%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP187^2 : 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 : n016.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 08:11:02 AM UTC 2026
% Result : Theorem 8.70s 1.90s
% Output : Refutation 8.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP187^2 : 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 : n016.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 20:13:50 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
% 5.54/1.11 % (848754)Will run a generic schedule for satisfiability detection.
% 5.54/1.11 % (848761)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2303711720:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.54/1.11 % (848760)% WARNING: option uhcvi not known.
% 5.54/1.11 % (848759)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1785139608_2999 on theBenchmark for (2999ds/0Mi)
% 5.54/1.11 % (848760)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3019627314:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.54/1.11 % (848762)dis+10_1_sil=32000:sp=arity:random_seed=2665460771:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.54/1.11 % (848763)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2342631919:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.54/1.11 % (848764)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3012229142:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.54/1.11 % (848765)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1649092592:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.54/1.11 % (848760)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.54/1.11 % (848763)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.54/1.11 % Exception at run slice level
% 5.54/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.54/1.11 % (848763)Instruction limit reached!
% 5.54/1.11 % (848763)------------------------------
% 5.54/1.11 % (848763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.54/1.11 % (848763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.11 % (848763)CaDiCaL version: 2.1.3
% 5.54/1.11 % (848763)Termination reason: Instruction limit
% 5.54/1.11 % (848763)Termination phase: Saturation
% 5.54/1.11 % (848763)Time elapsed: 0.053 s
% 5.54/1.11 % (848763)Peak memory usage: 11 MB
% 5.54/1.11 % (848763)Instructions burned: 126 (million)
% 5.54/1.11 % (848762)Instruction limit reached!
% 5.54/1.11 % (848762)------------------------------
% 5.54/1.11 % (848762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.54/1.11 % (848762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.11 % (848762)CaDiCaL version: 2.1.3
% 5.54/1.11 % (848762)Termination reason: Instruction limit
% 5.54/1.11 % (848762)Termination phase: Property scanning
% 5.54/1.11 % (848762)Time elapsed: 0.054 s
% 5.54/1.11 % (848762)Peak memory usage: 11 MB
% 5.54/1.11 % (848762)Instructions burned: 104 (million)
% 5.54/1.11 % (848760)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.54/1.11 % (848764)Instruction limit reached!
% 5.54/1.11 % (848764)------------------------------
% 5.54/1.11 % (848764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.54/1.11 % (848764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.11 % (848764)CaDiCaL version: 2.1.3
% 5.54/1.11 % (848764)Termination reason: Instruction limit
% 5.54/1.11 % (848764)Termination phase: Saturation
% 5.54/1.11 % (848764)Time elapsed: 0.065 s
% 5.54/1.11 % (848764)Peak memory usage: 12 MB
% 5.54/1.11 % (848764)Instructions burned: 133 (million)
% 5.54/1.11 % (848765)Instruction limit reached!
% 5.54/1.11 % (848765)------------------------------
% 5.54/1.11 % (848765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.54/1.11 % (848765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.11 % (848765)CaDiCaL version: 2.1.3
% 5.54/1.11 % (848765)Termination reason: Instruction limit
% 5.54/1.11 % (848765)Termination phase: Saturation
% 5.54/1.11 % (848765)Time elapsed: 0.069 s
% 5.54/1.11 % (848765)Peak memory usage: 13 MB
% 5.54/1.11 % (848765)Instructions burned: 159 (million)
% 5.54/1.11 % (848773)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3104159513:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 5.54/1.11 % (848774)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2152599079:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 5.54/1.11 % (848775)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=962863986:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.54/1.11 % (848776)ott-21_1_sil=16000:fs=off:random_seed=3784046216:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 8.70/1.90 % (848777)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1980157451:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 8.70/1.90 % (848775)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848775)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.70/1.90 % (848774)Instruction limit reached!
% 8.70/1.90 % (848774)------------------------------
% 8.70/1.90 % (848774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848774)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848774)Termination reason: Instruction limit
% 8.70/1.90 % (848774)Termination phase: Saturation
% 8.70/1.90 % (848774)Time elapsed: 0.060 s
% 8.70/1.90 % (848774)Peak memory usage: 13 MB
% 8.70/1.90 % (848774)Instructions burned: 141 (million)
% 8.70/1.90 % (848783)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3616004406:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 8.70/1.90 % (848784)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1327652079:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 8.70/1.90 % (848776)Instruction limit reached!
% 8.70/1.90 % (848776)------------------------------
% 8.70/1.90 % (848776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848776)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848776)Termination reason: Instruction limit
% 8.70/1.90 % (848776)Termination phase: Saturation
% 8.70/1.90 % (848776)Time elapsed: 0.076 s
% 8.70/1.90 % (848776)Peak memory usage: 13 MB
% 8.70/1.90 % (848776)Instructions burned: 181 (million)
% 8.70/1.90 % (848787)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3662925618:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848789)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=448139799:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 8.70/1.90 % (848789)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848791)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3889774718:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 8.70/1.90 % (848791)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.70/1.90 % (848777)Instruction limit reached!
% 8.70/1.90 % (848777)------------------------------
% 8.70/1.90 % (848777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848777)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848777)Termination reason: Instruction limit
% 8.70/1.90 % (848777)Termination phase: Saturation
% 8.70/1.90 % (848777)Time elapsed: 0.223 s
% 8.70/1.90 % (848777)Peak memory usage: 15 MB
% 8.70/1.90 % (848777)Instructions burned: 478 (million)
% 8.70/1.90 % (848793)fmb+10_1_sil=64000:random_seed=3355338735:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 8.70/1.90 % (848793)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848795)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3700102676:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 8.70/1.90 % (848775)Instruction limit reached!
