%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP036^2 : 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 : n001.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 08:10:27 AM UTC 2026
% Result : Theorem 6.14s 1.18s
% Output : Refutation 6.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP036^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 19:45:36 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 4.21/1.00 % (1723374)Will run a generic schedule for satisfiability detection.
% 4.21/1.00 % (1723382)dis+10_1_sil=32000:sp=arity:random_seed=3916013590:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.21/1.00 % (1723380)% WARNING: option uhcvi not known.
% 4.21/1.00 % (1723380)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1989721921:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.21/1.00 % (1723379)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2304128806_2999 on theBenchmark for (2999ds/0Mi)
% 4.21/1.00 % (1723381)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=757765696:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.21/1.00 % (1723383)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=355377963:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.21/1.00 % (1723384)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1729791211:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.21/1.00 % (1723385)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=913329480:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.21/1.00 % (1723382)Instruction limit reached!
% 4.21/1.00 % (1723382)------------------------------
% 4.21/1.00 % (1723382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.21/1.00 % (1723382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.00 % (1723382)CaDiCaL version: 2.1.3
% 4.21/1.00 % (1723382)Termination reason: Instruction limit
% 4.21/1.00 % (1723382)Termination phase: Property scanning
% 4.21/1.00 % (1723382)Time elapsed: 0.024 s
% 4.21/1.00 % (1723382)Peak memory usage: 12 MB
% 4.21/1.00 % (1723382)Instructions burned: 107 (million)
% 4.21/1.00 % (1723380)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.21/1.00 % (1723383)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.21/1.00 % (1723393)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1311489144:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.21/1.00 % Exception at run slice level% (1723380)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.21/1.00
% 4.21/1.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.21/1.00 % (1723383)Instruction limit reached!
% 4.21/1.00 % (1723383)------------------------------
% 4.21/1.00 % (1723383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.21/1.00 % (1723383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.00 % (1723383)CaDiCaL version: 2.1.3
% 4.21/1.00 % (1723383)Termination reason: Instruction limit
% 4.21/1.00 % (1723383)Termination phase: Saturation
% 4.21/1.00 % (1723383)Time elapsed: 0.051 s
% 4.21/1.00 % (1723383)Peak memory usage: 13 MB
% 4.21/1.00 % (1723383)Instructions burned: 117 (million)
% 4.21/1.00 % Exception at run slice level
% 4.21/1.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.21/1.00 % (1723384)Instruction limit reached!
% 4.21/1.00 % (1723384)------------------------------
% 4.21/1.00 % (1723384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.21/1.00 % (1723384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.00 % (1723384)CaDiCaL version: 2.1.3
% 4.21/1.00 % (1723384)Termination reason: Instruction limit
% 4.21/1.00 % (1723384)Termination phase: Saturation
% 4.21/1.00 % (1723384)Time elapsed: 0.057 s
% 4.21/1.00 % (1723384)Peak memory usage: 13 MB
% 4.21/1.00 % (1723384)Instructions burned: 134 (million)
% 4.21/1.00 % (1723397)ott-21_1_sil=16000:fs=off:random_seed=3626008688:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.21/1.00 % (1723395)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2162773461:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.21/1.00 % (1723396)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=3532677303:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 4.21/1.00 % (1723385)Instruction limit reached!
% 4.21/1.00 % (1723385)------------------------------
% 4.21/1.00 % (1723385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.21/1.00 % (1723385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723385)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723385)Termination reason: Instruction limit
% 6.14/1.18 % (1723385)Termination phase: Saturation
% 6.14/1.18 % (1723385)Time elapsed: 0.077 s
% 6.14/1.18 % (1723385)Peak memory usage: 14 MB
% 6.14/1.18 % (1723385)Instructions burned: 159 (million)
% 6.14/1.18 % (1723398)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3223281843:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.14/1.18 % (1723403)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1781578134:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.14/1.18 % (1723396)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.14/1.18 % (1723397)Instruction limit reached!
