%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP028^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:10:25 AM UTC 2026
% Result : Theorem 6.36s 1.36s
% Output : Refutation 6.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP028^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:41:49 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.36/1.35 % (4013261)Will run a generic schedule for satisfiability detection.
% 6.36/1.35 % (4013267)% WARNING: option uhcvi not known.
% 6.36/1.35 % (4013269)dis+10_1_sil=32000:sp=arity:random_seed=1816902255:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.36/1.35 % (4013266)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1237973642_2999 on theBenchmark for (2999ds/0Mi)
% 6.36/1.35 % (4013268)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2799418069:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.36/1.35 % (4013267)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2012177358:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.36/1.35 % (4013271)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=23557598:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.36/1.35 % (4013267)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.35 % (4013270)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=456582152:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.36/1.35 % (4013272)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1183559312:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.36/1.35 % (4013267)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.36/1.35 % (4013270)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.35 % Exception at run slice level
% 6.36/1.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.35 % (4013269)Instruction limit reached!
% 6.36/1.35 % (4013269)------------------------------
% 6.36/1.35 % (4013269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.35 % (4013269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.35 % (4013269)CaDiCaL version: 2.1.3
% 6.36/1.35 % (4013269)Termination reason: Instruction limit
% 6.36/1.35 % (4013269)Termination phase: Saturation
% 6.36/1.35 % (4013269)Time elapsed: 0.069 s
% 6.36/1.35 % (4013269)Peak memory usage: 12 MB
% 6.36/1.35 % (4013269)Instructions burned: 103 (million)
% 6.36/1.35 % (4013281)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=339420792:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 6.36/1.35 % (4013283)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=79215561:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 6.36/1.35 % (4013272)Instruction limit reached!
% 6.36/1.35 % (4013272)------------------------------
% 6.36/1.35 % (4013272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.35 % (4013272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.35 % (4013272)CaDiCaL version: 2.1.3
% 6.36/1.35 % (4013272)Termination reason: Instruction limit
% 6.36/1.35 % (4013272)Termination phase: Saturation
% 6.36/1.35 % (4013272)Time elapsed: 0.086 s
% 6.36/1.35 % (4013272)Peak memory usage: 14 MB
% 6.36/1.35 % (4013272)Instructions burned: 160 (million)
% 6.36/1.35 % (4013270)Instruction limit reached!
% 6.36/1.35 % (4013270)------------------------------
% 6.36/1.35 % (4013270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.35 % (4013270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.35 % (4013270)CaDiCaL version: 2.1.3
% 6.36/1.35 % (4013270)Termination reason: Instruction limit
% 6.36/1.35 % (4013270)Termination phase: Saturation
% 6.36/1.35 % (4013270)Time elapsed: 0.100 s
% 6.36/1.35 % (4013270)Peak memory usage: 13 MB
% 6.36/1.35 % (4013270)Instructions burned: 116 (million)
% 6.36/1.35 % (4013271)Instruction limit reached!
% 6.36/1.35 % (4013271)------------------------------
% 6.36/1.35 % (4013271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.35 % (4013271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.35 % (4013271)CaDiCaL version: 2.1.3
% 6.36/1.35 % (4013271)Termination reason: Instruction limit
% 6.36/1.35 % (4013271)Termination phase: Saturation
% 6.36/1.35 % (4013271)Time elapsed: 0.109 s
% 6.36/1.35 % (4013271)Peak memory usage: 13 MB
% 6.36/1.35 % (4013271)Instructions burned: 132 (million)
% 6.36/1.35 % (4013286)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=1522496313:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.36/1.36 % (4013287)ott-21_1_sil=16000:fs=off:random_seed=4214383858:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.36/1.36 % (4013288)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=360919023:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.36/1.36 % (4013286)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.36 % Exception at run slice level
% 6.36/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.36 % (4013283)Instruction limit reached!
% 6.36/1.36 % (4013283)------------------------------
% 6.36/1.36 % (4013283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.36 % (4013283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.36 % (4013283)CaDiCaL version: 2.1.3
% 6.36/1.36 % (4013283)Termination reason: Instruction limit
% 6.36/1.36 % (4013283)Termination phase: Saturation
% 6.36/1.36 % (4013283)Time elapsed: 0.100 s
% 6.36/1.36 % (4013283)Peak memory usage: 13 MB
% 6.36/1.36 % (4013283)Instructions burned: 131 (million)
% 6.36/1.36 % (4013292)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=281193280:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 6.36/1.36 % (4013286)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.36/1.36 % (4013293)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1761229440:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 6.36/1.36 % (4013287)Instruction limit reached!
% 6.36/1.36 % (4013287)------------------------------
% 6.36/1.36 % (4013287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.36 % (4013287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.36 % (4013287)CaDiCaL version: 2.1.3
% 6.36/1.36 % (4013287)Termination reason: Instruction limit
% 6.36/1.36 % (4013287)Termination phase: Saturation
% 6.36/1.36 % (4013287)Time elapsed: 0.123 s
% 6.36/1.36 % (4013287)Peak memory usage: 13 MB
% 6.36/1.36 % (4013287)Instructions burned: 182 (million)
% 6.36/1.36 % Exception at run slice level
% 6.36/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.36 % (4013296)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3318995684:i=889:ins=1_2996 on theBenchmark for (2996ds/889Mi)
% 6.36/1.36 % (4013297)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=3445103031:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 6.36/1.36 % (4013297)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.36 % Exception at run slice level
% 6.36/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.36 % (4013300)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3453460241:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 6.36/1.36 % (4013300)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.36 % (4013286)Instruction limit reached!
% 6.36/1.36 % (4013286)------------------------------
% 6.36/1.36 % (4013286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.36 % (4013286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.36 % (4013286)CaDiCaL version: 2.1.3
% 6.36/1.36 % (4013286)Termination reason: Instruction limit
% 6.36/1.36 % (4013286)Termination phase: Saturation
% 6.36/1.36 % (4013286)Time elapsed: 0.405 s
% 6.36/1.36 % (4013286)Peak memory usage: 16 MB
% 6.36/1.36 % (4013286)Instructions burned: 685 (million)
% 6.36/1.36 % (4013302)fmb+10_1_sil=64000:random_seed=1115178309:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 6.36/1.36 % (4013302)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.36/1.36 % Exception at run slice level
% 6.36/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.36 % (4013304)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1706988213:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 6.36/1.36 % (4013293)Instruction limit reached!
