: 2.1.3
% 8.61/1.51 % (167576)Termination reason: Instruction limit
% 8.61/1.51 % (167576)Termination phase: Property scanning
% 8.61/1.51 % (167576)Time elapsed: 0.082 s
% 8.61/1.51 % (167576)Peak memory usage: 12 MB
% 8.61/1.51 % (167576)Instructions burned: 103 (million)
% 8.61/1.51 % (167577)Instruction limit reached!
% 8.61/1.51 % (167577)------------------------------
% 8.61/1.51 % (167577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.51 % (167577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.51 % (167577)CaDiCaL version: 2.1.3
% 8.61/1.51 % (167577)Termination reason: Instruction limit
% 8.61/1.51 % (167577)Termination phase: Property scanning
% 8.61/1.51 % (167577)Time elapsed: 0.092 s
% 8.61/1.51 % (167577)Peak memory usage: 12 MB
% 8.61/1.51 % (167577)Instructions burned: 117 (million)
% 8.61/1.51 % Exception at run slice level
% 8.61/1.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.61/1.51 % (167578)Instruction limit reached!
% 8.61/1.51 % (167578)------------------------------
% 8.61/1.51 % (167578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.51 % (167578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.51 % (167578)CaDiCaL version: 2.1.3
% 8.61/1.51 % (167578)Termination reason: Instruction limit
% 8.61/1.51 % (167578)Termination phase: Function definition elimination
% 8.61/1.51 % (167578)Time elapsed: 0.103 s
% 8.61/1.51 % (167578)Peak memory usage: 12 MB
% 8.61/1.51 % (167578)Instructions burned: 131 (million)
% 8.61/1.51 % (167587)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=25608640:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 8.61/1.51 % (167588)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3233749478:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 8.61/1.51 % (167590)ott-21_1_sil=16000:fs=off:random_seed=2876240428:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 8.61/1.51 % (167579)Instruction limit reached!
% 8.61/1.51 % (167579)------------------------------
% 8.61/1.51 % (167579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.61/1.51 % (167579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.51 % (167579)CaDiCaL version: 2.1.3
% 8.61/1.51 % (167579)Termination reason: Instruction limit
% 8.61/1.51 % (167579)Termination phase: Property scanning
% 8.61/1.51 % (167579)Time elapsed: 0.123 s
% 8.61/1.51 % (167579)Peak memory usage: 12 MB
% 8.61/1.51 % (167579)Instructions burned: 160 (million)
% 8.61/1.51 % (167589)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=1314469285:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 29.36/4.47 % (167595)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3106086600:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 29.36/4.47 % (167589)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.36/4.47 % (167588)Instruction limit reached!
% 29.36/4.47 % (167588)------------------------------
% 29.36/4.47 % (167588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.36/4.47 % (167588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.36/4.47 % (167588)CaDiCaL version: 2.1.3
% 29.36/4.47 % (167588)Termination reason: Instruction limit
% 29.36/4.47 % (167588)Termination phase: Function definition elimination
% 29.36/4.47 % (167588)Time elapsed: 0.102 s
% 29.36/4.47 % (167588)Peak memory usage: 12 MB
% 29.36/4.47 % (167588)Instructions burned: 131 (million)
% 29.36/4.47 % (167590)Instruction limit reached!
% 29.36/4.47 % (167590)------------------------------
% 29.36/4.47 % (167590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.36/4.47 % (167590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.36/4.47 % (167590)CaDiCaL version: 2.1.3
% 29.36/4.47 % (167590)Termination reason: Instruction limit
% 29.36/4.47 % (167590)Termination phase: Saturation
% 29.36/4.47 % (167590)Time elapsed: 0.109 s
% 29.36/4.47 % (167590)Peak memory usage: 13 MB
% 29.36/4.47 % (167590)Instructions burned: 180 (million)
% 29.36/4.47 % (167589)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 29.36/4.47 % (167597)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2335681417:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 29.36/4.47 % Exception at run slice level
% 29.36/4.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.36/4.47 % (167598)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=338148900:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 29.36/4.47 % (167600)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=787548635:i=889:ins=1_2996 on theBenchmark for (2996ds/889Mi)
% 29.36/4.47 % Exception at run slice level
% 29.36/4.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.36/4.47 % (167603)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=2795793056:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2995 on theBenchmark for (2995ds/692Mi)
% 29.36/4.47 % Exception at run slice level
% 29.36/4.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.36/4.47 % (167603)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.36/4.47 % (167595)Instruction limit reached!
% 29.36/4.47 % (167595)------------------------------
% 29.36/4.47 % (167595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.36/4.47 % (167595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.36/4.47 % (167595)CaDiCaL version: 2.1.3
% 29.36/4.47 % (167595)Termination reason: Instruction limit
% 29.36/4.47 % (167595)Termination phase: Saturation
% 29.36/4.47 % (167595)Time elapsed: 0.256 s
% 29.36/4.47 % (167595)Peak memory usage: 16 MB
% 29.36/4.47 % (167595)Instructions burned: 477 (million)
% 29.36/4.47 % (167605)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2883665690:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 29.36/4.47 % (167606)fmb+10_1_sil=64000:random_seed=1295896752:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 29.36/4.47 % (167605)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.36/4.47 % (167606)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 29.36/4.47 % (167589)Instruction limit reached!
% 29.36/4.47 % (167589)------------------------------
% 29.36/4.47 % (167589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.36/4.47 % (167589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.36/4.47 % (167589)CaDiCaL version: 2.1.3
% 29.36/4.47 % (167589)Termination reason: Instruction limit
% 29.36/4.47 % (167589)Termination phase: Saturation
% 29.36/4.47 % (167589)Time elapsed: 0.393 s
% 80.69/11.60 % (167589)Peak memory usage: 17 MB
% 80.69/11.60 % (167589)Instructions burned: 686 (million)
% 80.69/11.60 % Exception at run slice level
% 80.69/11.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.69/11.60 % (167609)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=898780776:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 80.69/11.60 % (167610)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=948713606:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 80.69/11.60 % Exception at run slice level
% 80.69/11.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.69/11.60 % (167613)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=977159027:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 80.69/11.60 % (167613)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 80.69/11.60 % (167603)Instruction limit reached!
% 80.69/11.60 % (167603)------------------------------
% 80.69/11.60 % (167603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.69/11.60 % (167603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.69/11.60 % (167603)CaDiCaL version: 2.1.3
% 80.69/11.60 % (167603)Termination reason: Instruction limit
% 80.69/11.60 % (167603)Termination phase: Saturation
% 80.69/11.60 % (167603)Time elapsed: 0.321 s
% 80.69/11.60 % (167603)Peak memory usage: 18 MB
% 80.69/11.60 % (167603)Instructions burned: 692 (million)
% 80.69/11.60 % Exception at run slice level
% 80.69/11.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.69/11.60 % (167616)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1964251774:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 80.69/11.60 % (167615)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1604274937:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 80.69/11.60 % Exception at run slice level
% 80.69/11.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.69/11.60 % (167615)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 80.69/11.60 % (167620)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2877555333:fmbsr=2.30978:i=2174_2991 on theBenchmark for (2991ds/2174Mi)
% 80.69/11.60 % (167615)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 80.69/11.60 % (167605)Instruction limit reached!
% 80.69/11.60 % (167605)------------------------------
% 80.69/11.60 % (167605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.69/11.60 % (167605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.69/11.60 % (167605)CaDiCaL version: 2.1.3
% 80.69/11.60 % (167605)Termination reason: Instruction limit
% 80.69/11.60 % (167605)Termination phase: Saturation
% 80.69/11.60 % (167605)Time elapsed: 0.438 s
% 80.69/11.60 % (167605)Peak memory usage: 19 MB
% 80.69/11.60 % (167605)Instructions burned: 881 (million)
% 80.69/11.60 % (167625)ott-2_1_sil=16000:newcnf=on:random_seed=2715856592:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2990 on theBenchmark for (2990ds/869Mi)
% 80.69/11.60 % Exception at run slice level
% 80.69/11.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 80.69/11.60 % (167625)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 80.69/11.60 % (167627)ott+10_1_sil=32000:tgt=ground:random_seed=2774975503:i=5114:av=off_2990 on theBenchmark for (2990ds/5114Mi)
% 80.69/11.60 % (167625)Instruction limit reached!
% 80.69/11.60 % (167625)------------------------------
% 80.69/11.60 % (167625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 80.69/11.60 % (167625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 80.69/11.60 % (167625)CaDiCaL version: 2.1.3
% 80.69/11.60 % (167625)Termination reason: Instruction limit
% 80.69/11.60 % (167625)Termination phase: Saturation
% 80.69/11.60 % (167625)Time elapsed: 0.317 s
% 80.69/11.60 % (167625)Peak memory usage: 17 MB
% 80.69/11.60 % (167625)Instructions burned: 872 (million)
% 80.69/11.60 % (167630)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2147604588:i=54282_2987 on theBenchmark for (2987ds/54282Mi)
% 80.69/11.60 % (167598)Instruction limit reached!