% 6.14/1.18 % (1723397)------------------------------
% 6.14/1.18 % (1723397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.14/1.18 % (1723397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723397)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723397)Termination reason: Instruction limit
% 6.14/1.18 % (1723397)Termination phase: Saturation
% 6.14/1.18 % (1723397)Time elapsed: 0.042 s
% 6.14/1.18 % (1723397)Peak memory usage: 13 MB
% 6.14/1.18 % (1723397)Instructions burned: 181 (million)
% 6.14/1.18 % (1723405)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2635734173:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.14/1.18 % (1723396)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.14/1.18 % (1723395)Instruction limit reached!
% 6.14/1.18 % (1723395)------------------------------
% 6.14/1.18 % (1723395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.14/1.18 % (1723395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723395)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723395)Termination reason: Instruction limit
% 6.14/1.18 % (1723395)Termination phase: Saturation
% 6.14/1.18 % (1723395)Time elapsed: 0.058 s
% 6.14/1.18 % (1723395)Peak memory usage: 13 MB
% 6.14/1.18 % (1723395)Instructions burned: 131 (million)
% 6.14/1.18 % Exception at run slice level
% 6.14/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.14/1.18 % (1723407)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2729192020:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.14/1.18 % (1723409)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=3725996105:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 6.14/1.18 % (1723409)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.14/1.18 % Exception at run slice level
% 6.14/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.14/1.18 % (1723411)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3911638460:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 6.14/1.18 % (1723411)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.14/1.18 % (1723398)Instruction limit reached!
% 6.14/1.18 % (1723398)------------------------------
% 6.14/1.18 % (1723398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.14/1.18 % (1723398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723398)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723398)Termination reason: Instruction limit
% 6.14/1.18 % (1723398)Termination phase: Saturation
% 6.14/1.18 % (1723398)Time elapsed: 0.257 s
% 6.14/1.18 % (1723398)Peak memory usage: 14 MB
% 6.14/1.18 % (1723398)Instructions burned: 479 (million)
% 6.14/1.18 % (1723413)fmb+10_1_sil=64000:random_seed=273759879:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 6.14/1.18 % (1723413)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.14/1.18 % Exception at run slice level
% 6.14/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.14/1.18 % (1723396)Instruction limit reached!
% 6.14/1.18 % (1723396)------------------------------
% 6.14/1.18 % (1723396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.14/1.18 % (1723396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723396)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723396)Termination reason: Instruction limit
% 6.14/1.18 % (1723396)Termination phase: Saturation
% 6.14/1.18 % (1723396)Time elapsed: 0.351 s
% 6.14/1.18 % (1723396)Peak memory usage: 19 MB
% 6.14/1.18 % (1723396)Instructions burned: 685 (million)
% 6.14/1.18 % (1723415)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2609489451:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 6.14/1.18 % (1723405)Instruction limit reached!
% 6.14/1.18 % (1723405)------------------------------
% 6.14/1.18 % (1723405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.14/1.18 % (1723405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723405)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723405)Termination reason: Instruction limit
% 6.14/1.18 % (1723405)Termination phase: Saturation
% 6.14/1.18 % (1723405)Time elapsed: 0.313 s
% 6.14/1.18 % (1723405)Peak memory usage: 22 MB
% 6.14/1.18 % (1723405)Instructions burned: 1180 (million)
% 6.14/1.18 % (1723418)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4272236608:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 6.14/1.18 % (1723417)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2195996410:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 6.14/1.18 % (1723418)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.14/1.18 % Exception at run slice level
% 6.14/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.14/1.18 % Exception at run slice level
% 6.14/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.14/1.18 % (1723421)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2887245483:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 6.14/1.18 % (1723409)Instruction limit reached!