% 8.70/1.90 % (848775)------------------------------
% 8.70/1.90 % (848775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848775)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848775)Termination reason: Instruction limit
% 8.70/1.90 % (848775)Termination phase: Saturation
% 8.70/1.90 % (848775)Time elapsed: 0.332 s
% 8.70/1.90 % (848775)Peak memory usage: 16 MB
% 8.70/1.90 % (848775)Instructions burned: 684 (million)
% 8.70/1.90 % (848797)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2191050908:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848799)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3631300955:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848799)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.70/1.90 % (848801)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3368230231:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 8.70/1.90 % (848801)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.70/1.90 % (848801)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.70/1.90 % (848789)Instruction limit reached!
% 8.70/1.90 % (848789)------------------------------
% 8.70/1.90 % (848789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848789)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848789)Termination reason: Instruction limit
% 8.70/1.90 % (848789)Termination phase: Saturation
% 8.70/1.90 % (848789)Time elapsed: 0.348 s
% 8.70/1.90 % (848789)Peak memory usage: 21 MB
% 8.70/1.90 % (848789)Instructions burned: 692 (million)
% 8.70/1.90 % (848803)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3065121209:i=6324_2993 on theBenchmark for (2993ds/6324Mi)
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848805)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2893463211:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 8.70/1.90 % (848791)Instruction limit reached!
% 8.70/1.90 % (848791)------------------------------
% 8.70/1.90 % (848791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848791)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848791)Termination reason: Instruction limit
% 8.70/1.90 % (848791)Termination phase: Saturation
% 8.70/1.90 % (848791)Time elapsed: 0.417 s
% 8.70/1.90 % (848791)Peak memory usage: 19 MB
% 8.70/1.90 % (848791)Instructions burned: 879 (million)
% 8.70/1.90 % (848807)ott-2_1_sil=16000:newcnf=on:random_seed=1846541573:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848784)Instruction limit reached!
% 8.70/1.90 % (848784)------------------------------
% 8.70/1.90 % (848784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848784)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848784)Termination reason: Instruction limit
% 8.70/1.90 % (848784)Termination phase: Saturation
% 8.70/1.90 % (848784)Time elapsed: 0.562 s
% 8.70/1.90 % (848784)Peak memory usage: 24 MB
% 8.70/1.90 % (848784)Instructions burned: 1180 (million)
% 8.70/1.90 % (848807)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.70/1.90 % (848809)ott+10_1_sil=32000:tgt=ground:random_seed=2526266156:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 8.70/1.90 % (848810)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3992510094:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 8.70/1.90 % Exception at run slice level
% 8.70/1.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.70/1.90 % (848813)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1641923142:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 8.70/1.90 % (848813)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.70/1.90 % (848807)Instruction limit reached!
% 8.70/1.90 % (848807)------------------------------
% 8.70/1.90 % (848807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848807)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848807)Termination reason: Instruction limit
% 8.70/1.90 % (848807)Termination phase: Saturation
% 8.70/1.90 % (848807)Time elapsed: 0.403 s
% 8.70/1.90 % (848807)Peak memory usage: 17 MB
% 8.70/1.90 % (848807)Instructions burned: 869 (million)
% 8.70/1.90 % (848815)dis+21_1_sil=32000:sas=cadical:random_seed=2643455607:i=3773:amm=off_2988 on theBenchmark for (2988ds/3773Mi)
% 8.70/1.90 % (848801)Instruction limit reached!
% 8.70/1.90 % (848801)------------------------------
% 8.70/1.90 % (848801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848801)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848801)Termination reason: Instruction limit
% 8.70/1.90 % (848801)Termination phase: Saturation
% 8.70/1.90 % (848801)Time elapsed: 0.716 s
% 8.70/1.90 % (848801)Peak memory usage: 20 MB
% 8.70/1.90 % (848801)Instructions burned: 1474 (million)
% 8.70/1.90 % (848817)ott+11_1_sil=16000:gs=on:random_seed=3711436132:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 8.70/1.90 % (848817)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.70/1.90 % (848799) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-848754-848799"...
% 8.70/1.90 % (848799)...printing done.
% 8.70/1.90 % (848799)Refutation found. Thanks to Tanya!
% 8.70/1.90 % SZS status Theorem for theBenchmark
% 8.70/1.90 % SZS output start Proof for theBenchmark
% 8.70/1.90 thf(type_def_5, type, late_residual: $tType).
% 8.70/1.90 thf(type_def_6, type, late_subject: $tType).
% 8.70/1.90 thf(type_def_7, type, late_freeRes: $tType).
% 8.70/1.90 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 8.70/1.90 thf(type_def_9, type, noption: $tType > $tType).
% 8.70/1.90 thf(type_def_10, type, name: $tType).
% 8.70/1.90 thf(type_def_11, type, pi: $tType).
% 8.70/1.90 thf(type_def_12, type, set: $tType > $tType).
% 8.70/1.90 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 8.70/1.90 thf(func_def_0, type, fs_name: !>[X0: $tType]:($o)).
% 8.70/1.90 thf(func_def_1, type, bang: (pi > pi)).
% 8.70/1.90 thf(func_def_2, type, input: (name > name > pi > pi)).
% 8.70/1.90 thf(func_def_3, type, match: (name > name > pi > pi)).
% 8.70/1.90 thf(func_def_4, type, mismatch: (name > name > pi > pi)).
% 8.70/1.90 thf(func_def_5, type, output: (name > name > pi > pi)).
% 8.70/1.90 thf(func_def_6, type, par: (pi > pi > pi)).
% 8.70/1.90 thf(func_def_7, type, piNil: pi).
% 8.70/1.90 thf(func_def_8, type, res: (name > pi > pi)).
% 8.70/1.90 thf(func_def_9, type, sum: (pi > pi > pi)).
% 8.70/1.90 thf(func_def_10, type, tau: (pi > pi)).
% 8.70/1.90 thf(func_def_11, type, subs: (pi > name > name > pi)).