% 80.69/11.60 % (167598)------------------------------
% 80.69/11.60 % (167598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167598)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167598)Termination reason: Instruction limit
% 86.38/12.47 % (167598)Termination phase: Saturation
% 86.38/12.47 % (167598)Time elapsed: 0.953 s
% 86.38/12.47 % (167598)Peak memory usage: 21 MB
% 86.38/12.47 % (167598)Instructions burned: 1180 (million)
% 86.38/12.47 % (167632)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1966122912:i=3512:aac=none_2987 on theBenchmark for (2987ds/3512Mi)
% 86.38/12.47 % Exception at run slice level
% 86.38/12.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 86.38/12.47 % (167634)dis+21_1_sil=32000:sas=cadical:random_seed=860115018:i=3773:amm=off_2986 on theBenchmark for (2986ds/3773Mi)
% 86.38/12.47 % (167632)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 86.38/12.47 % (167615)Instruction limit reached!
% 86.38/12.47 % (167615)------------------------------
% 86.38/12.47 % (167615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167615)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167615)Termination reason: Instruction limit
% 86.38/12.47 % (167615)Termination phase: Saturation
% 86.38/12.47 % (167615)Time elapsed: 1.195 s
% 86.38/12.47 % (167615)Peak memory usage: 28 MB
% 86.38/12.47 % (167615)Instructions burned: 1472 (million)
% 86.38/12.47 % (167636)ott+11_1_sil=16000:gs=on:random_seed=456695560:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2980 on theBenchmark for (2980ds/2251Mi)
% 86.38/12.47 % (167636)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 86.38/12.47 % (167636)Instruction limit reached!
% 86.38/12.47 % (167636)------------------------------
% 86.38/12.47 % (167636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167636)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167636)Termination reason: Instruction limit
% 86.38/12.47 % (167636)Termination phase: Saturation
% 86.38/12.47 % (167636)Time elapsed: 0.998 s
% 86.38/12.47 % (167636)Peak memory usage: 19 MB
% 86.38/12.47 % (167636)Instructions burned: 2251 (million)
% 86.38/12.47 % (167638)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3271445197:fmbsr=1.6:i=67534_2969 on theBenchmark for (2969ds/67534Mi)
% 86.38/12.47 % Exception at run slice level
% 86.38/12.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 86.38/12.47 % (167641)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=72533544:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2968 on theBenchmark for (2968ds/4591Mi)
% 86.38/12.47 % (167632)Instruction limit reached!
% 86.38/12.47 % (167632)------------------------------
% 86.38/12.47 % (167632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167632)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167632)Termination reason: Instruction limit
% 86.38/12.47 % (167632)Termination phase: Saturation
% 86.38/12.47 % (167632)Time elapsed: 1.832 s
% 86.38/12.47 % (167632)Peak memory usage: 23 MB
% 86.38/12.47 % (167632)Instructions burned: 3514 (million)
% 86.38/12.47 % (167643)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=116181872:i=29340_2968 on theBenchmark for (2968ds/29340Mi)
% 86.38/12.47 % (167634)Instruction limit reached!
% 86.38/12.47 % (167634)------------------------------
% 86.38/12.47 % (167634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167634)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167634)Termination reason: Instruction limit
% 86.38/12.47 % (167634)Termination phase: Saturation
% 86.38/12.47 % (167634)Time elapsed: 2.623 s
% 86.38/12.47 % (167634)Peak memory usage: 23 MB
% 86.38/12.47 % (167634)Instructions burned: 3773 (million)
% 86.38/12.47 % (167650)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=3004740733:i=5211_2959 on theBenchmark for (2959ds/5211Mi)
% 86.38/12.47 % (167613)Instruction limit reached!
% 86.38/12.47 % (167613)------------------------------
% 86.38/12.47 % (167613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167613)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167613)Termination reason: Instruction limit
% 86.38/12.47 % (167613)Termination phase: Saturation
% 86.38/12.47 % (167613)Time elapsed: 3.542 s
% 86.38/12.47 % (167613)Peak memory usage: 25 MB
% 86.38/12.47 % (167613)Instructions burned: 5131 (million)
% 86.38/12.47 % (167652)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=1192368577:i=5497:nm=2_2957 on theBenchmark for (2957ds/5497Mi)
% 86.38/12.47 % Exception at run slice level
% 86.38/12.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 86.38/12.47 % (167654)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=1082932994:fmbsr=2:i=46332_2956 on theBenchmark for (2956ds/46332Mi)
% 86.38/12.47 % Exception at run slice level
% 86.38/12.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 86.38/12.47 % (167656)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=2224207884:i=14071_2955 on theBenchmark for (2955ds/14071Mi)
% 86.38/12.47 % Exception at run slice level
% 86.38/12.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 86.38/12.47 % (167658)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=754287512:i=22565:add=on:rawr=on_2953 on theBenchmark for (2953ds/22565Mi)
% 86.38/12.47 % (167627)Instruction limit reached!
% 86.38/12.47 % (167627)------------------------------
% 86.38/12.47 % (167627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167627)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167627)Termination reason: Instruction limit
% 86.38/12.47 % (167627)Termination phase: Saturation
% 86.38/12.47 % (167627)Time elapsed: 3.913 s
% 86.38/12.47 % (167627)Peak memory usage: 30 MB
% 86.38/12.47 % (167627)Instructions burned: 5114 (million)
% 86.38/12.47 % (167660)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=3842805196:i=8173:av=off_2950 on theBenchmark for (2950ds/8173Mi)
% 86.38/12.47 % (167641)Instruction limit reached!
% 86.38/12.47 % (167641)------------------------------
% 86.38/12.47 % (167641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167641)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167641)Termination reason: Instruction limit
% 86.38/12.47 % (167641)Termination phase: Saturation
% 86.38/12.47 % (167641)Time elapsed: 2.881 s
% 86.38/12.47 % (167641)Peak memory usage: 29 MB
% 86.38/12.47 % (167641)Instructions burned: 4591 (million)
% 86.38/12.47 % (167664)dis+10_16:1_sil=16000:random_seed=3570427837:i=9155:fsr=off_2939 on theBenchmark for (2939ds/9155Mi)
% 86.38/12.47 % (167650)Instruction limit reached!
% 86.38/12.47 % (167650)------------------------------
% 86.38/12.47 % (167650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167650)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167650)Termination reason: Instruction limit
% 86.38/12.47 % (167650)Termination phase: Saturation
% 86.38/12.47 % (167650)Time elapsed: 4.536 s
% 86.38/12.47 % (167650)Peak memory usage: 31 MB
% 86.38/12.47 % (167650)Instructions burned: 5211 (million)
% 86.38/12.47 % (167668)ott-3_8_sil=64000:random_seed=674387204:i=20139:bs=on_2914 on theBenchmark for (2914ds/20139Mi)
% 86.38/12.47 % (167664)Instruction limit reached!
% 86.38/12.47 % (167664)------------------------------
% 86.38/12.47 % (167664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167664)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167664)Termination reason: Instruction limit
% 86.38/12.47 % (167664)Termination phase: Saturation
% 86.38/12.47 % (167664)Time elapsed: 5.220 s
% 86.38/12.47 % (167664)Peak memory usage: 35 MB
% 86.38/12.47 % (167664)Instructions burned: 9155 (million)
% 86.38/12.47 % (167673)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=3768179544:fmbsr=2:i=32576_2887 on theBenchmark for (2887ds/32576Mi)
% 86.38/12.47 % Exception at run slice level
% 86.38/12.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 86.38/12.47 % (167675)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=3462555079:i=11404_2886 on theBenchmark for (2886ds/11404Mi)
% 86.38/12.47 % (167660)Instruction limit reached!
% 86.38/12.47 % (167660)------------------------------
% 86.38/12.47 % (167660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167660)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167660)Termination reason: Instruction limit
% 86.38/12.47 % (167660)Termination phase: Saturation
% 86.38/12.47 % (167660)Time elapsed: 6.511 s
% 86.38/12.47 % (167660)Peak memory usage: 31 MB
% 86.38/12.47 % (167660)Instructions burned: 8174 (million)
% 86.38/12.47 % (167677)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=1523428909:i=14134_2885 on theBenchmark for (2885ds/14134Mi)
% 86.38/12.47 % (167677)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 86.38/12.47 % (167574) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-167568-167574"...
% 86.38/12.47 % (167574)...printing done.
% 86.38/12.47 % (167574)Refutation found. Thanks to Tanya!
% 86.38/12.47 % SZS status Theorem for theBenchmark
% 86.38/12.47 % SZS output start Proof for theBenchmark
% 86.38/12.47 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 86.38/12.47 thf(func_def_0, type, in: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 86.38/12.47 thf(func_def_3, type, setextAx: $o).
% 86.38/12.47 thf(func_def_5, type, emptysetAx: $o).
% 86.38/12.47 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_7, type, setadjoinAx: $o).
% 86.38/12.47 thf(func_def_8, type, powerset: ($i > $i)).
% 86.38/12.47 thf(func_def_9, type, powersetAx: $o).
% 86.38/12.47 thf(func_def_10, type, setunion: ($i > $i)).
% 86.38/12.47 thf(func_def_11, type, setunionAx: $o).
% 86.38/12.47 thf(func_def_13, type, omega0Ax: $o).
% 86.38/12.47 thf(func_def_14, type, omegaSAx: $o).
% 86.38/12.47 thf(func_def_15, type, omegaIndAx: $o).
% 86.38/12.47 thf(func_def_16, type, replAx: $o).
% 86.38/12.47 thf(func_def_17, type, foundationAx: $o).