% 6.14/1.18 % (1723409)------------------------------
% 6.14/1.18 % (1723409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.14/1.18 % (1723409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723409)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723409)Termination reason: Instruction limit
% 6.14/1.18 % (1723409)Termination phase: Saturation
% 6.14/1.18 % (1723409)Time elapsed: 0.339 s
% 6.14/1.18 % (1723409)Peak memory usage: 18 MB
% 6.14/1.18 % (1723409)Instructions burned: 692 (million)
% 6.14/1.18 % (1723423)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=109528230:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 6.14/1.18 % (1723424)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4231440216:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 6.14/1.18 % (1723421)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.14/1.18 % (1723421)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.14/1.18 % Exception at run slice level
% 6.14/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.14/1.18 % Exception at run slice level
% 6.14/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.14/1.18 % (1723427)ott-2_1_sil=16000:newcnf=on:random_seed=4051227856:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 6.14/1.18 % (1723428)ott+10_1_sil=32000:tgt=ground:random_seed=3004757110:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.14/1.18 % (1723427)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.14/1.18 % (1723411)Instruction limit reached!
% 6.14/1.18 % (1723411)------------------------------
% 6.14/1.18 % (1723411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.14/1.18 % (1723411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723411)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723411)Termination reason: Instruction limit
% 6.14/1.18 % (1723411)Termination phase: Saturation
% 6.14/1.18 % (1723411)Time elapsed: 0.424 s
% 6.14/1.18 % (1723411)Peak memory usage: 19 MB
% 6.14/1.18 % (1723411)Instructions burned: 879 (million)
% 6.14/1.18 % (1723431)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1799067616:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 6.14/1.18 % Exception at run slice level
% 6.14/1.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.14/1.18 % (1723433)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2215841544:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 6.14/1.18 % (1723433)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.14/1.18 % (1723418) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1723374-1723418"...
% 6.14/1.18 % (1723418)...printing done.
% 6.14/1.18 % (1723418)Refutation found. Thanks to Tanya!
% 6.14/1.18 % SZS status Theorem for theBenchmark
% 6.14/1.18 % SZS output start Proof for theBenchmark
% 6.14/1.18 thf(type_def_5, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 6.14/1.18 thf(type_def_6, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 6.14/1.18 thf(type_def_7, type, product_unit: $tType).
% 6.14/1.18 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 6.14/1.18 thf(type_def_9, type, formula: ($tType * $tType * $tType) > $tType).
% 6.14/1.18 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 6.14/1.18 thf(type_def_11, type, trm: ($tType * $tType) > $tType).
% 6.14/1.18 thf(type_def_12, type, hp: ($tType * $tType * $tType) > $tType).
% 6.14/1.18 thf(type_def_13, type, real: $tType).
% 6.14/1.18 thf(type_def_14, type, list: $tType > $tType).
% 6.14/1.18 thf(type_def_15, type, set: $tType > $tType).
% 6.14/1.18 thf(type_def_16, type, c: $tType).
% 6.14/1.18 thf(type_def_17, type, b: $tType).
% 6.14/1.18 thf(type_def_18, type, a: $tType).
% 6.14/1.18 thf(type_def_19, type, sTfun: ($tType * $tType) > $tType).
% 6.14/1.18 thf(func_def_0, type, cARD_1: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_1, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_3, type, sup: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_4, type, ord: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_6, type, lattice: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_7, type, finite_finite: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_8, type, linorder: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_9, type, preorder: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_10, type, semilattice_sup: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_11, type, euclid1678468529ng_gcd: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_12, type, euclid1155270486miring: !>[X0: $tType]:($o)).
% 6.14/1.18 thf(func_def_13, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 6.14/1.18 thf(func_def_14, type, coinci32832645ide_hp: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 6.14/1.18 thf(func_def_15, type, coinci554967470ide_hp: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > $o))).
% 6.14/1.18 thf(func_def_16, type, coinci1495174342_equiv: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 6.14/1.18 thf(func_def_17, type, denotational_Iagree: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2 > $o))).
% 6.14/1.18 thf(func_def_18, type, denotational_Vagree: !>[X0: $tType]:((product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > set @ sum_sum @ X0 @ X0 > $o))).