% 6.36/1.36 % (4013293)------------------------------
% 6.36/1.36 % (4013293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.36 % (4013293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.36 % (4013293)CaDiCaL version: 2.1.3
% 6.36/1.36 % (4013293)Termination reason: Instruction limit
% 6.36/1.36 % (4013293)Termination phase: Saturation
% 6.36/1.36 % (4013293)Time elapsed: 0.392 s
% 6.36/1.36 % (4013293)Peak memory usage: 19 MB
% 6.36/1.36 % (4013293)Instructions burned: 1181 (million)
% 6.36/1.36 % (4013288)Instruction limit reached!
% 6.36/1.36 % (4013288)------------------------------
% 6.36/1.36 % (4013288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.36 % (4013288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.36 % (4013288)CaDiCaL version: 2.1.3
% 6.36/1.36 % (4013288)Termination reason: Instruction limit
% 6.36/1.36 % (4013288)Termination phase: Saturation
% 6.36/1.36 % (4013288)Time elapsed: 0.476 s
% 6.36/1.36 % (4013288)Peak memory usage: 14 MB
% 6.36/1.36 % (4013288)Instructions burned: 477 (million)
% 6.36/1.36 % (4013306)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2126415599:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 6.36/1.36 % Exception at run slice level
% 6.36/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.36 % Exception at run slice level
% 6.36/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.36 % (4013307)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1149564239:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 6.36/1.36 % (4013310)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1569110026:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 6.36/1.36 % (4013309)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2466588591:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 6.36/1.36 % Exception at run slice level
% 6.36/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.36 % (4013307)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.36 % (4013314)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=425300414:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 6.36/1.36 % (4013297)Instruction limit reached!
% 6.36/1.36 % (4013297)------------------------------
% 6.36/1.36 % (4013297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.36 % (4013297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.36 % (4013297)CaDiCaL version: 2.1.3
% 6.36/1.36 % (4013297)Termination reason: Instruction limit
% 6.36/1.36 % (4013297)Termination phase: Saturation
% 6.36/1.36 % (4013297)Time elapsed: 0.396 s
% 6.36/1.36 % (4013297)Peak memory usage: 16 MB
% 6.36/1.36 % (4013297)Instructions burned: 693 (million)
% 6.36/1.36 % Exception at run slice level
% 6.36/1.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.36/1.36 % (4013316)ott-2_1_sil=16000:newcnf=on:random_seed=1674628546:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 6.36/1.36 % (4013317)ott+10_1_sil=32000:tgt=ground:random_seed=2955198901:i=5114:av=off_2991 on theBenchmark for (2991ds/5114Mi)
% 6.36/1.36 % (4013309)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.36/1.36 % (4013316)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.36/1.36 % (4013309)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.36/1.36 % (4013300)Instruction limit reached!
% 6.36/1.36 % (4013300)------------------------------
% 6.36/1.36 % (4013300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.36 % (4013300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.36 % (4013300)CaDiCaL version: 2.1.3
% 6.36/1.36 % (4013300)Termination reason: Instruction limit
% 6.36/1.36 % (4013300)Termination phase: Saturation
% 6.36/1.36 % (4013300)Time elapsed: 0.601 s
% 6.36/1.36 % (4013300)Peak memory usage: 19 MB
% 6.36/1.36 % (4013300)Instructions burned: 879 (million)
% 6.36/1.36 % (4013320)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=288712433:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 6.36/1.36 % (4013317) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4013261-4013317"...
% 6.36/1.36 % (4013317)...printing done.
% 6.36/1.36 % (4013317)Refutation found. Thanks to Tanya!
% 6.36/1.36 % SZS status Theorem for theBenchmark
% 6.36/1.36 % SZS output start Proof for theBenchmark
% 6.36/1.36 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 6.36/1.36 thf(type_def_6, type, set: $tType > $tType).
% 6.36/1.36 thf(type_def_7, type, e: $tType).
% 6.36/1.36 thf(type_def_8, type, a: $tType).
% 6.36/1.36 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 6.36/1.36 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 6.36/1.36 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 6.36/1.36 thf(func_def_2, type, top: !>[X0: $tType]:($o)).
% 6.36/1.36 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 6.36/1.36 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 6.36/1.36 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 6.36/1.36 thf(func_def_6, type, order_top: !>[X0: $tType]:($o)).
% 6.36/1.36 thf(func_def_7, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 6.36/1.36 thf(func_def_8, type, bNF_csquare: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ X0 > (X1 > X2) > (X3 > X2) > (X0 > X1) > (X0 > X3) > $o))).
% 6.36/1.36 thf(func_def_9, type, bNF_fstOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X0 @ X1))).
% 6.36/1.36 thf(func_def_10, type, bNF_pick_middlep: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > X1))).
% 6.36/1.36 thf(func_def_11, type, bNF_sndOp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 6.36/1.36 thf(func_def_12, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2))).
% 6.36/1.36 thf(func_def_13, type, finite_Fpow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 6.36/1.36 thf(func_def_14, type, fun_in_rel: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > X1 > $o))).
% 6.36/1.36 thf(func_def_15, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.36/1.36 thf(func_def_16, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_17, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 6.36/1.36 thf(func_def_18, type, top_top: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_19, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 6.36/1.36 thf(func_def_20, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 6.36/1.36 thf(func_def_21, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 6.36/1.36 thf(func_def_22, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 6.36/1.36 thf(func_def_23, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 6.36/1.36 thf(func_def_24, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 6.36/1.36 thf(func_def_25, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 6.36/1.36 thf(func_def_26, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 6.36/1.36 thf(func_def_27, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 6.36/1.36 thf(func_def_28, type, domain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0))).
% 6.36/1.36 thf(func_def_29, type, range: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X1))).
% 6.36/1.36 thf(func_def_30, type, converse: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X1 @ X0))).
% 6.36/1.36 thf(func_def_31, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 6.36/1.36 thf(func_def_32, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 6.36/1.36 thf(func_def_33, type, relcompp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > $o))).
% 6.36/1.36 thf(func_def_34, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 6.36/1.36 thf(func_def_35, type, pow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 6.36/1.36 thf(func_def_36, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 6.36/1.36 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 6.36/1.36 thf(func_def_38, type, c: set @ product_prod @ set @ a @ (a > e)).