% 86.38/12.47 thf(func_def_18, type, wellorderingAx: $o).
% 86.38/12.47 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_20, type, descrp: $o).
% 86.38/12.47 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_22, type, dsetconstrI: $o).
% 86.38/12.47 thf(func_def_23, type, dsetconstrEL: $o).
% 86.38/12.47 thf(func_def_24, type, dsetconstrER: $o).
% 86.38/12.47 thf(func_def_25, type, exuE1: $o).
% 86.38/12.47 thf(func_def_26, type, prop2set: ($o > $i)).
% 86.38/12.47 thf(func_def_27, type, prop2setE: $o).
% 86.38/12.47 thf(func_def_28, type, emptysetE: $o).
% 86.38/12.47 thf(func_def_29, type, emptysetimpfalse: $o).
% 86.38/12.47 thf(func_def_30, type, notinemptyset: $o).
% 86.38/12.47 thf(func_def_31, type, exuE3e: $o).
% 86.38/12.47 thf(func_def_32, type, setext: $o).
% 86.38/12.47 thf(func_def_33, type, emptyI: $o).
% 86.38/12.47 thf(func_def_34, type, noeltsimpempty: $o).
% 86.38/12.47 thf(func_def_35, type, setbeta: $o).
% 86.38/12.47 thf(func_def_36, type, nonempty: ($i > $o)).
% 86.38/12.47 thf(func_def_37, type, nonemptyE1: $o).
% 86.38/12.47 thf(func_def_38, type, nonemptyI: $o).
% 86.38/12.47 thf(func_def_39, type, nonemptyI1: $o).
% 86.38/12.47 thf(func_def_40, type, setadjoinIL: $o).
% 86.38/12.47 thf(func_def_41, type, emptyinunitempty: $o).
% 86.38/12.47 thf(func_def_42, type, setadjoinIR: $o).
% 86.38/12.47 thf(func_def_43, type, setadjoinE: $o).
% 86.38/12.47 thf(func_def_44, type, setadjoinOr: $o).
% 86.38/12.47 thf(func_def_45, type, setoftrueEq: $o).
% 86.38/12.47 thf(func_def_46, type, powersetI: $o).
% 86.38/12.47 thf(func_def_47, type, emptyinPowerset: $o).
% 86.38/12.47 thf(func_def_48, type, emptyInPowerset: $o).
% 86.38/12.47 thf(func_def_49, type, powersetE: $o).
% 86.38/12.47 thf(func_def_50, type, setunionI: $o).
% 86.38/12.47 thf(func_def_51, type, setunionE: $o).
% 86.38/12.47 thf(func_def_52, type, subPowSU: $o).
% 86.38/12.47 thf(func_def_53, type, exuE2: $o).
% 86.38/12.47 thf(func_def_54, type, nonemptyImpWitness: $o).
% 86.38/12.47 thf(func_def_55, type, uniqinunit: $o).
% 86.38/12.47 thf(func_def_56, type, notinsingleton: $o).
% 86.38/12.47 thf(func_def_57, type, eqinunit: $o).
% 86.38/12.47 thf(func_def_58, type, singletonsswitch: $o).
% 86.38/12.47 thf(func_def_59, type, upairsetE: $o).
% 86.38/12.47 thf(func_def_60, type, upairsetIL: $o).
% 86.38/12.47 thf(func_def_61, type, upairsetIR: $o).
% 86.38/12.47 thf(func_def_62, type, emptyE1: $o).
% 86.38/12.47 thf(func_def_63, type, vacuousDall: $o).
% 86.38/12.47 thf(func_def_64, type, quantDeMorgan1: $o).
% 86.38/12.47 thf(func_def_65, type, quantDeMorgan2: $o).
% 86.38/12.47 thf(func_def_66, type, quantDeMorgan3: $o).
% 86.38/12.47 thf(func_def_67, type, quantDeMorgan4: $o).
% 86.38/12.47 thf(func_def_68, type, prop2setI: $o).
% 86.38/12.47 thf(func_def_69, type, set2prop: ($i > $o)).
% 86.38/12.47 thf(func_def_70, type, prop2set2propI: $o).
% 86.38/12.47 thf(func_def_71, type, notdexE: $o).
% 86.38/12.47 thf(func_def_72, type, notdallE: $o).
% 86.38/12.47 thf(func_def_73, type, exuI1: $o).
% 86.38/12.47 thf(func_def_74, type, exuI3: $o).
% 86.38/12.47 thf(func_def_75, type, exuI2: $o).
% 86.38/12.47 thf(func_def_76, type, inCongP: $o).
% 86.38/12.47 thf(func_def_77, type, in__Cong: $o).
% 86.38/12.47 thf(func_def_78, type, exuE3u: $o).
% 86.38/12.47 thf(func_def_79, type, exu__Cong: $o).
% 86.38/12.47 thf(func_def_80, type, emptyset__Cong: $o).
% 86.38/12.47 thf(func_def_81, type, setadjoin__Cong: $o).
% 86.38/12.47 thf(func_def_82, type, powerset__Cong: $o).
% 86.38/12.47 thf(func_def_83, type, setunion__Cong: $o).
% 86.38/12.47 thf(func_def_84, type, omega__Cong: $o).
% 86.38/12.47 thf(func_def_85, type, exuEu: $o).
% 86.38/12.47 thf(func_def_86, type, descr__Cong: $o).
% 86.38/12.47 thf(func_def_87, type, dsetconstr__Cong: $o).
% 86.38/12.47 thf(func_def_88, type, subset: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_91, type, subsetI1: $o).
% 86.38/12.47 thf(func_def_92, type, eqimpsubset2: $o).
% 86.38/12.47 thf(func_def_93, type, eqimpsubset1: $o).
% 86.38/12.47 thf(func_def_94, type, subsetI2: $o).
% 86.38/12.47 thf(func_def_95, type, emptysetsubset: $o).
% 86.38/12.47 thf(func_def_96, type, subsetE: $o).
% 86.38/12.47 thf(func_def_97, type, subsetE2: $o).
% 86.38/12.47 thf(func_def_98, type, notsubsetI: $o).
% 86.38/12.47 thf(func_def_99, type, notequalI1: $o).
% 86.38/12.47 thf(func_def_100, type, notequalI2: $o).
% 86.38/12.47 thf(func_def_101, type, subsetRefl: $o).
% 86.38/12.47 thf(func_def_102, type, subsetTrans: $o).
% 86.38/12.47 thf(func_def_103, type, setadjoinSub: $o).
% 86.38/12.47 thf(func_def_104, type, setadjoinSub2: $o).
% 86.38/12.47 thf(func_def_105, type, subset2powerset: $o).
% 86.38/12.47 thf(func_def_106, type, setextsub: $o).
% 86.38/12.47 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 86.38/12.47 thf(func_def_108, type, powersetI1: $o).
% 86.38/12.47 thf(func_def_109, type, powersetE1: $o).
% 86.38/12.47 thf(func_def_110, type, inPowerset: $o).
% 86.38/12.47 thf(func_def_111, type, powersetsubset: $o).
% 86.38/12.47 thf(func_def_112, type, sepInPowerset: $o).
% 86.38/12.47 thf(func_def_113, type, sepSubset: $o).
% 86.38/12.47 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_115, type, binunionIL: $o).
% 86.38/12.47 thf(func_def_116, type, upairset2IR: $o).
% 86.38/12.47 thf(func_def_117, type, binunionIR: $o).
% 86.38/12.47 thf(func_def_118, type, binunionEcases: $o).
% 86.38/12.47 thf(func_def_119, type, binunionE: $o).
% 86.38/12.47 thf(func_def_120, type, binunionLsub: $o).
% 86.38/12.47 thf(func_def_121, type, binunionRsub: $o).
% 86.38/12.47 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_123, type, binintersectI: $o).
% 86.38/12.47 thf(func_def_124, type, binintersectSubset5: $o).
% 86.38/12.47 thf(func_def_125, type, binintersectEL: $o).
% 86.38/12.47 thf(func_def_126, type, binintersectLsub: $o).
% 86.38/12.47 thf(func_def_127, type, binintersectSubset2: $o).
% 86.38/12.47 thf(func_def_128, type, binintersectSubset3: $o).
% 86.38/12.47 thf(func_def_129, type, binintersectER: $o).
% 86.38/12.47 thf(func_def_130, type, disjointsetsI1: $o).
% 86.38/12.47 thf(func_def_131, type, binintersectRsub: $o).
% 86.38/12.47 thf(func_def_132, type, binintersectSubset4: $o).
% 86.38/12.47 thf(func_def_133, type, binintersectSubset1: $o).
% 86.38/12.47 thf(func_def_134, type, bs114d: $o).
% 86.38/12.47 thf(func_def_135, type, regular: ($i > $o)).
% 86.38/12.47 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_137, type, setminusI: $o).
% 86.38/12.47 thf(func_def_138, type, setminusEL: $o).
% 86.38/12.47 thf(func_def_139, type, setminusER: $o).
% 86.38/12.47 thf(func_def_140, type, setminusSubset2: $o).
% 86.38/12.47 thf(func_def_141, type, setminusERneg: $o).
% 86.38/12.47 thf(func_def_142, type, setminusELneg: $o).
% 86.38/12.47 thf(func_def_143, type, setminusILneg: $o).