% 6.14/1.18 thf(func_def_19, type, denota1661140910og_sem: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > hp @ X0 @ X1 @ X2 > set @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 @ product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 6.14/1.18 thf(func_def_20, type, ids: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > X0 > X1 > X1 > X1 > X2 > X2 > X2 > X2 > $o))).
% 6.14/1.18 thf(func_def_21, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 6.14/1.18 thf(func_def_22, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.14/1.18 thf(func_def_23, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_24, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 6.14/1.18 thf(func_def_25, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 6.14/1.18 thf(func_def_26, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 6.14/1.18 thf(func_def_27, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 6.14/1.18 thf(func_def_28, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 6.14/1.18 thf(func_def_29, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 6.14/1.18 thf(func_def_30, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 6.14/1.18 thf(func_def_31, type, static_FVP: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > set @ sum_sum @ X2 @ X2))).
% 6.14/1.18 thf(func_def_32, type, static_MBV: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > set @ sum_sum @ X2 @ X2))).
% 6.14/1.18 thf(func_def_33, type, static_SIGP: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2))).
% 6.14/1.18 thf(func_def_34, type, choice: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > hp @ X0 @ X1 @ X2 > hp @ X0 @ X1 @ X2))).
% 6.14/1.18 thf(func_def_35, type, hpsafe: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > $o))).
% 6.14/1.18 thf(func_def_36, type, same_fst: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 6.14/1.18 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 6.14/1.18 thf(func_def_38, type, i: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 6.14/1.18 thf(func_def_39, type, j: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 6.14/1.18 thf(func_def_40, type, v: set @ sum_sum @ c @ c).
% 6.14/1.18 thf(func_def_41, type, mu: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 6.14/1.18 thf(func_def_42, type, mu2: finite_Cartesian_vec @ real @ c).
% 6.14/1.18 thf(func_def_43, type, mu3: finite_Cartesian_vec @ real @ c).
% 6.14/1.18 thf(func_def_44, type, nu_1: finite_Cartesian_vec @ real @ c).
% 6.14/1.18 thf(func_def_45, type, nu_12: finite_Cartesian_vec @ real @ c).
% 6.14/1.18 thf(func_def_46, type, nu_2: finite_Cartesian_vec @ real @ c).
% 6.14/1.18 thf(func_def_47, type, nu_22: finite_Cartesian_vec @ real @ c).
% 6.14/1.18 thf(func_def_48, type, a2: hp @ a @ b @ c).
% 6.14/1.18 thf(func_def_49, type, b2: hp @ a @ b @ c).
% 6.14/1.18 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.14/1.18 thf(func_def_54, type, vAND: ($o > $o > $o)).
% 6.14/1.18 thf(func_def_55, type, vOR: ($o > $o > $o)).
% 6.14/1.18 thf(func_def_56, type, db2: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_59, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.14/1.18 thf(func_def_60, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.14/1.18 thf(func_def_61, type, vIMP: ($o > $o > $o)).
% 6.14/1.18 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.14/1.18 thf(func_def_63, type, db5: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_64, type, db4: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_65, type, db6: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_66, type, db3: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_67, type, db7: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_68, type, db9: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_69, type, db8: !>[X0: $tType]:(X0)).
% 6.14/1.18 thf(func_def_70, type, vNOT: ($o > $o)).
% 6.14/1.18 thf(func_def_71, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 6.14/1.18 thf(func_def_72, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 6.14/1.18 thf(func_def_73, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 6.14/1.18 thf(func_def_74, type, sK3: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 6.14/1.18 thf(func_def_75, type, sK4: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 6.14/1.18 thf(func_def_76, type, sK5: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_77, type, sK6: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_78, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 6.14/1.18 thf(func_def_79, type, sK8: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 6.14/1.18 thf(func_def_80, type, sK9: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 6.14/1.18 thf(func_def_81, type, sK10: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 6.14/1.18 thf(func_def_82, type, sK11: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 6.14/1.18 thf(func_def_83, type, sK12: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 6.14/1.18 thf(func_def_84, type, sK13: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 6.14/1.18 thf(func_def_85, type, sK14: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 6.14/1.18 thf(func_def_86, type, sK15: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 6.14/1.18 thf(func_def_87, type, sK16: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 6.14/1.18 thf(func_def_88, type, sK17: (set @ sum_sum @ c @ c > product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c > product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c > denota1663640101rp_ext @ a @ b @ c @ product_unit > product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c)).