% 6.36/1.36 thf(func_def_39, type, a1: set @ a).
% 6.36/1.36 thf(func_def_40, type, a2: set @ a).
% 6.36/1.36 thf(func_def_41, type, a3: set @ a).
% 6.36/1.36 thf(func_def_42, type, b1: (a > e)).
% 6.36/1.36 thf(func_def_43, type, b2: (a > e)).
% 6.36/1.36 thf(func_def_44, type, b3: (a > e)).
% 6.36/1.36 thf(func_def_45, type, thesis: $o).
% 6.36/1.36 thf(func_def_49, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.36/1.36 thf(func_def_50, type, vIMP: ($o > $o > $o)).
% 6.36/1.36 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.36/1.36 thf(func_def_53, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.36/1.36 thf(func_def_54, type, vAND: ($o > $o > $o)).
% 6.36/1.36 thf(func_def_55, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.36/1.36 thf(func_def_56, type, db1: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_57, type, db2: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_59, type, vNOT: ($o > $o)).
% 6.36/1.36 thf(func_def_60, type, db4: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_61, type, db6: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_62, type, db5: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_63, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 6.36/1.36 thf(func_def_64, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 6.36/1.36 thf(func_def_65, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 6.36/1.36 thf(func_def_66, type, sK3: set @ a).
% 6.36/1.36 thf(func_def_67, type, sK4: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 6.36/1.36 thf(func_def_68, type, sK5: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 6.36/1.36 thf(func_def_69, type, sK6: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 6.36/1.36 thf(func_def_70, type, sK7: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 6.36/1.36 thf(func_def_71, type, sK8: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 6.36/1.36 thf(func_def_72, type, sK9: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_73, type, sK10: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_74, type, sK11: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_75, type, sK12: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_76, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 6.36/1.36 thf(func_def_77, type, sK14: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 6.36/1.36 thf(func_def_78, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_79, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_80, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 6.36/1.36 thf(func_def_81, type, sK18: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 6.36/1.36 thf(func_def_82, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_83, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_84, type, sK21: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_85, type, sK22: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_86, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 6.36/1.36 thf(func_def_88, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 6.36/1.36 thf(func_def_89, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_90, type, sK27: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_91, type, sK28: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_92, type, sK29: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_93, type, sK30: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_94, type, sK31: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_95, type, sK32: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_96, type, sK33: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 6.36/1.36 thf(func_def_97, type, sK34: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 6.36/1.36 thf(func_def_98, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 6.36/1.36 thf(func_def_99, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 6.36/1.36 thf(func_def_100, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 6.36/1.36 thf(func_def_101, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 6.36/1.36 thf(func_def_102, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 6.36/1.36 thf(func_def_103, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_104, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_105, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 6.36/1.36 thf(func_def_106, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 6.36/1.36 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 6.36/1.36 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 6.36/1.36 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_111, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 6.36/1.36 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 6.36/1.36 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 6.36/1.36 thf(func_def_114, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_115, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_116, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 6.36/1.36 thf(func_def_117, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 6.36/1.36 thf(func_def_118, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_119, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_120, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 6.36/1.36 thf(func_def_121, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_122, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_123, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 6.36/1.36 thf(func_def_124, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 6.36/1.36 thf(func_def_125, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 6.36/1.36 thf(func_def_126, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 6.36/1.36 thf(func_def_127, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 6.36/1.36 thf(func_def_128, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 6.36/1.36 thf(func_def_129, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 6.36/1.36 thf(func_def_130, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0))).
% 6.36/1.36 thf(func_def_131, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1))).
% 6.36/1.36 thf(func_def_132, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2))).
% 6.36/1.36 thf(func_def_133, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3))).
% 6.36/1.36 thf(func_def_134, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4))).
% 6.36/1.36 thf(func_def_135, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 6.36/1.36 thf(func_def_136, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 6.36/1.36 thf(func_def_137, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 6.36/1.36 thf(func_def_138, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 6.36/1.36 thf(func_def_139, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 6.36/1.36 thf(func_def_140, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 6.36/1.36 thf(func_def_141, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 6.36/1.36 thf(func_def_142, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 6.36/1.36 thf(func_def_143, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 6.36/1.36 thf(func_def_144, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 6.36/1.36 thf(func_def_145, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 6.36/1.36 thf(func_def_146, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 6.36/1.36 thf(func_def_147, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 6.36/1.36 thf(func_def_148, type, sK85: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_149, type, sK86: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_150, type, sK87: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 6.36/1.36 thf(func_def_151, type, sK88: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 6.36/1.36 thf(func_def_152, type, sK89: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > X0) > set @ X1 > X1))).
% 6.36/1.36 thf(func_def_153, type, sK90: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 6.36/1.36 thf(func_def_154, type, sK91: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 6.36/1.36 thf(func_def_155, type, sK92: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 6.36/1.36 thf(func_def_156, type, sK93: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 6.36/1.36 thf(func_def_157, type, sK94: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 6.36/1.36 thf(func_def_158, type, sK95: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 6.36/1.36 thf(func_def_159, type, sK96: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 6.36/1.36 thf(func_def_160, type, sK97: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 6.36/1.36 thf(func_def_161, type, sK98: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X0 @ X1 > X0))).
% 6.36/1.36 thf(func_def_162, type, sK99: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X0 @ X1 > X1))).
% 6.36/1.36 thf(func_def_163, type, sK100: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 6.36/1.36 thf(func_def_164, type, sK101: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 6.36/1.36 thf(func_def_165, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X1 @ X0 > X1))).
% 6.36/1.36 thf(func_def_166, type, sK103: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X1 @ X0 > X0))).
% 6.36/1.36 thf(func_def_167, type, sK104: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ X1 @ X0 > X1))).
% 6.36/1.36 thf(func_def_168, type, sK105: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ X1 @ X0 > X0))).
% 6.36/1.36 thf(func_def_169, type, sK106: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > product_prod @ X0 @ X1 > X1))).
% 6.36/1.36 thf(func_def_170, type, sK107: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > product_prod @ X0 @ X1 > X0))).