% 86.38/12.47 thf(func_def_144, type, setminusIRneg: $o).
% 86.38/12.47 thf(func_def_145, type, setminusLsub: $o).
% 86.38/12.47 thf(func_def_146, type, setminusSubset1: $o).
% 86.38/12.47 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_148, type, symdiffE: $o).
% 86.38/12.47 thf(func_def_149, type, symdiffI1: $o).
% 86.38/12.47 thf(func_def_150, type, symdiffI2: $o).
% 86.38/12.47 thf(func_def_151, type, symdiffIneg1: $o).
% 86.38/12.47 thf(func_def_152, type, symdiffIneg2: $o).
% 86.38/12.47 thf(func_def_153, type, iskpair: ($i > $o)).
% 86.38/12.47 thf(func_def_154, type, secondinupair: $o).
% 86.38/12.47 thf(func_def_155, type, setukpairIL: $o).
% 86.38/12.47 thf(func_def_156, type, setukpairIR: $o).
% 86.38/12.47 thf(func_def_157, type, kpairiskpair: $o).
% 86.38/12.47 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_159, type, kpairp: $o).
% 86.38/12.47 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_161, type, singletonsubset: $o).
% 86.38/12.47 thf(func_def_162, type, singletoninpowerset: $o).
% 86.38/12.47 thf(func_def_163, type, singletoninpowunion: $o).
% 86.38/12.47 thf(func_def_164, type, upairset2E: $o).
% 86.38/12.47 thf(func_def_165, type, upairsubunion: $o).
% 86.38/12.47 thf(func_def_166, type, upairinpowunion: $o).
% 86.38/12.47 thf(func_def_167, type, ubforcartprodlem1: $o).
% 86.38/12.47 thf(func_def_168, type, ubforcartprodlem2: $o).
% 86.38/12.47 thf(func_def_169, type, ubforcartprodlem3: $o).
% 86.38/12.47 thf(func_def_170, type, cartprodpairin: $o).
% 86.38/12.47 thf(func_def_171, type, cartprodmempair1: $o).
% 86.38/12.47 thf(func_def_172, type, cartprodmempair: $o).
% 86.38/12.47 thf(func_def_173, type, setunionE2: $o).
% 86.38/12.47 thf(func_def_174, type, setunionsingleton1: $o).
% 86.38/12.47 thf(func_def_175, type, setunionsingleton2: $o).
% 86.38/12.47 thf(func_def_176, type, setunionsingleton: $o).
% 86.38/12.47 thf(func_def_177, type, singleton: ($i > $o)).
% 86.38/12.47 thf(func_def_178, type, singletonprop: $o).
% 86.38/12.47 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 86.38/12.47 thf(func_def_180, type, ex1E1: $o).
% 86.38/12.47 thf(func_def_181, type, ex1I: $o).
% 86.38/12.47 thf(func_def_182, type, ex1I2: $o).
% 86.38/12.47 thf(func_def_183, type, singletonsuniq: $o).
% 86.38/12.47 thf(func_def_184, type, atmost1p: ($i > $o)).
% 86.38/12.47 thf(func_def_185, type, atleast2p: ($i > $o)).
% 86.38/12.47 thf(func_def_186, type, atmost2p: ($i > $o)).
% 86.38/12.47 thf(func_def_187, type, upairsetp: ($i > $o)).
% 86.38/12.47 thf(func_def_188, type, setukpairinjL1: $o).
% 86.38/12.47 thf(func_def_189, type, kfstsingleton: $o).
% 86.38/12.47 thf(func_def_190, type, theprop: $o).
% 86.38/12.47 thf(func_def_191, type, kfst: ($i > $i)).
% 86.38/12.47 thf(func_def_192, type, kfstpairEq: $o).
% 86.38/12.47 thf(func_def_193, type, cartprodfstin: $o).
% 86.38/12.47 thf(func_def_194, type, setukpairinjL2: $o).
% 86.38/12.47 thf(func_def_195, type, setukpairinjL: $o).
% 86.38/12.47 thf(func_def_196, type, setukpairinjR11: $o).
% 86.38/12.47 thf(func_def_197, type, setukpairinjR12: $o).
% 86.38/12.47 thf(func_def_198, type, setukpairinjR1: $o).
% 86.38/12.47 thf(func_def_199, type, upairequniteq: $o).
% 86.38/12.47 thf(func_def_200, type, setukpairinjR2: $o).
% 86.38/12.47 thf(func_def_201, type, setukpairinjR: $o).
% 86.38/12.47 thf(func_def_202, type, ksndsingleton: $o).
% 86.38/12.47 thf(func_def_203, type, ksnd: ($i > $i)).
% 86.38/12.47 thf(func_def_204, type, ksndpairEq: $o).
% 86.38/12.47 thf(func_def_205, type, kpairsurjEq: $o).
% 86.38/12.47 thf(func_def_206, type, cartprodsndin: $o).
% 86.38/12.47 thf(func_def_207, type, cartprodpairmemEL: $o).
% 86.38/12.47 thf(func_def_208, type, cartprodpairmemER: $o).
% 86.38/12.47 thf(func_def_209, type, cartprodmempaircEq: $o).
% 86.38/12.47 thf(func_def_210, type, cartprodfstpairEq: $o).
% 86.38/12.47 thf(func_def_211, type, cartprodsndpairEq: $o).
% 86.38/12.47 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 86.38/12.47 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 86.38/12.47 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 86.38/12.47 thf(func_def_215, type, dpsetconstrI: $o).
% 86.38/12.47 thf(func_def_216, type, dpsetconstrSub: $o).
% 86.38/12.47 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 86.38/12.47 thf(func_def_218, type, dpsetconstrERa: $o).
% 86.38/12.47 thf(func_def_219, type, dpsetconstrEL1: $o).
% 86.38/12.47 thf(func_def_220, type, dpsetconstrEL2: $o).
% 86.38/12.47 thf(func_def_221, type, dpsetconstrER: $o).
% 86.38/12.47 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 86.38/12.47 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_224, type, funcImageSingleton: $o).
% 86.38/12.47 thf(func_def_225, type, apProp: $o).
% 86.38/12.47 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_227, type, app: $o).
% 86.38/12.47 thf(func_def_228, type, infuncsetfunc: $o).
% 86.38/12.47 thf(func_def_229, type, ap2p: $o).
% 86.38/12.47 thf(func_def_230, type, funcinfuncset: $o).
% 86.38/12.47 thf(func_def_231, type, lamProp: $o).
% 86.38/12.47 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 86.38/12.47 thf(func_def_233, type, lamp: $o).
% 86.38/12.47 thf(func_def_234, type, lam2p: $o).
% 86.38/12.47 thf(func_def_235, type, brelnall1: $o).
% 86.38/12.47 thf(func_def_236, type, brelnall2: $o).
% 86.38/12.47 thf(func_def_237, type, ex1E2: $o).
% 86.38/12.47 thf(func_def_238, type, funcGraphProp1: $o).
% 86.38/12.47 thf(func_def_239, type, funcGraphProp3: $o).
% 86.38/12.47 thf(func_def_240, type, funcGraphProp2: $o).
% 86.38/12.47 thf(func_def_241, type, funcextLem: $o).
% 86.38/12.47 thf(func_def_242, type, funcGraphProp4: $o).
% 86.38/12.47 thf(func_def_243, type, subbreln: $o).
% 86.38/12.47 thf(func_def_244, type, eqbreln: $o).
% 86.38/12.47 thf(func_def_245, type, funcext: $o).
% 86.38/12.47 thf(func_def_246, type, funcext2: $o).
% 86.38/12.47 thf(func_def_247, type, ap2apEq1: $o).
% 86.38/12.47 thf(func_def_248, type, ap2apEq2: $o).
% 86.38/12.47 thf(func_def_249, type, beta1: $o).
% 86.38/12.47 thf(func_def_250, type, eta1: $o).
% 86.38/12.47 thf(func_def_251, type, lam2lamEq: $o).
% 86.38/12.47 thf(func_def_252, type, beta2: $o).
% 86.38/12.47 thf(func_def_253, type, eta2: $o).
% 86.38/12.47 thf(func_def_254, type, iffalseProp1: $o).
% 86.38/12.47 thf(func_def_255, type, iffalseProp2: $o).
% 86.38/12.47 thf(func_def_256, type, iftrueProp1: $o).
% 86.38/12.47 thf(func_def_257, type, iftrueProp2: $o).
% 86.38/12.47 thf(func_def_258, type, ifSingleton: $o).
% 86.38/12.47 thf(func_def_259, type, if: ($i > $o > $i > $i > $i)).
% 86.38/12.47 thf(func_def_260, type, ifp: $o).
% 86.38/12.47 thf(func_def_261, type, theeq: $o).
% 86.38/12.47 thf(func_def_262, type, iftrue: $o).
% 86.38/12.47 thf(func_def_263, type, iffalse: $o).
% 86.38/12.47 thf(func_def_264, type, iftrueorfalse: $o).
% 86.38/12.47 thf(func_def_265, type, binintersectT_lem: $o).
% 86.38/12.47 thf(func_def_266, type, binunionT_lem: $o).
% 86.38/12.47 thf(func_def_267, type, powersetT_lem: $o).
% 86.38/12.47 thf(func_def_268, type, setminusT_lem: $o).