% 8.70/1.90 thf(func_def_12, type, subst_name: (name > name > name > name)).
% 8.70/1.90 thf(func_def_13, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 8.70/1.90 thf(func_def_14, type, late_OutputR: (name > name > late_freeRes)).
% 8.70/1.90 thf(func_def_15, type, late_TauR: late_freeRes).
% 8.70/1.90 thf(func_def_16, type, late_freeRes_rec: !>[X0: $tType]:(((name > name > X0) > X0 > late_freeRes > X0))).
% 8.70/1.90 thf(func_def_17, type, late_BoundR: (late_subject > name > pi > late_residual)).
% 8.70/1.90 thf(func_def_18, type, late_FreeR: (late_freeRes > pi > late_residual)).
% 8.70/1.90 thf(func_def_19, type, late_BoundOutputS: (name > late_subject)).
% 8.70/1.90 thf(func_def_20, type, late_InputS: (name > late_subject)).
% 8.70/1.90 thf(func_def_21, type, late_subject_rec: !>[X0: $tType]:(((name > X0) > (name > X0) > late_subject > X0))).
% 8.70/1.90 thf(func_def_22, type, late_transitions: (pi > late_residual > $o)).
% 8.70/1.90 thf(func_def_23, type, abs_fun: !>[X0: $tType, X1: $tType]:((X0 > X1 > X0 > noption @ X1))).
% 8.70/1.90 thf(func_def_24, type, fresh: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o))).
% 8.70/1.90 thf(func_def_25, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 8.70/1.90 thf(func_def_26, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 8.70/1.90 thf(func_def_27, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 8.70/1.90 thf(func_def_28, type, eqvt: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 8.70/1.90 thf(func_def_29, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 8.70/1.90 thf(func_def_30, type, strong2129052853vative: (pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o)).
% 8.70/1.90 thf(func_def_31, type, strong743114133lation: (pi > set @ product_prod @ pi @ pi > pi > $o)).
% 8.70/1.90 thf(func_def_32, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 8.70/1.90 thf(func_def_33, type, p: pi).
% 8.70/1.90 thf(func_def_34, type, pqr: pi).
% 8.70/1.90 thf(func_def_35, type, p2: pi).
% 8.70/1.90 thf(func_def_36, type, q: pi).
% 8.70/1.90 thf(func_def_37, type, qr: pi).
% 8.70/1.90 thf(func_def_38, type, q2: pi).
% 8.70/1.90 thf(func_def_39, type, r: pi).
% 8.70/1.90 thf(func_def_40, type, rel: set @ product_prod @ pi @ pi).
% 8.70/1.90 thf(func_def_41, type, alpha: late_freeRes).
% 8.70/1.90 thf(func_def_42, type, a: name).
% 8.70/1.90 thf(func_def_43, type, x: name).
% 8.70/1.90 thf(func_def_44, type, y: name).
% 8.70/1.90 thf(func_def_48, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 8.70/1.90 thf(func_def_49, type, vAND: ($o > $o > $o)).
% 8.70/1.90 thf(func_def_50, type, db0: !>[X0: $tType]:(X0)).
% 8.70/1.90 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 8.70/1.90 thf(func_def_52, type, db1: !>[X0: $tType]:(X0)).
% 8.70/1.90 thf(func_def_53, type, vNOT: ($o > $o)).
% 8.70/1.90 thf(func_def_54, type, db2: !>[X0: $tType]:(X0)).
% 8.70/1.90 thf(func_def_55, type, vOR: ($o > $o > $o)).
% 8.70/1.90 thf(func_def_56, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.70/1.90 thf(func_def_57, type, vIMP: ($o > $o > $o)).
% 8.70/1.90 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 8.70/1.90 thf(func_def_59, type, db5: !>[X0: $tType]:(X0)).
% 8.70/1.90 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.70/1.90 thf(func_def_61, type, db6: !>[X0: $tType]:(X0)).
% 8.70/1.90 thf(func_def_62, type, db4: !>[X0: $tType]:(X0)).
% 8.70/1.90 thf(func_def_63, type, sP0: (pi > pi > late_subject > name > pi > $o)).
% 8.70/1.90 thf(func_def_64, type, sP1: (name > pi > late_subject > name > pi > $o)).
% 8.70/1.90 thf(func_def_65, type, sP2: (name > pi > late_residual > $o)).
% 8.70/1.90 thf(func_def_66, type, sP3: (name > pi > late_residual > $o)).
% 8.70/1.90 thf(func_def_67, type, sP4: !>[X0: $tType]:((pi > X0 > pi > name > set @ product_prod @ pi @ pi > $o))).
% 8.70/1.90 thf(func_def_68, type, sP5: (pi > pi > name > set @ product_prod @ pi @ pi > $o)).
% 8.70/1.90 thf(func_def_69, type, sP6: !>[X0: $tType]:((pi > X0 > pi > set @ product_prod @ pi @ pi > $o))).
% 8.70/1.90 thf(func_def_70, type, sP7: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_71, type, sP8: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_72, type, sP9: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_73, type, sP10: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_74, type, sP11: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_75, type, sP12: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_76, type, sP13: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_77, type, sP14: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_78, type, sP15: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_79, type, sP16: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_80, type, sP17: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_81, type, sP18: !>[X0: $tType]:(((X0 > pi > $o) > $o))).
% 8.70/1.90 thf(func_def_82, type, sK19: !>[X0: $tType]:((X0 > name))).
% 8.70/1.90 thf(func_def_83, type, sK20: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 8.70/1.90 thf(func_def_84, type, sK21: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 8.70/1.90 thf(func_def_85, type, sK22: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 8.70/1.90 thf(func_def_86, type, sK23: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 8.70/1.90 thf(func_def_87, type, sK24: !>[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))).
% 8.70/1.90 thf(func_def_88, type, sK25: !>[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))).
