%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT136^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 07:48:56 AM UTC 2026
% Result : Theorem 8.43s 1.68s
% Output : Refutation 8.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT136^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:59:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.27/1.30 % (152690)Will run a generic schedule for satisfiability detection.
% 6.27/1.30 % (152696)% WARNING: option uhcvi not known.
% 6.27/1.30 % (152696)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1074868240:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.27/1.30 % (152696)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.27/1.30 % (152695)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2395548477_2999 on theBenchmark for (2999ds/0Mi)
% 6.27/1.30 % (152697)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2099421301:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.27/1.30 % (152696)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.27/1.30 % (152698)dis+10_1_sil=32000:sp=arity:random_seed=3759716026:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.27/1.30 % (152700)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3031169192:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.27/1.30 % Exception at run slice level
% 6.27/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.27/1.30 % (152699)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3524259464:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.27/1.30 % (152701)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=450050396:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.27/1.30 % (152699)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.27/1.30 % (152709)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=730063006:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.27/1.30 % (152698)Instruction limit reached!
% 6.27/1.30 % (152698)------------------------------
% 6.27/1.30 % (152698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.27/1.30 % (152698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.30 % (152698)CaDiCaL version: 2.1.3
% 6.27/1.30 % (152698)Termination reason: Instruction limit
% 6.27/1.30 % (152698)Termination phase: Saturation
% 6.27/1.30 % (152698)Time elapsed: 0.092 s
% 6.27/1.30 % (152698)Peak memory usage: 12 MB
% 6.27/1.30 % (152698)Instructions burned: 103 (million)
% 6.27/1.30 % (152701)Instruction limit reached!
% 6.27/1.30 % (152701)------------------------------
% 6.27/1.30 % (152701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.27/1.30 % (152701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.30 % (152701)CaDiCaL version: 2.1.3
% 6.27/1.30 % (152701)Termination reason: Instruction limit
% 6.27/1.30 % (152701)Termination phase: Saturation
% 6.27/1.30 % (152701)Time elapsed: 0.080 s
% 6.27/1.30 % (152701)Peak memory usage: 13 MB
% 6.27/1.30 % (152701)Instructions burned: 160 (million)
% 6.27/1.30 % Exception at run slice level
% 6.27/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.27/1.30 % (152713)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=40976422:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 6.27/1.30 % (152700)Instruction limit reached!
% 6.27/1.30 % (152700)------------------------------
% 6.27/1.30 % (152700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.27/1.30 % (152700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.30 % (152700)CaDiCaL version: 2.1.3
% 6.27/1.30 % (152700)Termination reason: Instruction limit
% 6.27/1.30 % (152700)Termination phase: Saturation
% 6.27/1.30 % (152700)Time elapsed: 0.111 s
% 6.27/1.30 % (152700)Peak memory usage: 13 MB
% 6.27/1.30 % (152700)Instructions burned: 132 (million)
% 6.27/1.30 % (152699)Instruction limit reached!
% 6.27/1.30 % (152699)------------------------------
% 6.27/1.30 % (152699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.27/1.30 % (152699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/1.30 % (152699)CaDiCaL version: 2.1.3
% 6.27/1.30 % (152699)Termination reason: Instruction limit
% 6.27/1.30 % (152699)Termination phase: Saturation
% 6.27/1.30 % (152699)Time elapsed: 0.097 s
% 6.27/1.30 % (152699)Peak memory usage: 13 MB
% 6.27/1.30 % (152699)Instructions burned: 117 (million)
% 6.27/1.30 % (152715)ott-21_1_sil=16000:fs=off:random_seed=150883684:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 8.43/1.68 % (152714)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=3897718601:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 8.43/1.68 % (152717)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1450998741:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 8.43/1.68 % (152718)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2509785309:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 8.43/1.68 % (152714)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.43/1.68 % (152714)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.43/1.68 % Exception at run slice level
% 8.43/1.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.43/1.68 % (152713)Instruction limit reached!
% 8.43/1.68 % (152713)------------------------------
% 8.43/1.68 % (152713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152713)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152713)Termination reason: Instruction limit
% 8.43/1.68 % (152713)Termination phase: Saturation
% 8.43/1.68 % (152713)Time elapsed: 0.096 s
% 8.43/1.68 % (152713)Peak memory usage: 13 MB
% 8.43/1.68 % (152713)Instructions burned: 131 (million)
% 8.43/1.68 % (152723)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2365188190:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 8.43/1.68 % (152724)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1715251018:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 8.43/1.68 % Exception at run slice level
% 8.43/1.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.43/1.68 % (152715)Instruction limit reached!