% 86.38/12.47 thf(func_def_269, type, complementT_lem: $o).
% 86.38/12.47 thf(func_def_270, type, setextT: $o).
% 86.38/12.47 thf(func_def_271, type, subsetTI: $o).
% 86.38/12.47 thf(func_def_272, type, powersetTI1: $o).
% 86.38/12.47 thf(func_def_273, type, powersetTE1: $o).
% 86.38/12.47 thf(func_def_274, type, complementTI1: $o).
% 86.38/12.47 thf(func_def_275, type, complementTE1: $o).
% 86.38/12.47 thf(func_def_276, type, binintersectTELcontra: $o).
% 86.38/12.47 thf(func_def_277, type, binintersectTERcontra: $o).
% 86.38/12.47 thf(func_def_278, type, contrasubsetT: $o).
% 86.38/12.47 thf(func_def_279, type, contrasubsetT1: $o).
% 86.38/12.47 thf(func_def_280, type, contrasubsetT2: $o).
% 86.38/12.47 thf(func_def_281, type, contrasubsetT3: $o).
% 86.38/12.47 thf(func_def_282, type, doubleComplementI1: $o).
% 86.38/12.47 thf(func_def_283, type, doubleComplementE1: $o).
% 86.38/12.47 thf(func_def_284, type, doubleComplementSub1: $o).
% 86.38/12.47 thf(func_def_285, type, doubleComplementSub2: $o).
% 86.38/12.47 thf(func_def_286, type, doubleComplementEq: $o).
% 86.38/12.47 thf(func_def_287, type, complementTnotintersectT: $o).
% 86.38/12.47 thf(func_def_288, type, complementImpComplementIntersect: $o).
% 86.38/12.47 thf(func_def_289, type, complementSubsetComplementIntersect: $o).
% 86.38/12.47 thf(func_def_290, type, complementInPowersetComplementIntersect: $o).
% 86.38/12.47 thf(func_def_291, type, contraSubsetComplement: $o).
% 86.38/12.47 thf(func_def_292, type, complementTcontraSubset: $o).
% 86.38/12.47 thf(func_def_293, type, binunionTILcontra: $o).
% 86.38/12.47 thf(func_def_294, type, binunionTIRcontra: $o).
% 86.38/12.47 thf(func_def_295, type, inIntersectImpInUnion: $o).
% 86.38/12.47 thf(func_def_296, type, inIntersectImpInUnion2: $o).
% 86.38/12.47 thf(func_def_297, type, inIntersectImpInIntersectUnions: $o).
% 86.38/12.47 thf(func_def_298, type, intersectInPowersetIntersectUnions: $o).
% 86.38/12.47 thf(func_def_299, type, inComplementUnionImpNotIn1: $o).
% 86.38/12.47 thf(func_def_300, type, inComplementUnionImpInComplement1: $o).
% 86.38/12.47 thf(func_def_301, type, binunionTE: $o).
% 86.38/12.47 thf(func_def_302, type, binunionTEcontra: $o).
% 86.38/12.47 thf(func_def_303, type, demorgan2a1: $o).
% 86.38/12.47 thf(func_def_304, type, complementUnionInPowersetComplement: $o).
% 86.38/12.47 thf(func_def_305, type, demorgan2a2: $o).
% 86.38/12.47 thf(func_def_306, type, demorgan1a: $o).
% 86.38/12.47 thf(func_def_307, type, demorgan1b: $o).
% 86.38/12.47 thf(func_def_308, type, demorgan1: $o).
% 86.38/12.47 thf(func_def_309, type, demorgan2a: $o).
% 86.38/12.47 thf(func_def_310, type, demorgan2b2: $o).
% 86.38/12.47 thf(func_def_311, type, demorgan2b: $o).
% 86.38/12.47 thf(func_def_312, type, demorgan2: $o).
% 86.38/12.47 thf(func_def_313, type, woz13rule0: $o).
% 86.38/12.47 thf(func_def_314, type, woz13rule1: $o).
% 86.38/12.47 thf(func_def_315, type, woz13rule2: $o).
% 86.38/12.47 thf(func_def_316, type, woz13rule3: $o).
% 86.38/12.47 thf(func_def_317, type, woz13rule4: $o).
% 86.38/12.47 thf(func_def_318, type, woz1_1: $o).
% 86.38/12.47 thf(func_def_319, type, woz1_2: $o).
% 86.38/12.47 thf(func_def_320, type, woz1_3: $o).
% 86.38/12.47 thf(func_def_321, type, woz1_4: $o).
% 86.38/12.47 thf(func_def_322, type, woz1_5: $o).
% 86.38/12.47 thf(func_def_323, type, breln1: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_324, type, breln1all2: $o).
% 86.38/12.47 thf(func_def_325, type, breln1Set: ($i > $i)).
% 86.38/12.47 thf(func_def_326, type, breln1SetBreln1: $o).
% 86.38/12.47 thf(func_def_327, type, transitive: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_328, type, antisymmetric: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_329, type, reflexive: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_330, type, refltransitive: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_331, type, refllinearorder: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_332, type, reflwellordering: ($i > $i > $o)).
% 86.38/12.47 thf(func_def_333, type, choice2fnsingleton: $o).
% 86.38/12.47 thf(func_def_334, type, setOfPairsIsBReln1: $o).
% 86.38/12.47 thf(func_def_335, type, breln1all1: $o).
% 86.38/12.47 thf(func_def_336, type, subbreln1: $o).
% 86.38/12.47 thf(func_def_337, type, eqbreln1: $o).
% 86.38/12.47 thf(func_def_338, type, breln1invset: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_339, type, breln1invprop: $o).
% 86.38/12.47 thf(func_def_340, type, breln1invI: $o).
% 86.38/12.47 thf(func_def_341, type, breln1invE: $o).
% 86.38/12.47 thf(func_def_342, type, breln1compset: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_343, type, breln1compprop: $o).
% 86.38/12.47 thf(func_def_344, type, breln1compI: $o).
% 86.38/12.47 thf(func_def_345, type, breln1compE: $o).
% 86.38/12.47 thf(func_def_346, type, breln1compEex: $o).
% 86.38/12.47 thf(func_def_347, type, breln1unionprop: $o).
% 86.38/12.47 thf(func_def_348, type, breln1unionIL: $o).
% 86.38/12.47 thf(func_def_349, type, breln1unionIR: $o).
% 86.38/12.47 thf(func_def_350, type, breln1unionI: $o).
% 86.38/12.47 thf(func_def_351, type, breln1unionE: $o).
% 86.38/12.47 thf(func_def_352, type, breln1unionEcases: $o).
% 86.38/12.47 thf(func_def_353, type, breln1unionCommutes: $o).
% 86.38/12.47 thf(func_def_354, type, woz2Ex: $o).
% 86.38/12.47 thf(func_def_355, type, woz2W: $o).
% 86.38/12.47 thf(func_def_356, type, woz2A: $o).
% 86.38/12.47 thf(func_def_357, type, woz2B: $o).
% 86.38/12.47 thf(func_def_358, type, image1Ex: $o).
% 86.38/12.47 thf(func_def_359, type, image1Ex1: $o).
% 86.38/12.47 thf(func_def_360, type, image1: ($i > ($i > $i) > $i)).
% 86.38/12.47 thf(func_def_361, type, image1Equiv: $o).
% 86.38/12.47 thf(func_def_362, type, image1E: $o).
% 86.38/12.47 thf(func_def_363, type, image1I: $o).
% 86.38/12.47 thf(func_def_364, type, injective: ($i > $i > $i > $o)).
% 86.38/12.47 thf(func_def_365, type, injFuncSet: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_366, type, injFuncInInjFuncSet: $o).
% 86.38/12.47 thf(func_def_367, type, injFuncSetFuncIn: $o).
% 86.38/12.47 thf(func_def_368, type, injFuncSetFuncInj: $o).
% 86.38/12.47 thf(func_def_369, type, surjective: ($i > $i > $i > $o)).
% 86.38/12.47 thf(func_def_370, type, surjFuncSet: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_371, type, surjFuncSetFuncIn: $o).
% 86.38/12.47 thf(func_def_372, type, surjFuncSetFuncSurj: $o).
% 86.38/12.47 thf(func_def_373, type, leftInvIsSurj: $o).
% 86.38/12.47 thf(func_def_374, type, surjCantorThm: $o).
% 86.38/12.47 thf(func_def_375, type, foundation2: $o).
% 86.38/12.47 thf(func_def_376, type, notinself: $o).
% 86.38/12.47 thf(func_def_377, type, notinself2: $o).
% 86.38/12.47 thf(func_def_378, type, omegaS: ($i > $i)).
% 86.38/12.47 thf(func_def_379, type, omegaSp: $o).
% 86.38/12.47 thf(func_def_380, type, omegaSclos: $o).
% 86.38/12.47 thf(func_def_381, type, peano0notS: $o).
% 86.38/12.47 thf(func_def_382, type, peano3: ($i > $i > $i > $o)).
% 86.38/12.47 thf(func_def_383, type, peano4: ($i > $i > $i > $o)).
% 86.38/12.47 thf(func_def_384, type, peano5: ($i > $i > $i > $o)).
% 86.38/12.47 thf(func_def_385, type, peanoSinj: $o).