% 6.14/1.18 thf(func_def_89, type, sK18: (set @ sum_sum @ c @ c > product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c > product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c > denota1663640101rp_ext @ a @ b @ c @ product_unit > product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c)).
% 6.14/1.18 thf(func_def_90, type, sK19: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_91, type, sK20: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_92, type, sK21: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_93, type, sK22: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_94, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 6.14/1.18 thf(func_def_95, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 6.14/1.18 thf(func_def_96, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 6.14/1.18 thf(func_def_97, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 6.14/1.18 thf(func_def_98, type, sK27: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 6.14/1.18 thf(func_def_99, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 6.14/1.18 thf(func_def_100, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 6.14/1.18 thf(func_def_101, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 6.14/1.18 thf(func_def_102, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 6.14/1.18 thf(func_def_103, type, sK32: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 6.14/1.18 thf(func_def_104, type, sK33: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 6.14/1.18 thf(func_def_105, type, sK34: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 6.14/1.18 thf(func_def_106, type, sK35: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_107, type, sK36: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 6.14/1.18 thf(func_def_108, type, sK37: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 6.14/1.18 thf(func_def_109, type, sK38: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 6.14/1.18 thf(func_def_110, type, sK39: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_111, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 6.14/1.18 thf(func_def_112, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 6.14/1.18 thf(func_def_113, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 6.14/1.18 thf(func_def_114, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 6.14/1.18 thf(func_def_115, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 6.14/1.18 thf(func_def_116, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 6.14/1.18 thf(func_def_117, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 6.14/1.18 thf(func_def_118, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 6.14/1.18 thf(func_def_119, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 6.14/1.18 thf(func_def_120, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 6.14/1.18 thf(func_def_121, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 6.14/1.18 thf(func_def_122, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 6.14/1.18 thf(func_def_123, type, sK52: !>[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))).
% 6.14/1.18 thf(func_def_124, type, sK53: !>[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))).
% 6.14/1.18 thf(func_def_125, type, sK54: !>[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))).
% 6.14/1.18 thf(func_def_126, type, sK55: !>[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))).
% 6.14/1.18 thf(func_def_127, type, sK56: !>[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))).
% 6.14/1.18 thf(func_def_128, 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 > X5))).
% 6.14/1.18 thf(func_def_129, type, sK58: !>[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))).
% 6.14/1.18 thf(func_def_130, type, sK59: !>[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))).
% 6.14/1.18 thf(func_def_131, 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 > X2))).
% 6.14/1.18 thf(func_def_132, 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 > X3))).
% 6.14/1.18 thf(func_def_133, 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 > X4))).
% 6.14/1.18 thf(func_def_134, 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 > X5))).
% 6.14/1.18 thf(func_def_135, 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 > X6))).
% 6.14/1.18 thf(func_def_136, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 6.14/1.18 thf(func_def_137, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 6.14/1.18 thf(func_def_138, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_139, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 6.14/1.18 thf(func_def_140, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 6.14/1.18 thf(func_def_141, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 6.14/1.18 thf(func_def_142, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_143, type, sK72: !>[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))).
% 6.14/1.18 thf(func_def_144, type, sK73: !>[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))).
% 6.14/1.18 thf(func_def_145, type, sK74: !>[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))).
% 6.14/1.18 thf(func_def_146, type, sK75: !>[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))).
% 6.14/1.18 thf(func_def_147, type, sK76: !>[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))).
% 6.14/1.18 thf(func_def_148, type, sK77: !>[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))).
% 6.14/1.18 thf(func_def_149, type, sK78: !>[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))).
% 6.14/1.18 thf(func_def_150, type, sK79: !>[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))).