% 6.36/1.36 thf(func_def_171, type, sK108: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 6.36/1.36 thf(func_def_172, type, sK109: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_173, type, sK110: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 6.36/1.36 thf(func_def_174, type, sK111: !>[X0: $tType]:((set @ X0 > X0))).
% 6.36/1.36 thf(func_def_175, type, sK112: !>[X0: $tType]:(X0)).
% 6.36/1.36 thf(func_def_176, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X3))).
% 6.36/1.36 thf(func_def_177, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X2))).
% 6.36/1.36 thf(func_def_178, type, sK115: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 6.36/1.36 thf(func_def_179, type, sK116: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 6.36/1.36 thf(func_def_180, type, sK117: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 6.36/1.36 thf(func_def_181, type, sK118: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X0))).
% 6.36/1.36 thf(func_def_182, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2))).
% 6.36/1.36 thf(func_def_183, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1))).
% 6.36/1.36 thf(func_def_184, type, sK121: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_185, type, sK122: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_186, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0))).
% 6.36/1.36 thf(func_def_187, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2))).
% 6.36/1.36 thf(func_def_188, type, sK125: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_189, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X3 > X0 > (X2 > X3 > $o) > (X0 > X2 > $o) > (X1 > X2) > X1))).
% 6.36/1.36 thf(func_def_190, type, sK127: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 6.36/1.36 thf(func_def_191, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2 > $o) > (X0 > X2 > $o) > (X1 > X0 > $o) > X1))).
% 6.36/1.36 thf(func_def_192, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2 > $o) > (X0 > X2 > $o) > (X1 > X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_193, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2 > $o) > (X0 > X2 > $o) > (X1 > X0 > $o) > X2))).
% 6.36/1.36 thf(func_def_194, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0 > (X1 > X2 > $o) > (X0 > X1 > $o) > X1))).
% 6.36/1.36 thf(func_def_195, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0 > (X1 > X2 > $o) > (X0 > X1 > $o) > X1))).
% 6.36/1.36 thf(func_def_196, type, sK133: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 6.36/1.36 thf(func_def_197, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > (X1 > X2 > $o) > X1 > (X2 > X0 > $o) > X2))).
% 6.36/1.36 thf(func_def_198, type, sK135: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 6.36/1.36 thf(func_def_199, type, sK136: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 6.36/1.36 thf(func_def_200, type, sK137: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 6.36/1.36 thf(func_def_201, type, sK138: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X1 @ X0 > X0 > X0))).
% 6.36/1.36 thf(func_def_202, type, sK139: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X1 @ X0 > X0 > X1))).
% 6.36/1.36 thf(func_def_203, type, sK140: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 6.36/1.36 thf(func_def_204, type, sK141: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X1))).
% 6.36/1.36 thf(func_def_205, type, sK142: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > X1))).
% 6.36/1.36 thf(func_def_206, type, sK143: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X0))).
% 6.36/1.36 thf(func_def_207, type, sK144: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 6.36/1.36 thf(func_def_208, type, sK145: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 6.36/1.36 thf(func_def_209, type, sK146: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X0))).
% 6.36/1.36 thf(func_def_210, type, sK147: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 6.36/1.36 thf(func_def_211, type, sK148: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 6.36/1.36 thf(func_def_212, type, sK149: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 6.36/1.36 thf(func_def_213, type, sK150: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 6.36/1.36 thf(func_def_214, type, sK151: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 6.36/1.36 thf(func_def_215, type, sK152: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 6.36/1.36 thf(f3,axiom,(
% 6.36/1.36 (ord_less_eq @ set @ a @ a2 @ a1) | (ord_less_eq @ set @ a @ a1 @ a2)),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062)).
% 6.36/1.36 thf(f4,axiom,(
% 6.36/1.36 (ord_less_eq @ set @ a @ a3 @ a1) | (ord_less_eq @ set @ a @ a1 @ a3)),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062)).
% 6.36/1.36 thf(f5,axiom,(
% 6.36/1.36 (ord_less_eq @ set @ a @ a3 @ a2) | (ord_less_eq @ set @ a @ a2 @ a3)),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062a2_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa2_092_060close_062)).
% 6.36/1.36 thf(f6,axiom,(
% 6.36/1.36 (member @ set @ a @ a3 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_A_I3_J)).
% 6.36/1.36 thf(f7,axiom,(
% 6.36/1.36 (member @ set @ a @ a2 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_A_I2_J)).
% 6.36/1.36 thf(f8,axiom,(
% 6.36/1.36 (member @ set @ a @ a1 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_A_I1_J)).
% 6.36/1.36 thf(f27,axiom,(
% 6.36/1.36 ! [X0 : $tType] : (preorder @ X0 => ! [X1 : X0,X2 : X0,X3 : X0] : ((ord_less_eq @ X0 @ X1 @ X2) => ((ord_less_eq @ X0 @ X2 @ X3) => (ord_less_eq @ X0 @ X1 @ X3))))),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_order__trans)).
% 6.36/1.36 thf(f67,axiom,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((member @ X0 @ X3 @ X1) => (member @ X0 @ X3 @ X2)))),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_in__mono)).
% 6.36/1.36 thf(f106,axiom,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0] : (ord_less_eq @ set @ X0 @ X1 @ X1)),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_subset__self)).
% 6.36/1.36 thf(f107,axiom,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((X1 != X2) => ((ord_less_eq @ set @ X0 @ X2 @ X1) => ? [X3 : X0] : (~(member @ X0 @ X3 @ X2) & (member @ X0 @ X3 @ X1))))),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_sets__not__eq)).
% 6.36/1.36 thf(f261,axiom,(
% 6.36/1.36 ! [X0 : $tType] : preorder @ set @ X0),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_2)).
% 6.36/1.36 thf(f271,axiom,(
% 6.36/1.36 ! [X0 : set @ a] : ((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c)) => ((ord_less_eq @ set @ a @ a1 @ X0) => ((ord_less_eq @ set @ a @ a2 @ X0) => ((ord_less_eq @ set @ a @ a3 @ X0) => thesis))))),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 6.36/1.36 thf(f272,conjecture,(
% 6.36/1.36 thesis),
% 6.36/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 6.36/1.36 thf(f273,negated_conjecture,(
% 6.36/1.36 ~thesis),
% 6.36/1.36 inference(negated_conjecture,[status(cth)],[f272])).