% 86.38/12.47 thf(func_def_386, type, peano: ($i > $i > $i > $o)).
% 86.38/12.47 thf(func_def_387, type, transitiveset: ($i > $o)).
% 86.38/12.47 thf(func_def_388, type, transitivesetOp1: $o).
% 86.38/12.47 thf(func_def_389, type, binintTransitive: $o).
% 86.38/12.47 thf(func_def_390, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 86.38/12.47 thf(func_def_391, type, vAND: ($o > $o > $o)).
% 86.38/12.47 thf(func_def_392, type, db1: !>[X0: $tType]:(X0)).
% 86.38/12.47 thf(func_def_393, type, db0: !>[X0: $tType]:(X0)).
% 86.38/12.47 thf(func_def_394, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 86.38/12.47 thf(func_def_395, type, vIMP: ($o > $o > $o)).
% 86.38/12.47 thf(func_def_396, type, db2: !>[X0: $tType]:(X0)).
% 86.38/12.47 thf(func_def_397, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 86.38/12.47 thf(func_def_398, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 86.38/12.47 thf(func_def_399, type, vIFF: ($o > $o > $o)).
% 86.38/12.47 thf(func_def_400, type, vNOT: ($o > $o)).
% 86.38/12.47 thf(func_def_401, type, vOR: ($o > $o > $o)).
% 86.38/12.47 thf(func_def_402, type, db4: !>[X0: $tType]:(X0)).
% 86.38/12.47 thf(func_def_403, type, db3: !>[X0: $tType]:(X0)).
% 86.38/12.47 thf(func_def_406, type, db5: !>[X0: $tType]:(X0)).
% 86.38/12.47 thf(func_def_407, type, db6: !>[X0: $tType]:(X0)).
% 86.38/12.47 thf(func_def_411, type, sK3: ($i > $i)).
% 86.38/12.47 thf(func_def_412, type, sK4: ($i > $i)).
% 86.38/12.47 thf(func_def_413, type, sK5: ($i > $i)).
% 86.38/12.47 thf(func_def_414, type, sK6: ($i > $i)).
% 86.38/12.47 thf(func_def_415, type, sK7: ($i > $i)).
% 86.38/12.47 thf(func_def_416, type, sK8: ($i > ($i > $i) > $i > $i)).
% 86.38/12.47 thf(func_def_417, type, sK9: ($i > ($i > $i) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_418, type, sK10: ($i > ($i > $i) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_419, type, sK11: ($i > $i > ($i > $i) > $i)).
% 86.38/12.47 thf(func_def_420, type, sK12: ($i > $i > ($i > $i) > $i)).
% 86.38/12.47 thf(func_def_421, type, sK13: (($i > $i) > $i > $i)).
% 86.38/12.47 thf(func_def_422, type, sK14: ($i > ($i > $i) > $i > $i)).
% 86.38/12.47 thf(func_def_423, type, sK15: ($i > ($i > $i) > $i > $i)).
% 86.38/12.47 thf(func_def_424, type, sK16: ($i > ($i > $i) > $i > $i)).
% 86.38/12.47 thf(func_def_425, type, sK17: (($i > $i) > $i > $i)).
% 86.38/12.47 thf(func_def_426, type, sK18: ($i > ($i > $i) > $i > $i)).
% 86.38/12.47 thf(func_def_427, type, sK19: ($i > $i > $i > $o > $i > $i > $i)).
% 86.38/12.47 thf(func_def_428, type, sK20: ($i > $i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_429, type, sK21: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_430, type, sK22: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_431, type, sK23: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_432, type, sK24: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_433, type, sK25: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_434, type, sK26: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_435, type, sK27: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_436, type, sK28: ($i > $i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_437, type, sK29: ($i > $i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_438, type, sK30: (($i > $i > $o) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_439, type, sK31: ($i > $i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_440, type, sK32: ($i > $i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_441, type, sK33: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_442, type, sK34: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_443, type, sK35: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_444, type, sK36: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_445, type, sK37: (($i > $i) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_446, type, sK38: (($i > $i) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_447, type, sK39: (($i > $i) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_448, type, sK40: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_449, type, sK41: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_450, type, sK42: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_451, type, sK43: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_452, type, sK44: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_453, type, sK45: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_454, type, sK46: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_455, type, sK47: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_456, type, sK48: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_457, type, sK49: ($i > $i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_458, type, sK50: ($i > $i > $i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_459, type, sK51: ($i > $i > $i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_460, type, sK52: ($i > $i > $i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_461, type, sK53: ($i > $i > $i > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_462, type, sK54: (($i > $i) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_463, type, sK55: (($i > $i) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_464, type, sK56: (($i > $i) > $i > $i > $i)).
% 86.38/12.47 thf(func_def_465, type, sK57: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_466, type, sK58: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_467, type, sK59: ($i > ($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_468, type, sK60: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_469, type, sK61: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_470, type, sK62: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_471, type, sK63: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_472, type, sK64: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_473, type, sK65: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_474, type, sK66: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_475, type, sK67: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_476, type, sK68: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_477, type, sK69: ($i > $i > ($i > $o) > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_478, type, sK70: ($i > ($i > $o) > ($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_479, type, sK71: (($i > $o) > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_480, type, sK72: (($i > $o) > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_481, type, sK73: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_482, type, sK74: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_483, type, sK75: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_484, type, sK76: (($i > $o) > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_485, type, sK77: (($i > $o) > ($i > $o) > $i)).
% 86.38/12.47 thf(func_def_486, type, sK78: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_487, type, sK79: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_488, type, sK80: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_489, type, sK81: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_490, type, sK82: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_491, type, sK83: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_492, type, sK84: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_493, type, sK85: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_494, type, sK86: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_495, type, sK87: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_496, type, sK88: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_497, type, sK89: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_498, type, sK90: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_499, type, sK91: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_500, type, sK92: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_501, type, sK93: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_502, type, sK94: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_503, type, sK95: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_504, type, sK96: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_505, type, sK97: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_506, type, sK98: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_507, type, sK99: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_508, type, sK100: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_509, type, sK101: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_510, type, sK102: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_511, type, sK103: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_512, type, sK104: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_513, type, sK105: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_514, type, sK106: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_515, type, sK107: ($i > $i)).
% 86.38/12.47 thf(func_def_516, type, sK108: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_517, type, sK109: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_518, type, sK110: ($i > $o > $i > $i)).
% 86.38/12.47 thf(func_def_519, type, sK111: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_520, type, sK112: ($i > $i)).
% 86.38/12.47 thf(func_def_521, type, sK113: ($i > $i)).
% 86.38/12.47 thf(func_def_522, type, sK114: ($i > $i)).
% 86.38/12.47 thf(func_def_523, type, sK115: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_524, type, sK116: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_525, type, sK117: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_526, type, sK118: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_527, type, sK119: (($i > $o) > $i)).
% 86.38/12.47 thf(func_def_528, type, sK120: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_529, type, sK121: (($i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_530, type, sK122: ($i > $i)).
% 86.38/12.47 thf(func_def_531, type, sK123: ($i > $i > $i > $i)).
% 86.38/12.47 thf(func_def_532, type, sK124: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_533, type, sK125: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_534, type, sK126: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_535, type, sK127: ($i > $i)).
% 86.38/12.47 thf(func_def_536, type, sK128: ($i > ($i > $i > $o) > $i)).
% 86.38/12.47 thf(func_def_537, type, sK129: ($i > ($i > $i > $o) > $i)).
% 86.38/12.47 thf(func_def_538, type, sK130: ($i > $i > ($i > $i > $o) > $i)).
% 86.38/12.47 thf(func_def_539, type, sK131: ($i > ($i > $i > $o) > $i > $i)).
% 86.38/12.47 thf(func_def_540, type, sK132: ($i > $i > ($i > $i > $o) > $i)).
% 86.38/12.47 thf(func_def_541, type, sK133: ($i > $i > ($i > $i > $o) > $i)).
% 86.38/12.47 thf(func_def_542, type, sK134: ($i > $i)).
% 86.38/12.47 thf(func_def_543, type, sK135: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_544, type, sK136: ($i > $i > $i)).
% 86.38/12.47 thf(func_def_545, type, sK137: ($i > $i > $i)).
% 86.38/12.47 thf(f85,axiom,(
% 86.38/12.47 (notsubsetI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1))))),
% 86.38/12.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI)).
% 86.38/12.47 thf(f331,axiom,(
% 86.38/12.47 (transitiveset = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 86.38/12.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset)).
% 86.38/12.47 thf(f334,conjecture,(
% 86.38/12.47 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => ! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 86.38/12.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivesetOp2)).
% 86.38/12.47 thf(f335,negated_conjecture,(
% 86.38/12.47 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => ! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 86.38/12.47 inference(negated_conjecture,[status(cth)],[f334])).
% 86.38/12.47 thf(f494,plain,(
% 86.38/12.47 (notsubsetI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1))))),
% 86.38/12.47 inference(rectify,[],[f85])).
% 86.38/12.47 thf(f495,plain,(
% 86.38/12.47 (notsubsetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1))))))))))))),
% 86.38/12.47 inference(fool_elimination,[],[f494])).
% 86.38/12.47 thf(f973,plain,(
% 86.38/12.47 (transitiveset = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 86.38/12.47 inference(rectify,[],[f331])).