% 8.70/1.90 thf(func_def_89, type, sK26: !>[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))).
% 8.70/1.90 thf(func_def_90, type, sK27: !>[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))).
% 8.70/1.90 thf(func_def_91, type, sK28: !>[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))).
% 8.70/1.90 thf(func_def_92, type, sK29: !>[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))).
% 8.70/1.90 thf(func_def_93, type, sK30: !>[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))).
% 8.70/1.90 thf(func_def_94, type, sK31: !>[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))).
% 8.70/1.90 thf(func_def_95, type, sK32: !>[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))).
% 8.70/1.90 thf(func_def_96, type, sK33: !>[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))).
% 8.70/1.90 thf(func_def_97, type, sK34: !>[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))).
% 8.70/1.90 thf(func_def_98, type, sK35: !>[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))).
% 8.70/1.90 thf(func_def_99, type, sK36: !>[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))).
% 8.70/1.90 thf(func_def_100, type, sK37: !>[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))).
% 8.70/1.90 thf(func_def_101, type, sK38: !>[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))).
% 8.70/1.90 thf(func_def_102, type, sK39: !>[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))).
% 8.70/1.90 thf(func_def_103, type, sK40: !>[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))).
% 8.70/1.90 thf(func_def_104, type, sK41: !>[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))).
% 8.70/1.90 thf(func_def_105, type, sK42: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 8.70/1.90 thf(func_def_106, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 8.70/1.90 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 8.70/1.90 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 8.70/1.90 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 8.70/1.90 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 8.70/1.90 thf(func_def_111, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 8.70/1.90 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 8.70/1.90 thf(func_def_113, type, sK50: !>[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))).
% 8.70/1.90 thf(func_def_114, type, sK51: !>[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))).
% 8.70/1.90 thf(func_def_115, type, sK52: !>[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))).
% 8.70/1.90 thf(func_def_116, type, sK53: !>[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))).
% 8.70/1.90 thf(func_def_117, type, sK54: !>[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))).
% 8.70/1.90 thf(func_def_118, type, sK55: !>[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))).
% 8.70/1.90 thf(func_def_119, type, sK56: !>[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))).
% 8.70/1.90 thf(func_def_120, type, sK57: !>[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))).
% 8.70/1.90 thf(func_def_121, type, sK58: !>[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))).
% 8.70/1.90 thf(func_def_122, type, sK59: !>[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))).
% 8.70/1.90 thf(func_def_123, type, sK60: !>[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))).
% 8.70/1.90 thf(func_def_124, type, sK61: !>[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))).
% 8.70/1.90 thf(func_def_125, type, sK62: !>[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))).
% 8.70/1.90 thf(func_def_126, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 8.70/1.90 thf(func_def_127, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 8.70/1.90 thf(func_def_128, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 8.70/1.90 thf(func_def_129, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 8.70/1.90 thf(func_def_130, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 8.70/1.90 thf(func_def_131, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 8.70/1.90 thf(func_def_132, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 8.70/1.90 thf(func_def_133, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 8.70/1.90 thf(func_def_134, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 8.70/1.90 thf(func_def_135, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 8.70/1.90 thf(func_def_136, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 8.70/1.90 thf(func_def_137, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 8.70/1.90 thf(func_def_138, type, sK75: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 8.70/1.90 thf(func_def_139, type, sK76: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 8.70/1.90 thf(func_def_140, type, sK77: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 8.70/1.90 thf(func_def_141, type, sK78: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 8.70/1.90 thf(func_def_142, type, sK79: !>[X0: $tType]:(((name > name > X0) > (X0 > $o) > name))).
% 8.70/1.90 thf(func_def_143, type, sK80: !>[X0: $tType]:(((name > name > X0) > (X0 > $o) > name))).
% 8.70/1.90 thf(func_def_144, type, sK81: ((late_subject > $o) > name)).
% 8.70/1.90 thf(func_def_145, type, sK82: ((late_subject > $o) > name)).
% 8.70/1.90 thf(func_def_146, type, sK83: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 8.70/1.90 thf(func_def_147, type, sK84: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 8.70/1.90 thf(func_def_148, type, sK85: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 8.70/1.90 thf(func_def_149, type, sK86: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 8.70/1.90 thf(func_def_150, type, sK87: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 8.70/1.90 thf(func_def_151, type, sK88: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 8.70/1.90 thf(func_def_152, type, sK89: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 8.70/1.90 thf(func_def_153, type, sK90: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 8.70/1.90 thf(func_def_154, type, sK91: ((late_residual > $o) > late_freeRes)).
% 8.70/1.90 thf(func_def_155, type, sK92: ((late_residual > $o) > pi)).
% 8.70/1.90 thf(func_def_156, type, sK93: ((late_residual > $o) > late_subject)).
% 8.70/1.90 thf(func_def_157, type, sK94: ((late_residual > $o) > name)).
% 8.70/1.90 thf(func_def_158, type, sK95: ((late_residual > $o) > pi)).
% 8.70/1.90 thf(func_def_159, type, sK96: (pi > pi > late_subject > name > pi > pi)).
% 8.70/1.90 thf(func_def_160, type, sK97: (pi > pi > late_subject > name > pi > late_subject)).
% 8.70/1.90 thf(func_def_161, type, sK98: (pi > pi > late_subject > name > pi > name)).
% 8.70/1.90 thf(func_def_162, type, sK99: (pi > pi > late_subject > name > pi > pi)).
% 8.70/1.90 thf(func_def_163, type, sK100: (pi > pi > late_subject > name > pi > pi)).
% 8.70/1.90 thf(func_def_164, type, sK101: (pi > name > late_subject > pi > pi > pi)).
% 8.70/1.90 thf(func_def_165, type, sK102: (pi > name > late_subject > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_166, type, sK103: (pi > name > late_subject > pi > pi > name)).