% 6.36/1.36 thf(f278,plain,(
% 6.36/1.36 (ord_less_eq @ set @ a @ a2 @ a1) | (ord_less_eq @ set @ a @ a1 @ a2)),
% 6.36/1.36 inference(rectify,[],[f3])).
% 6.36/1.36 thf(f279,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a1)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f278])).
% 6.36/1.36 thf(f280,plain,(
% 6.36/1.36 (ord_less_eq @ set @ a @ a3 @ a1) | (ord_less_eq @ set @ a @ a1 @ a3)),
% 6.36/1.36 inference(rectify,[],[f4])).
% 6.36/1.36 thf(f281,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a3 @ a1)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f280])).
% 6.36/1.36 thf(f282,plain,(
% 6.36/1.36 (ord_less_eq @ set @ a @ a3 @ a2) | (ord_less_eq @ set @ a @ a2 @ a3)),
% 6.36/1.36 inference(rectify,[],[f5])).
% 6.36/1.36 thf(f283,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a3 @ a2)) = $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f282])).
% 6.36/1.36 thf(f284,plain,(
% 6.36/1.36 (member @ set @ a @ a3 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))),
% 6.36/1.36 inference(rectify,[],[f6])).
% 6.36/1.36 thf(f285,plain,(
% 6.36/1.36 (((member @ set @ a @ a3 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f284])).
% 6.36/1.36 thf(f286,plain,(
% 6.36/1.36 (member @ set @ a @ a2 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))),
% 6.36/1.36 inference(rectify,[],[f7])).
% 6.36/1.36 thf(f287,plain,(
% 6.36/1.36 (((member @ set @ a @ a2 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f286])).
% 6.36/1.36 thf(f288,plain,(
% 6.36/1.36 (member @ set @ a @ a1 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))),
% 6.36/1.36 inference(rectify,[],[f8])).
% 6.36/1.36 thf(f289,plain,(
% 6.36/1.36 (((member @ set @ a @ a1 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f288])).
% 6.36/1.36 thf(f324,plain,(
% 6.36/1.36 ! [X0 : $tType] : (preorder @ X0 => ! [X1 : X0,X2 : X0,X3 : X0] : ((ord_less_eq @ X0 @ X1 @ X2) => ((ord_less_eq @ X0 @ X2 @ X3) => (ord_less_eq @ X0 @ X1 @ X3))))),
% 6.36/1.36 inference(rectify,[],[f27])).
% 6.36/1.36 thf(f325,plain,(
% 6.36/1.36 ! [X0 : $tType] : ((preorder @ X0 = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((((ord_less_eq @ X0 @ X1 @ X2)) = $true) => ((((ord_less_eq @ X0 @ X2 @ X3)) = $true) => (((ord_less_eq @ X0 @ X1 @ X3)) = $true))))),
% 6.36/1.36 inference(fool_elimination,[],[f324])).
% 6.36/1.36 thf(f398,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((member @ X0 @ X3 @ X1) => (member @ X0 @ X3 @ X2)))),
% 6.36/1.36 inference(rectify,[],[f67])).
% 6.36/1.36 thf(f399,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((((ord_less_eq @ set @ X0 @ X1 @ X2)) = $true) => ((((member @ X0 @ X3 @ X1)) = $true) => (((member @ X0 @ X3 @ X2)) = $true)))),
% 6.36/1.36 inference(fool_elimination,[],[f398])).
% 6.36/1.36 thf(f449,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0] : (ord_less_eq @ set @ X0 @ X1 @ X1)),
% 6.36/1.36 inference(rectify,[],[f106])).
% 6.36/1.36 thf(f450,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X1)) = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f449])).
% 6.36/1.36 thf(f451,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((X1 != X2) => ((ord_less_eq @ set @ X0 @ X2 @ X1) => ? [X3 : X0] : (~(member @ X0 @ X3 @ X2) & (member @ X0 @ X3 @ X1))))),
% 6.36/1.36 inference(rectify,[],[f107])).
% 6.36/1.36 thf(f452,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((X1 != X2) => ((((ord_less_eq @ set @ X0 @ X2 @ X1)) = $true) => ? [X3 : X0] : (~ (((member @ X0 @ X3 @ X2)) = $true) & (((member @ X0 @ X3 @ X1)) = $true))))),
% 6.36/1.36 inference(fool_elimination,[],[f451])).
% 6.36/1.36 thf(f652,plain,(
% 6.36/1.36 ! [X0 : $tType] : preorder @ set @ X0),
% 6.36/1.36 inference(rectify,[],[f261])).
% 6.36/1.36 thf(f653,plain,(
% 6.36/1.36 ! [X0 : $tType] : (preorder @ set @ X0 = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f652])).
% 6.36/1.36 thf(f672,plain,(
% 6.36/1.36 ! [X0 : set @ a] : ((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c)) => ((ord_less_eq @ set @ a @ a1 @ X0) => ((ord_less_eq @ set @ a @ a2 @ X0) => ((ord_less_eq @ set @ a @ a3 @ X0) => thesis))))),
% 6.36/1.36 inference(rectify,[],[f271])).
% 6.36/1.36 thf(f673,plain,(
% 6.36/1.36 ! [X0 : set @ a] : ((((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true) => ((((ord_less_eq @ set @ a @ a1 @ X0)) = $true) => ((((ord_less_eq @ set @ a @ a2 @ X0)) = $true) => ((((ord_less_eq @ set @ a @ a3 @ X0)) = $true) => (thesis = $true)))))),
% 6.36/1.36 inference(fool_elimination,[],[f672])).
% 6.36/1.36 thf(f674,plain,(
% 6.36/1.36 ~thesis),
% 6.36/1.36 inference(rectify,[],[f273])).
% 6.36/1.36 thf(f675,plain,(
% 6.36/1.36 ~ (thesis = $true)),
% 6.36/1.36 inference(fool_elimination,[],[f674])).
% 6.36/1.36 thf(f683,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((X1 != X2) => ((((ord_less_eq @ set @ X0 @ X2 @ X1)) = $true) => ? [X3 : X0] : ((((member @ X0 @ X3 @ X2)) != $true) & (((member @ X0 @ X3 @ X1)) = $true))))),
% 6.36/1.36 inference(flattening,[],[f452])).
% 6.36/1.36 thf(f697,plain,(
% 6.36/1.36 (thesis != $true)),
% 6.36/1.36 inference(flattening,[],[f675])).