% 6.14/1.18 thf(func_def_151, type, sK80: !>[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))).
% 6.14/1.18 thf(func_def_152, type, sK81: !>[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))).
% 6.14/1.18 thf(func_def_153, type, sK82: !>[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))).
% 6.14/1.18 thf(func_def_154, type, sK83: !>[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))).
% 6.14/1.18 thf(func_def_155, type, sK84: !>[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))).
% 6.14/1.18 thf(func_def_156, type, sK85: !>[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))).
% 6.14/1.18 thf(func_def_157, type, sK86: !>[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))).
% 6.14/1.18 thf(func_def_158, type, sK87: !>[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))).
% 6.14/1.18 thf(func_def_159, type, sK88: !>[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))).
% 6.14/1.18 thf(func_def_160, type, sK89: !>[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))).
% 6.14/1.18 thf(func_def_161, type, sK90: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 6.14/1.18 thf(func_def_162, type, sK91: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 6.14/1.18 thf(func_def_163, type, sK92: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 6.14/1.18 thf(func_def_164, type, sK93: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 6.14/1.18 thf(func_def_165, type, sK94: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 6.14/1.18 thf(func_def_166, type, sK95: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 6.14/1.18 thf(func_def_167, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit @ product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit))).
% 6.14/1.18 thf(func_def_168, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit @ product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0))).
% 6.14/1.18 thf(func_def_169, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > $o) > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit))).
% 6.14/1.18 thf(func_def_170, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > $o) > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0))).
% 6.14/1.18 thf(func_def_171, type, sK100: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > trm @ X0 @ X1))).
% 6.14/1.18 thf(func_def_172, type, sK101: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > X1))).
% 6.14/1.18 thf(func_def_173, type, sK102: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X0 @ X1 @ X1 > trm @ X0 @ X1))).
% 6.14/1.18 thf(func_def_174, type, sK103: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X0 @ X1 @ X1 > X1))).
% 6.14/1.18 thf(func_def_175, type, sK104: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 6.14/1.18 thf(func_def_176, type, sK105: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 6.14/1.18 thf(func_def_177, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit @ X2 > denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit))).
% 6.14/1.18 thf(func_def_178, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit @ X2 > X2))).
% 6.14/1.18 thf(func_def_179, type, sK108: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_180, type, sK109: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_181, type, sK110: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_182, type, sK111: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 6.14/1.18 thf(func_def_183, type, sK112: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 6.14/1.18 thf(func_def_184, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X2 @ X1 @ X0 > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit))).
% 6.14/1.18 thf(func_def_185, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X1 @ X0 @ X2 > denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit))).
% 6.14/1.18 thf(func_def_186, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > set @ sum_sum @ X2 @ X2 > denota1663640101rp_ext @ X1 @ X0 @ X2 @ product_unit > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > hp @ X1 @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 6.14/1.18 thf(func_def_187, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > hp @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > set @ sum_sum @ X1 @ X1))).
% 6.14/1.18 thf(func_def_188, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > hp @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 6.14/1.18 thf(func_def_189, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > hp @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 6.14/1.18 thf(func_def_190, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > hp @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 6.14/1.18 thf(func_def_191, type, sK120: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_192, type, sK121: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_193, type, sK122: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 6.14/1.18 thf(func_def_194, type, sK123: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 6.14/1.18 thf(func_def_195, type, sK124: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_196, type, sK125: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 6.14/1.18 thf(func_def_197, type, sK126: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 6.14/1.18 thf(f3,axiom,(
% 6.14/1.18 (member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ mu) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2)))),
% 6.14/1.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_prog__sem_H)).
% 6.14/1.18 thf(f4,axiom,(
% 6.14/1.18 (denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ mu @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))),
% 6.14/1.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_agree_H)).
% 6.14/1.18 thf(f317,conjecture,(
% 6.14/1.18 ? [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ X0 @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v)) & (member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ X0) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2))))),
% 6.14/1.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 6.14/1.18 thf(f318,negated_conjecture,(
% 6.14/1.18 ~ ? [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ X0 @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v)) & (member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ X0) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2))))),
% 6.14/1.18 inference(negated_conjecture,[status(cth)],[f317])).