% 8.70/1.90 thf(func_def_167, type, sK104: (pi > name > late_subject > pi > pi > pi)).
% 8.70/1.90 thf(func_def_168, type, sK105: (pi > name > late_subject > pi > pi > pi)).
% 8.70/1.90 thf(func_def_169, type, sK106: !>[X0: $tType]:(((X0 > late_residual > $o) > late_freeRes))).
% 8.70/1.90 thf(func_def_170, type, sK107: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 8.70/1.90 thf(func_def_171, type, sK108: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 8.70/1.90 thf(func_def_172, type, sK109: !>[X0: $tType]:(((X0 > late_residual > $o) > late_subject))).
% 8.70/1.90 thf(func_def_173, type, sK110: !>[X0: $tType]:(((X0 > late_residual > $o) > name))).
% 8.70/1.90 thf(func_def_174, type, sK111: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 8.70/1.90 thf(func_def_175, type, sK112: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 8.70/1.90 thf(func_def_176, type, sK113: !>[X0: $tType]:(((X0 > late_residual > $o) > late_freeRes))).
% 8.70/1.90 thf(func_def_177, type, sK114: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 8.70/1.90 thf(func_def_178, type, sK115: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 8.70/1.90 thf(func_def_179, type, sK116: !>[X0: $tType]:(((X0 > late_residual > $o) > late_subject))).
% 8.70/1.90 thf(func_def_180, type, sK117: !>[X0: $tType]:(((X0 > late_residual > $o) > name))).
% 8.70/1.90 thf(func_def_181, type, sK118: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 8.70/1.90 thf(func_def_182, type, sK119: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 8.70/1.90 thf(func_def_183, type, sK120: ((pi > $o) > late_freeRes > pi > name > pi)).
% 8.70/1.90 thf(func_def_184, type, sK121: (pi > late_freeRes > pi > name > pi)).
% 8.70/1.90 thf(func_def_185, type, sK122: (pi > late_freeRes > pi > name > late_freeRes)).
% 8.70/1.90 thf(func_def_186, type, sK123: (pi > late_freeRes > pi > name > pi)).
% 8.70/1.90 thf(func_def_187, type, sK124: (pi > late_freeRes > pi > name > name)).
% 8.70/1.90 thf(func_def_188, type, sK125: ((pi > $o) > name > late_subject > pi > pi > pi)).
% 8.70/1.90 thf(func_def_189, type, sK126: ((pi > $o) > name > late_subject > pi > pi > pi)).
% 8.70/1.90 thf(func_def_190, type, sK127: (late_subject > name)).
% 8.70/1.90 thf(func_def_191, type, sK128: (late_subject > name)).
% 8.70/1.90 thf(func_def_192, type, sK129: (late_freeRes > name)).
% 8.70/1.90 thf(func_def_193, type, sK130: (late_freeRes > name)).
% 8.70/1.90 thf(func_def_194, type, sK131: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 8.70/1.90 thf(func_def_195, type, sK132: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 8.70/1.90 thf(func_def_196, type, sK133: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 8.70/1.90 thf(func_def_197, type, sK134: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 8.70/1.90 thf(func_def_198, type, sK135: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 8.70/1.90 thf(func_def_199, type, sK136: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 8.70/1.90 thf(func_def_200, type, sK137: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 8.70/1.90 thf(func_def_201, type, sK138: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 8.70/1.90 thf(func_def_202, type, sK139: ((late_freeRes > $o) > name)).
% 8.70/1.90 thf(func_def_203, type, sK140: ((late_freeRes > $o) > name)).
% 8.70/1.90 thf(func_def_204, type, sK141: !>[X0: $tType]:(((name > name > X0) > (X0 > $o) > name))).
% 8.70/1.90 thf(func_def_205, type, sK142: !>[X0: $tType]:(((name > name > X0) > (X0 > $o) > name))).
% 8.70/1.90 thf(func_def_206, type, sK143: (late_residual > pi > name > name > name)).
% 8.70/1.90 thf(func_def_207, type, sK144: (late_residual > pi > name > name > name)).
% 8.70/1.90 thf(func_def_208, type, sK145: (late_residual > pi > name > name > pi)).
% 8.70/1.90 thf(func_def_209, type, sK146: (name > pi > late_subject > name > pi > pi)).
% 8.70/1.90 thf(func_def_210, type, sK147: (name > pi > late_subject > name > pi > late_subject)).
% 8.70/1.90 thf(func_def_211, type, sK148: (name > pi > late_subject > name > pi > name)).
% 8.70/1.90 thf(func_def_212, type, sK149: (name > pi > late_subject > name > pi > pi)).
% 8.70/1.90 thf(func_def_213, type, sK150: (name > pi > late_subject > name > pi > name)).
% 8.70/1.90 thf(func_def_214, type, sK151: (pi > name > late_subject > pi > name > pi)).
% 8.70/1.90 thf(func_def_215, type, sK152: (pi > name > late_subject > pi > name > name)).
% 8.70/1.90 thf(func_def_216, type, sK153: (pi > name > late_subject > pi > name > name)).
% 8.70/1.90 thf(func_def_217, type, sK154: (pi > name > late_subject > pi > name > pi)).
% 8.70/1.90 thf(func_def_218, type, sK155: (name > pi > late_residual > pi)).
% 8.70/1.90 thf(func_def_219, type, sK156: (name > pi > late_residual > name)).
% 8.70/1.90 thf(func_def_220, type, sK157: (name > pi > late_residual > name)).
% 8.70/1.90 thf(func_def_221, type, sK158: (name > pi > late_residual > pi)).
% 8.70/1.90 thf(func_def_222, type, sK159: (name > pi > late_residual > pi)).
% 8.70/1.90 thf(func_def_223, type, sK160: (name > pi > late_residual > late_subject)).
% 8.70/1.90 thf(func_def_224, type, sK161: (name > pi > late_residual > name)).