% 86.38/12.47 thf(f974,plain,(
% 86.38/12.47 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 86.38/12.47 inference(fool_elimination,[],[f973])).
% 86.38/12.47 thf(f979,plain,(
% 86.38/12.47 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => ! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 86.38/12.47 inference(rectify,[],[f335])).
% 86.38/12.47 thf(f980,plain,(
% 86.38/12.47 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ((image1E = $true) => ((image1I = $true) => ((injFuncInInjFuncSet = $true) => ((injFuncSetFuncIn = $true) => ((injFuncSetFuncInj = $true) => ((surjFuncSetFuncIn = $true) => ((surjFuncSetFuncSurj = $true) => ((leftInvIsSurj = $true) => ((surjCantorThm = $true) => ((foundation2 = $true) => ((notinself = $true) => ((notinself2 = $true) => ((omegaSp = $true) => ((omegaSclos = $true) => ((peano0notS = $true) => ((peanoSinj = $true) => ((transitivesetOp1 = $true) => ((binintTransitive = $true) => ! [X0 : $i] : ((((transitiveset @ X0)) = $true) => ! [X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) => ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 86.38/12.47 inference(fool_elimination,[],[f979])).
% 86.38/12.47 thf(f981,plain,(
% 86.38/12.47 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (? [X1 : $i,X2 : $i] : (((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) & (((in @ X1 @ X0)) = $true)) & (((transitiveset @ X0)) = $true)) & (binintTransitive = $true)) & (transitivesetOp1 = $true)) & (peanoSinj = $true)) & (peano0notS = $true)) & (omegaSclos = $true)) & (omegaSp = $true)) & (notinself2 = $true)) & (notinself = $true)) & (foundation2 = $true)) & (surjCantorThm = $true)) & (leftInvIsSurj = $true)) & (surjFuncSetFuncSurj = $true)) & (surjFuncSetFuncIn = $true)) & (injFuncSetFuncInj = $true)) & (injFuncSetFuncIn = $true)) & (injFuncInInjFuncSet = $true)) & (image1I = $true)) & (image1E = $true)) & (image1Equiv = $true)) & (image1Ex1 = $true)) & (image1Ex = $true)) & (woz2B = $true)) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1unionEcases = $true)) & (breln1unionE = $true)) & (breln1unionI = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)) & (breln1unionprop = $true)) & (breln1compEex = $true)) & (breln1compE = $true)) & (breln1compI = $true)) & (breln1compprop = $true)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 86.38/12.47 inference(ennf_transformation,[],[f980])).
% 86.38/12.47 thf(f982,plain,(
% 86.38/12.47 ? [X0 : $i] : (? [X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true) & (((in @ X1 @ X0)) = $true)) & (((transitiveset @ X0)) = $true)) & (binintTransitive = $true) & (transitivesetOp1 = $true) & (peanoSinj = $true) & (peano0notS = $true) & (omegaSclos = $true) & (omegaSp = $true) & (notinself2 = $true) & (notinself = $true) & (foundation2 = $true) & (surjCantorThm = $true) & (leftInvIsSurj = $true) & (surjFuncSetFuncSurj = $true) & (surjFuncSetFuncIn = $true) & (injFuncSetFuncInj = $true) & (injFuncSetFuncIn = $true) & (injFuncInInjFuncSet = $true) & (image1I = $true) & (image1E = $true) & (image1Equiv = $true) & (image1Ex1 = $true) & (image1Ex = $true) & (woz2B = $true) & (woz2A = $true) & (woz2W = $true) & (woz2Ex = $true) & (breln1unionCommutes = $true) & (breln1unionEcases = $true) & (breln1unionE = $true) & (breln1unionI = $true) & (breln1unionIR = $true) & (breln1unionIL = $true) & (breln1unionprop = $true) & (breln1compEex = $true) & (breln1compE = $true) & (breln1compI = $true) & (breln1compprop = $true) & (breln1invE = $true) & (breln1invI = $true) & (breln1invprop = $true) & (eqbreln1 = $true) & (subbreln1 = $true) & (breln1all1 = $true) & (setOfPairsIsBReln1 = $true) & (choice2fnsingleton = $true) & (breln1SetBreln1 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (woz1_4 = $true) & (woz1_3 = $true) & (woz1_2 = $true) & (woz1_1 = $true) & (woz13rule4 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (woz13rule0 = $true) & (demorgan2 = $true) & (demorgan2b = $true) & (demorgan2b2 = $true) & (demorgan2a = $true) & (demorgan1 = $true) & (demorgan1b = $true) & (demorgan1a = $true) & (demorgan2a2 = $true) & (complementUnionInPowersetComplement = $true) & (demorgan2a1 = $true) & (binunionTEcontra = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (inComplementUnionImpNotIn1 = $true) & (intersectInPowersetIntersectUnions = $true) & (inIntersectImpInIntersectUnions = $true) & (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTcontraSubset = $true) & (contraSubsetComplement = $true) & (complementInPowersetComplementIntersect = $true) & (complementSubsetComplementIntersect = $true) & (complementImpComplementIntersect = $true) & (complementTnotintersectT = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (doubleComplementSub1 = $true) & (doubleComplementE1 = $true) & (doubleComplementI1 = $true) & (contrasubsetT3 = $true) & (contrasubsetT2 = $true) & (contrasubsetT1 = $true) & (contrasubsetT = $true) & (binintersectTERcontra = $true) & (binintersectTELcontra = $true) & (complementTE1 = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 86.38/12.47 inference(flattening,[],[f981])).
% 86.38/12.47 thf(f983,plain,(
% 86.38/12.47 ((($true != ((in @ sK2 @ sK0))) & ($true = ((in @ sK2 @ sK1))) & ($true = ((in @ sK1 @ sK0)))) & ($true = ((transitiveset @ sK0)))) & (binintTransitive = $true) & (transitivesetOp1 = $true) & (peanoSinj = $true) & (peano0notS = $true) & (omegaSclos = $true) & (omegaSp = $true) & (notinself2 = $true) & (notinself = $true) & (foundation2 = $true) & (surjCantorThm = $true) & (leftInvIsSurj = $true) & (surjFuncSetFuncSurj = $true) & (surjFuncSetFuncIn = $true) & (injFuncSetFuncInj = $true) & (injFuncSetFuncIn = $true) & (injFuncInInjFuncSet = $true) & (image1I = $true) & (image1E = $true) & (image1Equiv = $true) & (image1Ex1 = $true) & (image1Ex = $true) & (woz2B = $true) & (woz2A = $true) & (woz2W = $true) & (woz2Ex = $true) & (breln1unionCommutes = $true) & (breln1unionEcases = $true) & (breln1unionE = $true) & (breln1unionI = $true) & (breln1unionIR = $true) & (breln1unionIL = $true) & (breln1unionprop = $true) & (breln1compEex = $true) & (breln1compE = $true) & (breln1compI = $true) & (breln1compprop = $true) & (breln1invE = $true) & (breln1invI = $true) & (breln1invprop = $true) & (eqbreln1 = $true) & (subbreln1 = $true) & (breln1all1 = $true) & (setOfPairsIsBReln1 = $true) & (choice2fnsingleton = $true) & (breln1SetBreln1 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (woz1_4 = $true) & (woz1_3 = $true) & (woz1_2 = $true) & (woz1_1 = $true) & (woz13rule4 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (woz13rule0 = $true) & (demorgan2 = $true) & (demorgan2b = $true) & (demorgan2b2 = $true) & (demorgan2a = $true) & (demorgan1 = $true) & (demorgan1b = $true) & (demorgan1a = $true) & (demorgan2a2 = $true) & (complementUnionInPowersetComplement = $true) & (demorgan2a1 = $true) & (binunionTEcontra = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (inComplementUnionImpNotIn1 = $true) & (intersectInPowersetIntersectUnions = $true) & (inIntersectImpInIntersectUnions = $true) & (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTcontraSubset = $true) & (contraSubsetComplement = $true) & (complementInPowersetComplementIntersect = $true) & (complementSubsetComplementIntersect = $true) & (complementImpComplementIntersect = $true) & (complementTnotintersectT = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (doubleComplementSub1 = $true) & (doubleComplementE1 = $true) & (doubleComplementI1 = $true) & (contrasubsetT3 = $true) & (contrasubsetT2 = $true) & (contrasubsetT1 = $true) & (contrasubsetT = $true) & (binintersectTERcontra = $true) & (binintersectTELcontra = $true) & (complementTE1 = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 86.38/12.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f982])).
% 86.38/12.47 thf(f1068,plain,(
% 86.38/12.47 (notsubsetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1))))))))))))),
% 86.38/12.47 inference(cnf_transformation,[],[f495])).
% 86.38/12.47 thf(f1314,plain,(
% 86.38/12.47 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 86.38/12.47 inference(cnf_transformation,[],[f974])).
% 86.38/12.47 thf(f1399,plain,(
% 86.38/12.47 (notsubsetI = $true)),
% 86.38/12.47 inference(cnf_transformation,[],[f983])).
% 86.38/12.47 thf(f1647,plain,(
% 86.38/12.47 ($true = ((transitiveset @ sK0)))),
% 86.38/12.47 inference(cnf_transformation,[],[f983])).
% 86.38/12.47 thf(f1648,plain,(
% 86.38/12.47 ($true = ((in @ sK1 @ sK0)))),
% 86.38/12.47 inference(cnf_transformation,[],[f983])).