% 8.43/1.68 % (152715)------------------------------
% 8.43/1.68 % (152715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152715)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152715)Termination reason: Instruction limit
% 8.43/1.68 % (152715)Termination phase: Saturation
% 8.43/1.68 % (152715)Time elapsed: 0.149 s
% 8.43/1.68 % (152715)Peak memory usage: 13 MB
% 8.43/1.68 % (152715)Instructions burned: 180 (million)
% 8.43/1.68 % (152727)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=1487476165:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 8.43/1.68 % (152727)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.43/1.68 % (152728)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=999734965:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 8.43/1.68 % (152728)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.43/1.68 % (152717)Instruction limit reached!
% 8.43/1.68 % (152717)------------------------------
% 8.43/1.68 % (152717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152717)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152717)Termination reason: Instruction limit
% 8.43/1.68 % (152717)Termination phase: Saturation
% 8.43/1.68 % (152717)Time elapsed: 0.308 s
% 8.43/1.68 % (152717)Peak memory usage: 14 MB
% 8.43/1.68 % (152717)Instructions burned: 477 (million)
% 8.43/1.68 % (152731)fmb+10_1_sil=64000:random_seed=1520212355:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 8.43/1.68 % (152731)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.43/1.68 % Exception at run slice level
% 8.43/1.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.43/1.68 % (152733)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1178617182:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 8.43/1.68 % (152714)Instruction limit reached!
% 8.43/1.68 % (152714)------------------------------
% 8.43/1.68 % (152714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152714)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152714)Termination reason: Instruction limit
% 8.43/1.68 % (152714)Termination phase: Saturation
% 8.43/1.68 % (152714)Time elapsed: 0.441 s
% 8.43/1.68 % (152714)Peak memory usage: 14 MB
% 8.43/1.68 % (152714)Instructions burned: 685 (million)
% 8.43/1.68 % Exception at run slice level
% 8.43/1.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.43/1.68 % (152735)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=318363295:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 8.43/1.68 % (152736)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2131972670:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 8.43/1.68 % (152727)Instruction limit reached!
% 8.43/1.68 % (152727)------------------------------
% 8.43/1.68 % (152727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152727)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152727)Termination reason: Instruction limit
% 8.43/1.68 % (152727)Termination phase: Saturation
% 8.43/1.68 % (152727)Time elapsed: 0.325 s
% 8.43/1.68 % (152727)Peak memory usage: 15 MB
% 8.43/1.68 % (152727)Instructions burned: 693 (million)
% 8.43/1.68 % (152736)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.43/1.68 % Exception at run slice level
% 8.43/1.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.43/1.68 % (152739)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3980621512:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 8.43/1.68 % (152740)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=635034517:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 8.43/1.68 % (152739)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.43/1.68 % (152739)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.43/1.68 % Exception at run slice level
% 8.43/1.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.43/1.68 % (152743)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1251777383:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 8.43/1.68 % Exception at run slice level
% 8.43/1.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.43/1.68 % (152745)ott-2_1_sil=16000:newcnf=on:random_seed=2426079422:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 8.43/1.68 % (152745)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.43/1.68 % (152728)Instruction limit reached!
% 8.43/1.68 % (152728)------------------------------
% 8.43/1.68 % (152728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152728)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152728)Termination reason: Instruction limit
% 8.43/1.68 % (152728)Termination phase: Saturation
% 8.43/1.68 % (152728)Time elapsed: 0.502 s
% 8.43/1.68 % (152728)Peak memory usage: 20 MB
% 8.43/1.68 % (152728)Instructions burned: 879 (million)
% 8.43/1.68 % (152747)ott+10_1_sil=32000:tgt=ground:random_seed=501312602:i=5114:av=off_2991 on theBenchmark for (2991ds/5114Mi)
% 8.43/1.68 % (152723)Instruction limit reached!