% 8.70/1.90 thf(func_def_225, type, sK162: (name > pi > late_residual > pi)).
% 8.70/1.90 thf(func_def_226, type, sK163: (name > pi > late_residual > name)).
% 8.70/1.90 thf(func_def_227, type, sK164: (late_residual > pi > name > pi)).
% 8.70/1.90 thf(func_def_228, type, sK165: (late_residual > pi > name > late_freeRes)).
% 8.70/1.90 thf(func_def_229, type, sK166: (late_residual > pi > name > pi)).
% 8.70/1.90 thf(func_def_230, type, sK167: (late_residual > pi > name > name)).
% 8.70/1.90 thf(func_def_231, type, sK168: !>[X0: $tType]:(((name > X0) > (X0 > $o) > name))).
% 8.70/1.90 thf(func_def_232, type, sK169: !>[X0: $tType]:(((name > X0) > (X0 > $o) > name))).
% 8.70/1.90 thf(func_def_233, type, sK170: !>[X0: $tType]:(((name > X0) > (X0 > $o) > name))).
% 8.70/1.90 thf(func_def_234, type, sK171: !>[X0: $tType]:(((name > X0) > (X0 > $o) > name))).
% 8.70/1.90 thf(func_def_235, type, sK172: (late_residual > pi > pi)).
% 8.70/1.90 thf(func_def_236, type, sK173: (late_residual > pi > name > name > name)).
% 8.70/1.90 thf(func_def_237, type, sK174: (late_residual > pi > name > name > name)).
% 8.70/1.90 thf(func_def_238, type, sK175: (late_residual > pi > name > name > pi)).
% 8.70/1.90 thf(func_def_239, type, sK176: (pi > pi > name > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_240, type, sK177: (pi > pi > name > set @ product_prod @ pi @ pi > name)).
% 8.70/1.90 thf(func_def_241, type, sK178: !>[X0: $tType]:((pi > X0 > pi > name > set @ product_prod @ pi @ pi > pi))).
% 8.70/1.90 thf(func_def_242, type, sK179: !>[X0: $tType]:((pi > X0 > pi > name > set @ product_prod @ pi @ pi > late_subject))).
% 8.70/1.90 thf(func_def_243, type, sK180: !>[X0: $tType]:((pi > X0 > pi > name > set @ product_prod @ pi @ pi > name))).
% 8.70/1.90 thf(func_def_244, type, sK181: (pi > name > pi > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_245, type, sK182: (pi > name > pi > set @ product_prod @ pi @ pi > late_freeRes)).
% 8.70/1.90 thf(func_def_246, type, sK183: (set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_247, type, sK184: (set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_248, type, sK185: (set @ product_prod @ pi @ pi > name)).
% 8.70/1.90 thf(func_def_249, type, sK186: (set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_250, type, sK187: (set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_251, type, sK188: (pi > name > late_subject > set @ product_prod @ pi @ pi > pi > pi)).
% 8.70/1.90 thf(func_def_252, type, sK189: (pi > late_freeRes > set @ product_prod @ pi @ pi > pi > pi)).
% 8.70/1.90 thf(func_def_253, type, sK190: !>[X0: $tType]:((pi > X0 > pi > set @ product_prod @ pi @ pi > late_subject))).
% 8.70/1.90 thf(func_def_254, type, sK191: !>[X0: $tType]:((pi > X0 > pi > set @ product_prod @ pi @ pi > name))).
% 8.70/1.90 thf(func_def_255, type, sK192: !>[X0: $tType]:((pi > X0 > pi > set @ product_prod @ pi @ pi > pi))).
% 8.70/1.90 thf(func_def_256, type, sK193: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes)).
% 8.70/1.90 thf(func_def_257, type, sK194: (pi > pi > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_258, type, sK195: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 8.70/1.90 thf(func_def_259, type, sK196: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_260, type, sK197: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_261, type, sK198: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 8.70/1.90 thf(func_def_262, type, sK199: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_263, type, sK200: (set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_264, type, sK201: (set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_265, type, sK202: (late_residual > pi > name > name > pi)).
% 8.70/1.90 thf(func_def_266, type, sK203: (late_residual > pi > name > name > pi)).
% 8.70/1.90 thf(func_def_267, type, sK204: (late_residual > pi > name > name > name)).
% 8.70/1.90 thf(func_def_268, type, sK205: (late_residual > pi > name > name > name)).
% 8.70/1.90 thf(func_def_269, type, sK206: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_270, type, sK207: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_271, type, sK208: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_272, type, sK209: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_273, type, sK210: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_274, type, sK211: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_275, type, sK212: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_276, type, sK213: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_277, type, sK214: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_278, type, sK215: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_279, type, sK216: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_280, type, sK217: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_281, type, sK218: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_282, type, sK219: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_283, type, sK220: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_284, type, sK221: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_285, type, sK222: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_286, type, sK223: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_287, type, sK224: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_288, type, sK225: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_289, type, sK226: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_290, type, sK227: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_291, type, sK228: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_292, type, sK229: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_293, type, sK230: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_294, type, sK231: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_295, type, sK232: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_296, type, sK233: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_297, type, sK234: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_298, type, sK235: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_299, type, sK236: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_300, type, sK237: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_301, type, sK238: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_302, type, sK239: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_303, type, sK240: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_304, type, sK241: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_305, type, sK242: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_306, type, sK243: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_307, type, sK244: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_308, type, sK245: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_309, type, sK246: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_310, type, sK247: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_311, type, sK248: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_312, type, sK249: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_313, type, sK250: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_314, type, sK251: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_315, type, sK252: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_316, type, sK253: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_317, type, sK254: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_318, type, sK255: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_319, type, sK256: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_320, type, sK257: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_321, type, sK258: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_322, type, sK259: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_323, type, sK260: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_324, type, sK261: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_325, type, sK262: !>[X0: $tType]:(((X0 > pi > $o) > name))).