% 6.36/1.36 thf(f717,plain,(
% 6.36/1.36 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (((((ord_less_eq @ X0 @ X1 @ X3)) = $true) | (((ord_less_eq @ X0 @ X2 @ X3)) != $true)) | (((ord_less_eq @ X0 @ X1 @ X2)) != $true)) | (preorder @ X0 != $true))),
% 6.36/1.36 inference(ennf_transformation,[],[f325])).
% 6.36/1.36 thf(f718,plain,(
% 6.36/1.36 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((((ord_less_eq @ X0 @ X1 @ X3)) = $true) | (((ord_less_eq @ X0 @ X2 @ X3)) != $true) | (((ord_less_eq @ X0 @ X1 @ X2)) != $true)) | (preorder @ X0 != $true))),
% 6.36/1.36 inference(flattening,[],[f717])).
% 6.36/1.36 thf(f765,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : (((((member @ X0 @ X3 @ X2)) = $true) | (((member @ X0 @ X3 @ X1)) != $true)) | (((ord_less_eq @ set @ X0 @ X1 @ X2)) != $true))),
% 6.36/1.36 inference(ennf_transformation,[],[f399])).
% 6.36/1.36 thf(f766,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((((member @ X0 @ X3 @ X2)) = $true) | (((member @ X0 @ X3 @ X1)) != $true) | (((ord_less_eq @ set @ X0 @ X1 @ X2)) != $true))),
% 6.36/1.36 inference(flattening,[],[f765])).
% 6.36/1.36 thf(f805,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((? [X3 : X0] : ((((member @ X0 @ X3 @ X2)) != $true) & (((member @ X0 @ X3 @ X1)) = $true)) | (((ord_less_eq @ set @ X0 @ X2 @ X1)) != $true)) | (X1 = X2))),
% 6.36/1.36 inference(ennf_transformation,[],[f683])).
% 6.36/1.36 thf(f806,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (? [X3 : X0] : ((((member @ X0 @ X3 @ X2)) != $true) & (((member @ X0 @ X3 @ X1)) = $true)) | (((ord_less_eq @ set @ X0 @ X2 @ X1)) != $true) | (X1 = X2))),
% 6.36/1.36 inference(flattening,[],[f805])).
% 6.36/1.36 thf(f916,plain,(
% 6.36/1.36 ! [X0 : set @ a] : (((((thesis = $true) | (((ord_less_eq @ set @ a @ a3 @ X0)) != $true)) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true)) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true)) | (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true))),
% 6.36/1.36 inference(ennf_transformation,[],[f673])).
% 6.36/1.36 thf(f917,plain,(
% 6.36/1.36 ! [X0 : set @ a] : ((thesis = $true) | (((ord_less_eq @ set @ a @ a3 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true) | (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true))),
% 6.36/1.36 inference(flattening,[],[f916])).
% 6.36/1.36 thf(f968,plain,(
% 6.36/1.36 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((($true != ((member @ X0 @ (sK91 @ X0 @ X2 @ X1) @ X2))) & ($true = ((member @ X0 @ (sK91 @ X0 @ X2 @ X1) @ X1)))) | (((ord_less_eq @ set @ X0 @ X2 @ X1)) != $true) | (X1 = X2))),
% 6.36/1.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK4 @ X0 @ X2 @ X1)],[f806])).
% 6.36/1.36 thf(f1003,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a1)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(cnf_transformation,[],[f279])).
% 6.36/1.36 thf(f1004,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a3 @ a1)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)),
% 6.36/1.36 inference(cnf_transformation,[],[f281])).
% 6.36/1.36 thf(f1005,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a3 @ a2)) = $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true)),
% 6.36/1.36 inference(cnf_transformation,[],[f283])).
% 6.36/1.36 thf(f1006,plain,(
% 6.36/1.36 (((member @ set @ a @ a3 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true)),
% 6.36/1.36 inference(cnf_transformation,[],[f285])).
% 6.36/1.36 thf(f1007,plain,(
% 6.36/1.36 (((member @ set @ a @ a2 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true)),
% 6.36/1.36 inference(cnf_transformation,[],[f287])).
% 6.36/1.36 thf(f1008,plain,(
% 6.36/1.36 (((member @ set @ a @ a1 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $true)),
% 6.36/1.36 inference(cnf_transformation,[],[f289])).
% 6.36/1.36 thf(f1033,plain,(
% 6.36/1.36 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((((ord_less_eq @ X0 @ X2 @ X3)) != $true) | (((ord_less_eq @ X0 @ X1 @ X3)) = $true) | (((ord_less_eq @ X0 @ X1 @ X2)) != $true) | (preorder @ X0 != $true)) )),
% 6.36/1.36 inference(cnf_transformation,[],[f718])).
% 6.36/1.36 thf(f1095,plain,(
% 6.36/1.36 ( ! [X0 : $tType,X2 : set @ X0,X3 : X0,X1 : set @ X0] : ((((ord_less_eq @ set @ X0 @ X1 @ X2)) != $true) | (((member @ X0 @ X3 @ X1)) != $true) | (((member @ X0 @ X3 @ X2)) = $true)) )),
% 6.36/1.36 inference(cnf_transformation,[],[f766])).
% 6.36/1.36 thf(f1146,plain,(
% 6.36/1.36 ( ! [X0 : $tType,X1 : set @ X0] : ((((ord_less_eq @ set @ X0 @ X1 @ X1)) = $true)) )),
% 6.36/1.36 inference(cnf_transformation,[],[f450])).
% 6.36/1.36 thf(f1147,plain,(
% 6.36/1.36 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : ((((ord_less_eq @ set @ X0 @ X2 @ X1)) != $true) | ($true = ((member @ X0 @ (sK91 @ X0 @ X2 @ X1) @ X1))) | (X1 = X2)) )),
% 6.36/1.36 inference(cnf_transformation,[],[f968])).
% 6.36/1.36 thf(f1148,plain,(
% 6.36/1.36 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : (($true != ((member @ X0 @ (sK91 @ X0 @ X2 @ X1) @ X2))) | (((ord_less_eq @ set @ X0 @ X2 @ X1)) != $true) | (X1 = X2)) )),
% 6.36/1.36 inference(cnf_transformation,[],[f968])).