% 8.43/1.68 % (152723)------------------------------
% 8.43/1.68 % (152723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152723)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152723)Termination reason: Instruction limit
% 8.43/1.68 % (152723)Termination phase: Saturation
% 8.43/1.68 % (152723)Time elapsed: 0.677 s
% 8.43/1.68 % (152723)Peak memory usage: 19 MB
% 8.43/1.68 % (152723)Instructions burned: 1180 (million)
% 8.43/1.68 % (152749)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3171586341:i=54282_2990 on theBenchmark for (2990ds/54282Mi)
% 8.43/1.68 % Exception at run slice level
% 8.43/1.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.43/1.68 % (152751)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=4260785464:i=3512:aac=none_2989 on theBenchmark for (2989ds/3512Mi)
% 8.43/1.68 % (152751)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.43/1.68 % (152745)Instruction limit reached!
% 8.43/1.68 % (152745)------------------------------
% 8.43/1.68 % (152745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152745)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152745)Termination reason: Instruction limit
% 8.43/1.68 % (152745)Termination phase: Saturation
% 8.43/1.68 % (152745)Time elapsed: 0.430 s
% 8.43/1.68 % (152745)Peak memory usage: 16 MB
% 8.43/1.68 % (152745)Instructions burned: 870 (million)
% 8.43/1.68 % (152753)dis+21_1_sil=32000:sas=cadical:random_seed=1387898829:i=3773:amm=off_2987 on theBenchmark for (2987ds/3773Mi)
% 8.43/1.68 % (152696) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-152690-152696"...
% 8.43/1.68 % (152696)...printing done.
% 8.43/1.68 % (152696)Refutation found. Thanks to Tanya!
% 8.43/1.68 % SZS status Theorem for theBenchmark
% 8.43/1.68 % SZS output start Proof for theBenchmark
% 8.43/1.68 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 8.43/1.68 thf(type_def_6, type, extended_enat: $tType).
% 8.43/1.68 thf(type_def_7, type, list: $tType > $tType).
% 8.43/1.68 thf(type_def_8, type, set: $tType > $tType).
% 8.43/1.68 thf(type_def_9, type, nat: $tType).
% 8.43/1.68 thf(type_def_10, type, itself: $tType > $tType).
% 8.43/1.68 thf(type_def_11, type, a: $tType).
% 8.43/1.68 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 8.43/1.68 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_2, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_3, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_4, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_5, type, monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_6, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_7, type, semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_8, type, comm_semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_9, type, comm_monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_10, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_11, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_12, type, cancel1352612707id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_13, type, linord219039673up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_14, type, ordere216010020id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_15, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_16, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_17, type, strict797366125id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_18, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_19, type, ordere223160158up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_20, type, strict2144017051up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_21, type, ordere516151231imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_22, type, semiri456707255roduct: !>[X0: $tType]:((itself @ X0 > $o))).
% 8.43/1.68 thf(func_def_23, type, coindu493225792length: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > extended_enat))).
% 8.43/1.68 thf(func_def_24, type, coindu441856546concat: !>[X0: $tType]:((coindu1593790203_llist @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_25, type, coindu531130065ldropn: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_26, type, coindu1213758845finite: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 8.43/1.68 thf(func_def_27, type, coindu1018505716length: !>[X0: $tType]:((coindu1593790203_llist @ X0 > extended_enat))).
% 8.43/1.68 thf(func_def_28, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_29, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 8.43/1.68 thf(func_def_30, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 8.43/1.68 thf(func_def_31, type, coindu1079202755ist_of: !>[X0: $tType]:((list @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_32, type, coindu749330388e_lnth: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 8.43/1.68 thf(func_def_33, type, extended_enat2: (nat > extended_enat)).
% 8.43/1.68 thf(func_def_34, type, extended_size_enat: (extended_enat > nat)).
% 8.43/1.68 thf(func_def_35, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 8.43/1.68 thf(func_def_36, type, zero_zero: !>[X0: $tType]:(X0)).
% 8.43/1.68 thf(func_def_37, type, groups15040474setsum: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X1))).
% 8.43/1.68 thf(func_def_38, type, suc: (nat > nat)).
% 8.43/1.68 thf(func_def_39, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 8.43/1.68 thf(func_def_40, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 8.43/1.68 thf(func_def_41, type, type2: !>[X0: $tType]:(itself @ X0)).