% 86.38/12.47 thf(f1649,plain,(
% 86.38/12.47 ($true = ((in @ sK2 @ sK1)))),
% 86.38/12.47 inference(cnf_transformation,[],[f983])).
% 86.38/12.47 thf(f1650,plain,(
% 86.38/12.47 ($true != ((in @ sK2 @ sK0)))),
% 86.38/12.47 inference(cnf_transformation,[],[f983])).
% 86.38/12.47 thf(f1652,definition,(
% 86.38/12.47 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 86.38/12.47 introduced(theory,[fool_exhaustiveness_axiom])).
% 86.38/12.47 thf(f1735,plain,(
% 86.38/12.47 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1))))))))))))),
% 86.38/12.47 inference(definition_unfolding,[],[f1068,f1399])).
% 86.38/12.47 thf(f1983,plain,(
% 86.38/12.47 ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ sK0)))),
% 86.38/12.47 inference(definition_unfolding,[],[f1647,f1314])).
% 86.38/12.47 thf(f1984,plain,(
% 86.38/12.47 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0))))))),
% 86.38/12.47 inference(beta-eta_normalization,[],[f1983])).
% 86.38/12.47 thf(f1985,plain,(
% 86.38/12.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0))) @ X1)))) )),
% 86.38/12.47 inference(pi_proxy_clausification,[],[f1984])).
% 86.38/12.47 thf(f1986,plain,(
% 86.38/12.47 ( ! [X1 : $i] : (($true = (((in @ X1 @ sK0) => (subset @ X1 @ sK0))))) )),
% 86.38/12.47 inference(beta-eta_normalization,[],[f1985])).
% 86.38/12.47 thf(f1987,plain,(
% 86.38/12.47 ( ! [X1 : $i] : (($true = ((subset @ X1 @ sK0))) | ($false = ((in @ X1 @ sK0)))) )),
% 86.38/12.47 inference(imp_proxy_clausification,[],[f1986])).
% 86.38/12.47 thf(f4657,plain,(
% 86.38/12.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1))))))))) @ X1)))) )),
% 86.38/12.47 inference(pi_proxy_clausification,[],[f1735])).
% 86.38/12.47 thf(f4658,plain,(
% 86.38/12.47 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((~ (in @ X1 @ Y0)) => (~ (subset @ Y1 @ Y0))))))))))) )),
% 86.38/12.47 inference(beta-eta_normalization,[],[f4657])).
% 86.38/12.47 thf(f4659,plain,(
% 86.38/12.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((~ (in @ X1 @ Y0)) => (~ (subset @ Y1 @ Y0))))))) @ X2)))) )),
% 86.38/12.47 inference(pi_proxy_clausification,[],[f4658])).
% 86.38/12.47 thf(f4660,plain,(
% 86.38/12.47 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => ((~ (in @ X1 @ X2)) => (~ (subset @ Y0 @ X2))))))))) )),
% 86.38/12.47 inference(beta-eta_normalization,[],[f4659])).
% 86.38/12.47 thf(f4661,plain,(
% 86.38/12.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => ((~ (in @ X1 @ X2)) => (~ (subset @ Y0 @ X2))))) @ X3)))) )),
% 86.38/12.47 inference(pi_proxy_clausification,[],[f4660])).
% 86.38/12.47 thf(f4662,plain,(
% 86.38/12.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => ((~ (in @ X1 @ X2)) => (~ (subset @ X3 @ X2))))))) )),
% 86.38/12.47 inference(beta-eta_normalization,[],[f4661])).
% 86.38/12.47 thf(f4663,plain,(
% 86.38/12.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X3)) = $false) | ($true = (((~ (in @ X1 @ X2)) => (~ (subset @ X3 @ X2)))))) )),
% 86.38/12.47 inference(imp_proxy_clausification,[],[f4662])).
% 86.38/12.47 thf(f4664,plain,(
% 86.38/12.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X3)) = $false) | ($false = ((~ (in @ X1 @ X2)))) | ($true = ((~ (subset @ X3 @ X2))))) )),
% 86.38/12.47 inference(imp_proxy_clausification,[],[f4663])).
% 86.38/12.47 thf(f4665,plain,(
% 86.38/12.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X3)) = $false) | (((in @ X1 @ X2)) = $true) | ($true = ((~ (subset @ X3 @ X2))))) )),
% 86.38/12.47 inference(not_proxy_clausification,[],[f4664])).
% 86.38/12.47 thf(f4666,plain,(
% 86.38/12.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X3)) = $false) | (((in @ X1 @ X2)) = $true) | ($false = ((subset @ X3 @ X2)))) )),
% 86.38/12.47 inference(not_proxy_clausification,[],[f4665])).
% 86.38/12.47 thf(f5767,definition,(
% 86.38/12.47 spl138_3 <=> ! [X6 : $o] : (($false = X6) | ($true = X6))),
% 86.38/12.47 introduced(definition,[new_symbols(definition,[spl138_3])],[avatar_definition])).
% 86.38/12.47 thf(f5768,plain,(
% 86.38/12.47 ( ! [X6 : $o] : (($true = X6) | ($false = X6)) ) | ~spl138_3),
% 86.38/12.47 inference(avatar_component_clause,[],[f5767])).
% 86.38/12.47 thf(f5880,plain,(
% 86.38/12.47 spl138_3),
% 86.38/12.47 inference(avatar_split_clause,[],[f1652,f5767])).
% 86.38/12.47 thf(f5896,plain,(
% 86.38/12.47 ($true != $true) | ($false = ((in @ sK2 @ sK0))) | ~spl138_3),
% 86.38/12.47 inference(constrained_superposition,[],[f1650,f5768])).
% 86.38/12.47 thf(f5897,plain,(
% 86.38/12.47 ($false = ((in @ sK2 @ sK0))) | ~spl138_3),
% 86.38/12.47 inference(trivial_inequality_removal,[],[f5896])).
% 86.38/12.47 thf(f7524,plain,(
% 86.38/12.47 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($false = ((in @ X0 @ sK0))) | (((in @ X1 @ X0)) = $false) | ($true = ((in @ X1 @ sK0)))) )),
% 86.38/12.47 inference(constrained_superposition,[],[f1987,f4666])).
% 86.38/12.47 thf(f7526,plain,(
% 86.38/12.47 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ X0 @ sK0))) | (((in @ X1 @ X0)) = $false) | ($true = ((in @ X1 @ sK0)))) )),
% 86.38/12.47 inference(trivial_inequality_removal,[],[f7524])).
% 86.38/12.47 thf(f95047,plain,(
% 86.38/12.47 ($false = $true) | ($false = ((in @ sK1 @ sK0))) | ($true = ((in @ sK2 @ sK0)))),
% 86.38/12.47 inference(constrained_superposition,[],[f7526,f1649])).
% 86.38/12.47 thf(f95732,plain,(
% 86.38/12.47 ($false = ((in @ sK1 @ sK0))) | ($true = ((in @ sK2 @ sK0)))),
% 86.38/12.47 inference(trivial_inequality_removal,[],[f95047])).
% 86.38/12.47 thf(f95923,plain,(
% 86.38/12.47 ($false = $true) | ($true = ((in @ sK2 @ sK0)))),
% 86.38/12.47 inference(forward_demodulation,[],[f95732,f1648])).
% 86.38/12.47 thf(f95924,plain,(
% 86.38/12.47 ($true = ((in @ sK2 @ sK0)))),
% 86.38/12.47 inference(trivial_inequality_removal,[],[f95923])).
% 86.38/12.47 thf(f95934,plain,(
% 86.38/12.47 ($false = $true) | ~spl138_3),
% 86.38/12.47 inference(forward_demodulation,[],[f95924,f5897])).
% 86.38/12.47 thf(f95935,plain,(
% 86.38/12.47 $false | ~spl138_3),
% 86.38/12.47 inference(trivial_inequality_removal,[],[f95934])).
% 86.38/12.47 thf(f95936,plain,(
% 86.38/12.47 ~spl138_3),
% 86.38/12.47 inference(avatar_contradiction_clause,[],[f95935])).
% 86.38/12.47 cnf(s32, plain, spl138_3, inference(sat_conversion,[],[f5880])).
% 86.38/12.47 cnf(s612, plain, ~spl138_3, inference(sat_conversion,[],[f95936])).
% 86.38/12.47 cnf(s689, plain, $false, inference(rat,[],[s32,s612])).
% 86.38/12.47 thf(f95937,plain,(
% 86.38/12.47 $false),
% 86.38/12.47 inference(avatar_sat_refutation,[],[s689])).
% 86.38/12.47 % SZS output end Proof for theBenchmark
% 86.38/12.47 % (167574)------------------------------
% 86.38/12.47 % (167574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.38/12.47 % (167574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.38/12.47 % (167574)CaDiCaL version: 2.1.3
% 86.38/12.47 % (167574)Termination reason: Refutation
% 86.38/12.47 % (167574)Time elapsed: 12.180 s
% 86.38/12.47 % (167574)Peak memory usage: 51 MB
% 86.38/12.47 % (167574)Instructions burned: 15269 (million)
% 86.38/12.47 % (167568)Success in time 12.252 s
% 86.38/12.47 % Vampire exiting
%------------------------------------------------------------------------------