% 6.36/1.36 thf(f1325,plain,(
% 6.36/1.36 ( ! [X0 : $tType] : ((preorder @ set @ X0 = $true)) )),
% 6.36/1.36 inference(cnf_transformation,[],[f653])).
% 6.36/1.36 thf(f1335,plain,(
% 6.36/1.36 ( ! [X0 : set @ a] : ((thesis = $true) | (((ord_less_eq @ set @ a @ a3 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true) | (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true)) )),
% 6.36/1.36 inference(cnf_transformation,[],[f917])).
% 6.36/1.36 thf(f1336,plain,(
% 6.36/1.36 (thesis != $true)),
% 6.36/1.36 inference(cnf_transformation,[],[f697])).
% 6.36/1.36 thf(f1338,definition,(
% 6.36/1.36 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 6.36/1.36 introduced(theory,[fool_exhaustiveness_axiom])).
% 6.36/1.36 thf(f1780,plain,(
% 6.36/1.36 ( ! [X0 : set @ a] : ((((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a3 @ X0)) != $true)) )),
% 6.36/1.36 inference(forward_subsumption_resolution,[],[f1335,f1336])).
% 6.36/1.36 thf(f1836,plain,(
% 6.36/1.36 ( ! [X0 : set @ a] : (($true != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a3 @ X0)) != $true) | (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false)) )),
% 6.36/1.36 inference(constrained_superposition,[],[f1780,f1338])).
% 6.36/1.36 thf(f1837,plain,(
% 6.36/1.36 ( ! [X0 : set @ a] : ((((ord_less_eq @ set @ a @ a3 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a1 @ X0)) != $true) | (((ord_less_eq @ set @ a @ a2 @ X0)) != $true) | (((member @ set @ a @ X0 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false)) )),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f1836])).
% 6.36/1.36 thf(f2147,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) != $true) | (((member @ set @ a @ a3 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false)),
% 6.36/1.36 inference(constrained_superposition,[],[f1837,f1146])).
% 6.36/1.36 thf(f2149,plain,(
% 6.36/1.36 ($true != $true) | ($true != ((ord_less_eq @ set @ a @ a1 @ a1))) | (((ord_less_eq @ set @ a @ a2 @ a1)) != $true) | (((member @ set @ a @ a1 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)),
% 6.36/1.36 inference(constrained_superposition,[],[f1837,f1004])).
% 6.36/1.36 thf(f2150,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) != $true) | ($true != ((ord_less_eq @ set @ a @ a2 @ a2))) | (((member @ set @ a @ a2 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true)),
% 6.36/1.36 inference(constrained_superposition,[],[f1837,f1005])).
% 6.36/1.36 thf(f2153,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a2)) != $true) | ($true != ((ord_less_eq @ set @ a @ a2 @ a2))) | (((member @ set @ a @ a2 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2150])).
% 6.36/1.36 thf(f2154,plain,(
% 6.36/1.36 ($true != ((ord_less_eq @ set @ a @ a1 @ a1))) | (((ord_less_eq @ set @ a @ a2 @ a1)) != $true) | (((member @ set @ a @ a1 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2149])).
% 6.36/1.36 thf(f2156,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a3)) != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) != $true) | (((member @ set @ a @ a3 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2147])).
% 6.36/1.36 thf(f2159,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a2)) != $true) | (((member @ set @ a @ a2 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true)),
% 6.36/1.36 inference(forward_subsumption_resolution,[],[f2153,f1146])).
% 6.36/1.36 thf(f2160,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a1)) != $true) | (((member @ set @ a @ a1 @ (image @ product_prod @ set @ a @ (a > e) @ set @ a @ product_fst @ set @ a @ (a > e) @ c))) = $false) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)),
% 6.36/1.36 inference(forward_subsumption_resolution,[],[f2154,f1146])).
% 6.36/1.36 thf(f2162,plain,(
% 6.36/1.36 ($true = $false) | (((ord_less_eq @ set @ a @ a1 @ a3)) != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) != $true)),
% 6.36/1.36 inference(forward_demodulation,[],[f2156,f1006])).
% 6.36/1.36 thf(f2163,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a3)) != $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) != $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2162])).
% 6.36/1.36 thf(f2165,plain,(
% 6.36/1.36 ($true = $false) | (((ord_less_eq @ set @ a @ a1 @ a2)) != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true)),
% 6.36/1.36 inference(forward_demodulation,[],[f2159,f1007])).
% 6.36/1.36 thf(f2166,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a2)) != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2165])).
% 6.36/1.36 thf(f2167,plain,(
% 6.36/1.36 ($true = $false) | (((ord_less_eq @ set @ a @ a2 @ a1)) != $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)),
% 6.36/1.36 inference(forward_demodulation,[],[f2160,f1008])).
% 6.36/1.36 thf(f2168,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a1)) != $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2167])).
% 6.36/1.36 thf(f2181,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $false)),
% 6.36/1.36 inference(constrained_superposition,[],[f2163,f1338])).
% 6.36/1.36 thf(f2182,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a3)) != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $false)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2181])).
% 6.36/1.36 thf(f2549,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(constrained_superposition,[],[f2168,f1003])).
% 6.36/1.36 thf(f2550,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a3)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2549])).
% 6.36/1.36 thf(f2828,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $false) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(constrained_superposition,[],[f2182,f2550])).
% 6.36/1.36 thf(f2833,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a3)) = $false) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f2828])).
% 6.36/1.36 thf(f3131,plain,(
% 6.36/1.36 ( ! [X0 : set @ a] : (($true != $true) | ($true = ((ord_less_eq @ set @ a @ X0 @ a3))) | ($true != ((ord_less_eq @ set @ a @ X0 @ a1))) | ($true != preorder @ set @ a) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)) )),
% 6.36/1.36 inference(constrained_superposition,[],[f1033,f2550])).
% 6.36/1.36 thf(f3140,plain,(
% 6.36/1.36 ( ! [X0 : set @ a] : (($true = ((ord_less_eq @ set @ a @ X0 @ a3))) | ($true != ((ord_less_eq @ set @ a @ X0 @ a1))) | ($true != preorder @ set @ a) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)) )),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f3131])).