% 8.43/1.68 thf(func_def_42, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 8.43/1.68 thf(func_def_43, type, set_ord_lessThan: !>[X0: $tType]:((X0 > set @ X0))).
% 8.43/1.68 thf(func_def_44, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 8.43/1.68 thf(func_def_45, type, n: nat).
% 8.43/1.68 thf(func_def_46, type, m: nat).
% 8.43/1.68 thf(func_def_47, type, n2: nat).
% 8.43/1.68 thf(func_def_48, type, n3: nat).
% 8.43/1.68 thf(func_def_49, type, na: nat).
% 8.43/1.68 thf(func_def_50, type, x: a).
% 8.43/1.68 thf(func_def_51, type, xs: coindu1593790203_llist @ a).
% 8.43/1.68 thf(func_def_52, type, xss: coindu1593790203_llist @ coindu1593790203_llist @ a).
% 8.43/1.68 thf(func_def_53, type, xss2: list @ coindu1593790203_llist @ a).
% 8.43/1.68 thf(func_def_54, type, xssa: coindu1593790203_llist @ coindu1593790203_llist @ a).
% 8.43/1.68 thf(func_def_58, type, db0: !>[X0: $tType]:(X0)).
% 8.43/1.68 thf(func_def_59, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 8.43/1.68 thf(func_def_60, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 8.43/1.68 thf(func_def_61, type, vNOT: ($o > $o)).
% 8.43/1.68 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.43/1.68 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 8.43/1.68 thf(func_def_64, type, db1: !>[X0: $tType]:(X0)).
% 8.43/1.68 thf(func_def_65, type, vAND: ($o > $o > $o)).
% 8.43/1.68 thf(func_def_66, type, vOR: ($o > $o > $o)).
% 8.43/1.68 thf(func_def_67, type, sP0: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X1 > X0) > $o))).
% 8.43/1.68 thf(func_def_68, type, sP1: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > $o))).
% 8.43/1.68 thf(func_def_69, type, sK2: (coindu1593790203_llist @ coindu1593790203_llist @ a > nat)).
% 8.43/1.68 thf(func_def_70, type, sK3: (coindu1593790203_llist @ coindu1593790203_llist @ a > nat)).
% 8.43/1.68 thf(func_def_71, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 8.43/1.68 thf(func_def_72, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 8.43/1.68 thf(func_def_73, type, sK6: (nat > nat > nat)).
% 8.43/1.68 thf(func_def_74, type, sK7: ((nat > $o) > nat > nat)).
% 8.43/1.68 thf(func_def_75, type, sK8: ((nat > $o) > nat > nat)).
% 8.43/1.68 thf(func_def_76, type, sK9: ((nat > nat > $o) > nat)).
% 8.43/1.68 thf(func_def_77, type, sK10: ((nat > nat > $o) > nat)).
% 8.43/1.68 thf(func_def_78, type, sK11: ((nat > nat > $o) > nat)).
% 8.43/1.68 thf(func_def_79, type, sK12: ((nat > nat > $o) > nat)).
% 8.43/1.68 thf(func_def_80, type, sK13: (nat > nat > nat)).
% 8.43/1.68 thf(func_def_81, type, sK14: (nat > nat > nat)).
% 8.43/1.68 thf(func_def_82, type, sK15: (nat > extended_enat > nat)).
% 8.43/1.68 thf(func_def_83, type, sK16: ((extended_enat > $o) > extended_enat)).
% 8.43/1.68 thf(func_def_84, type, sK17: !>[X0: $tType]:(((nat > X0) > nat))).
% 8.43/1.68 thf(func_def_85, type, sK18: !>[X0: $tType]:(((nat > X0) > nat))).
% 8.43/1.68 thf(func_def_86, type, sK19: (extended_enat > nat)).
% 8.43/1.68 thf(func_def_87, type, sK20: !>[X0: $tType]:((nat > (X0 > extended_enat) > X0))).
% 8.43/1.68 thf(func_def_88, type, sK21: !>[X0: $tType]:(((X0 > extended_enat) > X0))).
% 8.43/1.68 thf(func_def_89, type, sK22: a).
% 8.43/1.68 thf(func_def_90, type, sK23: coindu1593790203_llist @ a).
% 8.43/1.68 thf(func_def_91, type, sK24: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0))).