% 8.70/1.90 thf(func_def_326, type, sK263: !>[X0: $tType]:(((X0 > pi > $o) > pi))).
% 8.70/1.90 thf(func_def_327, type, sK264: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_328, type, sK265: !>[X0: $tType]:(((X0 > pi > $o) > X0))).
% 8.70/1.90 thf(func_def_329, type, sK266: (pi > set @ product_prod @ pi @ pi > late_subject > name > pi)).
% 8.70/1.90 thf(func_def_330, type, sK267: (pi > set @ product_prod @ pi @ pi > late_freeRes > pi)).
% 8.70/1.90 thf(func_def_331, type, sK268: (pi > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_332, type, sK269: (pi > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_333, type, sK270: (pi > set @ product_prod @ pi @ pi > late_freeRes)).
% 8.70/1.90 thf(func_def_334, type, sK271: (pi > set @ product_prod @ pi @ pi > name)).
% 8.70/1.90 thf(func_def_335, type, sK272: (pi > set @ product_prod @ pi @ pi > late_subject)).
% 8.70/1.90 thf(func_def_336, type, sK273: (pi > set @ product_prod @ pi @ pi > late_subject)).
% 8.70/1.90 thf(func_def_337, type, sK274: (pi > name > set @ product_prod @ pi @ pi > name > pi)).
% 8.70/1.90 thf(func_def_338, type, sK275: (pi > name > set @ product_prod @ pi @ pi > name > pi)).
% 8.70/1.90 thf(func_def_339, type, sK276: (name > name > pi > set @ product_prod @ pi @ pi > late_freeRes)).
% 8.70/1.90 thf(func_def_340, type, sK277: (name > pi > set @ product_prod @ pi @ pi > name > name)).
% 8.70/1.90 thf(func_def_341, type, sK278: (name > pi > set @ product_prod @ pi @ pi > name > late_subject)).
% 8.70/1.90 thf(func_def_342, type, sK279: (name > pi > set @ product_prod @ pi @ pi > name > late_subject)).
% 8.70/1.90 thf(func_def_343, type, sK280: (name > pi > set @ product_prod @ pi @ pi > name > pi)).
% 8.70/1.90 thf(func_def_344, type, sK281: (name > pi > set @ product_prod @ pi @ pi > name > pi)).
% 8.70/1.90 thf(func_def_345, type, sK282: (name > pi > set @ product_prod @ pi @ pi > name > late_freeRes)).
% 8.70/1.90 thf(func_def_346, type, sK283: (name > pi > set @ product_prod @ pi @ pi > name > name)).
% 8.70/1.90 thf(func_def_347, type, sK284: (name > pi > set @ product_prod @ pi @ pi > name > late_subject)).
% 8.70/1.90 thf(func_def_348, type, sK285: (name > pi > set @ product_prod @ pi @ pi > name > late_subject)).
% 8.70/1.90 thf(func_def_349, type, sK286: (set @ product_prod @ pi @ pi > pi > name > pi > late_subject > pi)).
% 8.70/1.90 thf(func_def_350, type, sK287: (set @ product_prod @ pi @ pi > pi > late_freeRes > pi > pi)).
% 8.70/1.90 thf(func_def_351, type, sK288: (set @ product_prod @ pi @ pi > late_subject > pi > name > pi)).
% 8.70/1.90 thf(func_def_352, type, sK289: (set @ product_prod @ pi @ pi > late_freeRes > pi > pi)).
% 8.70/1.90 thf(func_def_353, type, sK290: (pi > name > set @ product_prod @ pi @ pi > late_subject > pi > pi)).
% 8.70/1.90 thf(func_def_354, type, sK291: (pi > late_freeRes > set @ product_prod @ pi @ pi > pi > pi)).
% 8.70/1.90 thf(func_def_355, type, sK292: (pi > name > set @ product_prod @ pi @ pi > late_subject > pi > pi)).
% 8.70/1.90 thf(func_def_356, type, sK293: (pi > late_freeRes > set @ product_prod @ pi @ pi > pi > pi)).
% 8.70/1.90 thf(func_def_357, type, sK294: (pi > late_subject > name > pi > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_358, type, sK295: (pi > pi > late_freeRes > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_359, type, sK296: (pi > late_subject > name > pi > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_360, type, sK297: (pi > pi > late_freeRes > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_361, type, sK298: (pi > late_subject > name > pi > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_362, type, sK299: (pi > pi > late_freeRes > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_363, type, sK300: (pi > pi > late_subject > name > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_364, type, sK301: (pi > pi > late_freeRes > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_365, type, sK302: (pi > pi > late_subject > name > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_366, type, sK303: (pi > pi > late_freeRes > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_367, type, sK304: (pi > late_subject > name > pi > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_368, type, sK305: (pi > pi > late_freeRes > set @ product_prod @ pi @ pi > pi)).
% 8.70/1.90 thf(func_def_369, type, sK306: (set @ product_prod @ pi @ pi > pi > late_subject > name > pi > pi)).
% 8.70/1.90 thf(func_def_370, type, sK307: (set @ product_prod @ pi @ pi > pi > late_freeRes > pi > pi)).
% 8.70/1.90 thf(func_def_371, type, sK308: (set @ product_prod @ pi @ pi > pi > pi > late_subject > name > pi)).
% 8.70/1.90 thf(func_def_372, type, sK309: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes > pi)).