% 6.36/1.36 thf(f3151,plain,(
% 6.36/1.36 ( ! [X0 : set @ a] : (($true != ((ord_less_eq @ set @ a @ X0 @ a1))) | ($true = ((ord_less_eq @ set @ a @ X0 @ a3))) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)) )),
% 6.36/1.36 inference(forward_subsumption_resolution,[],[f3140,f1325])).
% 6.36/1.36 thf(f3468,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(constrained_superposition,[],[f3151,f1003])).
% 6.36/1.36 thf(f3473,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(duplicate_literal_removal,[],[f3468])).
% 6.36/1.36 thf(f3474,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a3)) = $true) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f3473])).
% 6.36/1.36 thf(f3477,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a3)) = $true)),
% 6.36/1.36 inference(forward_subsumption_resolution,[],[f3474,f2166])).
% 6.36/1.36 thf(f3491,plain,(
% 6.36/1.36 ($true = $false) | (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(constrained_superposition,[],[f2833,f3477])).
% 6.36/1.36 thf(f3493,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a1 @ a3)) != $true)),
% 6.36/1.36 inference(constrained_superposition,[],[f2163,f3477])).
% 6.36/1.36 thf(f3500,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a3)) != $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f3493])).
% 6.36/1.36 thf(f3502,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a2)) = $true)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f3491])).
% 6.36/1.36 thf(f3524,plain,(
% 6.36/1.36 ( ! [X0 : a] : (($true != $true) | ($true != ((member @ a @ X0 @ a3))) | ($true = ((member @ a @ X0 @ a1))) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)) )),
% 6.36/1.36 inference(constrained_superposition,[],[f1095,f1004])).
% 6.36/1.36 thf(f3545,plain,(
% 6.36/1.36 ( ! [X0 : a] : (($true != ((member @ a @ X0 @ a3))) | ($true = ((member @ a @ X0 @ a1))) | (((ord_less_eq @ set @ a @ a1 @ a3)) = $true)) )),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f3524])).
% 6.36/1.36 thf(f3551,plain,(
% 6.36/1.36 ( ! [X0 : a] : (($true != ((member @ a @ X0 @ a3))) | ($true = ((member @ a @ X0 @ a1)))) )),
% 6.36/1.36 inference(forward_subsumption_resolution,[],[f3545,f3500])).
% 6.36/1.36 thf(f3618,plain,(
% 6.36/1.36 ( ! [X0 : a] : (($true != $true) | ($true != ((member @ a @ X0 @ a1))) | ($true = ((member @ a @ X0 @ a2)))) )),
% 6.36/1.36 inference(constrained_superposition,[],[f1095,f3502])).
% 6.36/1.36 thf(f3625,plain,(
% 6.36/1.36 ( ! [X0 : a] : (($true != ((member @ a @ X0 @ a1))) | ($true = ((member @ a @ X0 @ a2)))) )),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f3618])).
% 6.36/1.36 thf(f3744,plain,(
% 6.36/1.36 ($true != $true) | ($true = ((member @ a @ (sK91 @ a @ a2 @ a3) @ a3))) | (a2 = a3)),
% 6.36/1.36 inference(constrained_superposition,[],[f1147,f3477])).
% 6.36/1.36 thf(f3761,plain,(
% 6.36/1.36 ($true = ((member @ a @ (sK91 @ a @ a2 @ a3) @ a3))) | (a2 = a3)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f3744])).
% 6.36/1.36 thf(f5673,plain,(
% 6.36/1.36 ($true != $true) | ($true = ((member @ a @ (sK91 @ a @ a2 @ a3) @ a1))) | (a2 = a3)),
% 6.36/1.36 inference(constrained_superposition,[],[f3551,f3761])).
% 6.36/1.36 thf(f5676,plain,(
% 6.36/1.36 ($true = ((member @ a @ (sK91 @ a @ a2 @ a3) @ a1))) | (a2 = a3)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f5673])).
% 6.36/1.36 thf(f6382,plain,(
% 6.36/1.36 ($true != $true) | ($true = ((member @ a @ (sK91 @ a @ a2 @ a3) @ a2))) | (a2 = a3)),
% 6.36/1.36 inference(constrained_superposition,[],[f3625,f5676])).
% 6.36/1.36 thf(f6385,plain,(
% 6.36/1.36 ($true = ((member @ a @ (sK91 @ a @ a2 @ a3) @ a2))) | (a2 = a3)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f6382])).
% 6.36/1.36 thf(f6925,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) != $true) | (a2 = a3) | (a2 = a3)),
% 6.36/1.36 inference(constrained_superposition,[],[f1148,f6385])).
% 6.36/1.36 thf(f6934,plain,(
% 6.36/1.36 ($true != $true) | (((ord_less_eq @ set @ a @ a2 @ a3)) != $true) | (a2 = a3)),
% 6.36/1.36 inference(duplicate_literal_removal,[],[f6925])).
% 6.36/1.36 thf(f6935,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a2 @ a3)) != $true) | (a2 = a3)),
% 6.36/1.36 inference(trivial_inequality_removal,[],[f6934])).
% 6.36/1.36 thf(f6954,plain,(
% 6.36/1.36 (a2 = a3)),
% 6.36/1.36 inference(forward_subsumption_resolution,[],[f6935,f3477])).
% 6.36/1.36 thf(f7007,plain,(
% 6.36/1.36 (((ord_less_eq @ set @ a @ a1 @ a2)) != $true)),
% 6.36/1.36 inference(constrained_superposition,[],[f3500,f6954])).
% 6.36/1.36 thf(f7023,plain,(
% 6.36/1.36 $false),
% 6.36/1.36 inference(forward_subsumption_resolution,[],[f7007,f3502])).
% 6.36/1.36 % SZS output end Proof for theBenchmark
% 6.36/1.36 % (4013317)------------------------------
% 6.36/1.36 % (4013317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.36/1.36 % (4013317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/1.36 % (4013317)CaDiCaL version: 2.1.3
% 6.36/1.36 % (4013317)Termination reason: Refutation
% 6.36/1.36 % (4013317)Time elapsed: 0.288 s
% 6.36/1.36 % (4013317)Peak memory usage: 20 MB
% 6.36/1.36 % (4013317)Instructions burned: 964 (million)
% 6.36/1.36 % (4013261)Success in time 1.113 s
% 6.36/1.36 % Vampire exiting
%------------------------------------------------------------------------------