% 6.14/1.18 thf(f323,plain,(
% 6.14/1.18 (member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ mu) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2)))),
% 6.14/1.18 inference(rectify,[],[f3])).
% 6.14/1.18 thf(f324,plain,(
% 6.14/1.18 (((member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ mu) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2)))) = $true)),
% 6.14/1.18 inference(fool_elimination,[],[f323])).
% 6.14/1.18 thf(f325,plain,(
% 6.14/1.18 (denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ mu @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))),
% 6.14/1.18 inference(rectify,[],[f4])).
% 6.14/1.18 thf(f326,plain,(
% 6.14/1.18 (((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ mu @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))) = $true)),
% 6.14/1.18 inference(fool_elimination,[],[f325])).
% 6.14/1.18 thf(f874,plain,(
% 6.14/1.18 ~ ? [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ X0 @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v)) & (member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ X0) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2))))),
% 6.14/1.18 inference(rectify,[],[f318])).
% 6.14/1.18 thf(f875,plain,(
% 6.14/1.18 ~ ? [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ X0 @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))) = $true) & (((member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ X0) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2)))) = $true))),
% 6.14/1.18 inference(fool_elimination,[],[f874])).
% 6.14/1.18 thf(f1225,plain,(
% 6.14/1.18 ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ X0 @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))) != $true) | (((member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ X0) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2)))) != $true))),
% 6.14/1.18 inference(ennf_transformation,[],[f875])).
% 6.14/1.18 thf(f1279,plain,(
% 6.14/1.18 (((member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ mu) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2)))) = $true)),
% 6.14/1.18 inference(cnf_transformation,[],[f324])).
% 6.14/1.18 thf(f1280,plain,(
% 6.14/1.18 (((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ mu @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))) = $true)),
% 6.14/1.18 inference(cnf_transformation,[],[f326])).
% 6.14/1.18 thf(f1636,plain,(
% 6.14/1.18 ( ! [X0 : product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c] : ((((member @ product_prod @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ nu_22 @ nu_2) @ X0) @ (denota1661140910og_sem @ a @ b @ c @ j @ (choice @ a @ b @ c @ a2 @ b2)))) != $true) | (((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ X0 @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))) != $true)) )),
% 6.14/1.18 inference(cnf_transformation,[],[f1225])).
% 6.14/1.18 thf(f17530,plain,(
% 6.14/1.18 ($true != $true) | (((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ mu @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))) != $true)),
% 6.14/1.18 inference(constrained_superposition,[],[f1636,f1279])).
% 6.14/1.18 thf(f17531,plain,(
% 6.14/1.18 (((denotational_Vagree @ c @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ mu3 @ mu2) @ mu @ (sup_sup @ set @ sum_sum @ c @ c @ (static_MBV @ a @ b @ c @ (choice @ a @ b @ c @ a2 @ b2)) @ v))) != $true)),
% 6.14/1.18 inference(trivial_inequality_removal,[],[f17530])).
% 6.14/1.18 thf(f17548,plain,(
% 6.14/1.18 $false),
% 6.14/1.18 inference(forward_subsumption_resolution,[],[f17531,f1280])).
% 6.14/1.18 % SZS output end Proof for theBenchmark
% 6.14/1.18 % (1723418)------------------------------
% 6.14/1.18 % (1723418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.14/1.18 % (1723418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/1.18 % (1723418)CaDiCaL version: 2.1.3
% 6.14/1.18 % (1723418)Termination reason: Refutation
% 6.14/1.18 % (1723418)Time elapsed: 0.447 s
% 6.14/1.18 % (1723418)Peak memory usage: 25 MB
% 6.14/1.18 % (1723418)Instructions burned: 1717 (million)
% 6.14/1.18 % (1723374)Success in time 0.947 s
% 6.14/1.18 % Vampire exiting
%------------------------------------------------------------------------------