% 8.70/1.90 thf(func_def_373, type, sK310: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_374, type, sK311: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_375, type, sK312: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 8.70/1.90 thf(func_def_376, type, sK313: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 8.70/1.90 thf(func_def_377, type, sK314: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_378, type, sK315: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_379, type, sK316: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_380, type, sK317: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_381, type, sK318: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 8.70/1.90 thf(func_def_382, type, sK319: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 8.70/1.90 thf(func_def_383, type, sK320: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_384, type, sK321: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_385, type, sK322: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_386, type, sK323: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_387, type, sK324: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 8.70/1.90 thf(func_def_388, type, sK325: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 8.70/1.90 thf(func_def_389, type, sK326: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_390, type, sK327: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_391, type, sK328: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_392, type, sK329: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 8.70/1.90 thf(func_def_393, type, sK330: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 8.70/1.90 thf(func_def_394, type, sK331: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 8.70/1.90 thf(func_def_395, type, sK332: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_396, type, sK333: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 8.70/1.90 thf(func_def_397, type, sK334: (pi > late_subject > set @ product_prod @ pi @ pi > name > pi > pi > pi)).
% 8.70/1.90 thf(func_def_398, type, sK335: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes > pi > pi)).
% 8.70/1.90 thf(func_def_399, type, sK336: (pi > late_subject > set @ product_prod @ pi @ pi > name > pi > pi > pi)).
% 8.70/1.90 thf(func_def_400, type, sK337: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes > pi > pi)).
% 8.70/1.90 thf(func_def_401, type, sK338: (set @ product_prod @ pi @ pi > late_subject > pi > name > pi > pi)).
% 8.70/1.90 thf(func_def_402, type, sK339: (set @ product_prod @ pi @ pi > pi > late_freeRes > pi > pi)).
% 8.70/1.90 thf(func_def_403, type, sK340: (set @ product_prod @ pi @ pi > late_subject > pi > name > pi > pi)).
% 8.70/1.90 thf(func_def_404, type, sK341: (set @ product_prod @ pi @ pi > pi > late_freeRes > pi > pi)).
% 8.70/1.90 thf(func_def_405, type, sK342: (set @ product_prod @ pi @ pi > name > late_subject > pi > pi > pi)).
% 8.70/1.90 thf(func_def_406, type, sK343: (set @ product_prod @ pi @ pi > late_freeRes > pi > pi > pi)).
% 8.70/1.90 thf(f7,axiom,(
% 8.70/1.90 (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)),
% 8.70/1.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062)).
% 8.70/1.90 thf(f8,axiom,(
% 8.70/1.90 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))),
% 8.70/1.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062)).
% 8.70/1.90 thf(f267,conjecture,(
% 8.70/1.90 ? [X0 : pi] : ((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)))),
% 8.70/1.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 8.70/1.90 thf(f268,negated_conjecture,(
% 8.70/1.90 ~ ? [X0 : pi] : ((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)))),
% 8.70/1.90 inference(negated_conjecture,[status(cth)],[f267])).
% 8.70/1.90 thf(f273,plain,(
% 8.70/1.90 (member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)),
% 8.70/1.90 inference(rectify,[],[f7])).
% 8.70/1.90 thf(f274,plain,(
% 8.70/1.90 (((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)) = $true)),
% 8.70/1.90 inference(fool_elimination,[],[f273])).
% 8.70/1.90 thf(f275,plain,(
% 8.70/1.90 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))),
% 8.70/1.90 inference(rectify,[],[f8])).
% 8.70/1.90 thf(f276,plain,(
% 8.70/1.90 (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))) = $true)),
% 8.70/1.90 inference(fool_elimination,[],[f275])).
% 8.70/1.90 thf(f620,plain,(
% 8.70/1.90 ~ ? [X0 : pi] : ((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)))),
% 8.70/1.90 inference(rectify,[],[f268])).
% 8.70/1.90 thf(f621,plain,(
% 8.70/1.90 ~ ? [X0 : pi] : ((((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)) = $true) & (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0))) = $true))),
% 8.70/1.90 inference(fool_elimination,[],[f620])).
% 8.70/1.90 thf(f825,plain,(
% 8.70/1.90 ! [X0 : pi] : ((((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)) != $true) | (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0))) != $true))),
% 8.70/1.90 inference(ennf_transformation,[],[f621])).
% 8.70/1.90 thf(f987,plain,(
% 8.70/1.90 (((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)) = $true)),
% 8.70/1.90 inference(cnf_transformation,[],[f274])).
% 8.70/1.90 thf(f988,plain,(
% 8.70/1.90 (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))) = $true)),
% 8.70/1.90 inference(cnf_transformation,[],[f276])).
% 8.70/1.90 thf(f1391,plain,(
% 8.70/1.90 ( ! [X0 : pi] : ((((member @ product_prod @ pi @ pi @ (product_Pair @ pi @ pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)) != $true) | (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0))) != $true)) )),
% 8.70/1.90 inference(cnf_transformation,[],[f825])).
% 8.70/1.90 thf(f29352,plain,(
% 8.70/1.90 ($true != $true) | (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))) != $true)),
% 8.70/1.90 inference(constrained_superposition,[],[f1391,f987])).
% 8.70/1.90 thf(f29365,plain,(
% 8.70/1.90 (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))) != $true)),
% 8.70/1.90 inference(trivial_inequality_removal,[],[f29352])).
% 8.70/1.90 thf(f29400,plain,(
% 8.70/1.90 $false),
% 8.70/1.90 inference(forward_subsumption_resolution,[],[f29365,f988])).
% 8.70/1.90 % SZS output end Proof for theBenchmark
% 8.70/1.90 % (848799)------------------------------
% 8.70/1.90 % (848799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.70/1.90 % (848799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/1.90 % (848799)CaDiCaL version: 2.1.3
% 8.70/1.90 % (848799)Termination reason: Refutation
% 8.70/1.90 % (848799)Time elapsed: 1.114 s
% 8.70/1.90 % (848799)Peak memory usage: 30 MB
% 8.70/1.90 % (848799)Instructions burned: 2426 (million)
% 8.70/1.90 % (848754)Success in time 1.656 s
% 8.70/1.90 % Vampire exiting
%------------------------------------------------------------------------------