% 8.43/1.68 thf(func_def_92, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X0))).
% 8.43/1.68 thf(func_def_93, type, sK26: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 8.43/1.68 thf(func_def_94, type, sK27: ((nat > $o) > nat)).
% 8.43/1.68 thf(func_def_95, type, sK28: ((nat > $o) > nat)).
% 8.43/1.68 thf(func_def_96, type, sK29: ((nat > $o) > nat)).
% 8.43/1.68 thf(func_def_97, type, sK30: !>[X0: $tType]:((set @ X0 > (X0 > nat) > X0))).
% 8.43/1.68 thf(func_def_98, type, sK31: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 8.43/1.68 thf(func_def_99, type, sK32: (nat > nat > nat)).
% 8.43/1.68 thf(func_def_100, type, sK33: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 8.43/1.68 thf(func_def_101, type, sK34: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 8.43/1.68 thf(func_def_102, type, sK35: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 8.43/1.68 thf(func_def_103, type, sK36: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_104, type, sK37: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 8.43/1.68 thf(func_def_105, type, sK38: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 8.43/1.68 thf(func_def_106, type, sK39: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_107, type, sK40: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_108, type, sK41: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 8.43/1.68 thf(func_def_109, type, sK42: ((nat > $o) > nat)).
% 8.43/1.68 thf(func_def_110, type, sK43: ((nat > nat > $o) > nat)).
% 8.43/1.68 thf(func_def_111, type, sK44: ((nat > nat > $o) > nat)).
% 8.43/1.68 thf(func_def_112, type, sK45: ((nat > nat > $o) > nat)).
% 8.43/1.68 thf(func_def_113, type, sK46: ((nat > nat > $o) > nat)).
% 8.43/1.68 thf(func_def_114, type, sK47: ((nat > $o) > nat)).
% 8.43/1.68 thf(func_def_115, type, sK48: (nat > nat)).
% 8.43/1.68 thf(func_def_116, type, sK49: ((nat > $o) > nat)).
% 8.43/1.68 thf(func_def_117, type, sK50: (nat > nat)).
% 8.43/1.68 thf(func_def_118, type, sK51: (nat > nat)).
% 8.43/1.68 thf(func_def_119, type, sK52: !>[X0: $tType]:(((nat > X0) > (nat > X0) > set @ nat > nat))).
% 8.43/1.68 thf(func_def_120, type, sK53: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_121, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 8.43/1.68 thf(func_def_122, type, sK55: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > X1))).
% 8.43/1.68 thf(func_def_123, type, sK56: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X1 > X0) > X1))).
% 8.43/1.68 thf(func_def_124, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > (X0 > X2) > set @ X0 > X0))).
% 8.43/1.68 thf(func_def_125, type, sK58: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > X1))).
% 8.43/1.68 thf(func_def_126, type, sK59: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X1 > X0) > X1))).
% 8.43/1.68 thf(func_def_127, type, sK60: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 8.43/1.68 thf(func_def_128, type, sK61: !>[X0: $tType]:((nat > list @ X0))).
% 8.43/1.68 thf(func_def_129, type, sK62: !>[X0: $tType]:((list @ X0 > nat))).
% 8.43/1.68 thf(func_def_130, type, sK63: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_131, type, sK64: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_132, type, sK65: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_133, type, sK66: (nat > nat)).
% 8.43/1.68 thf(func_def_134, type, sK67: (nat > nat > nat)).
% 8.43/1.68 thf(func_def_135, type, sK68: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_136, type, sK69: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_137, type, sK70: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 8.43/1.68 thf(func_def_138, type, sK71: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_139, type, sK72: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 8.43/1.68 thf(func_def_140, type, sK73: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > nat))).
% 8.43/1.68 thf(func_def_141, type, sK74: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_142, type, sK75: !>[X0: $tType]:(nat)).
% 8.43/1.68 thf(func_def_143, type, sK76: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > nat))).
% 8.43/1.68 thf(func_def_144, type, sK77: !>[X0: $tType]:(nat)).
% 8.43/1.68 thf(func_def_145, type, sK78: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_146, type, sK79: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_147, type, sK80: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_148, type, sK81: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_149, type, sK82: (nat > nat > nat)).
% 8.43/1.68 thf(func_def_151, type, db3: !>[X0: $tType]:(X0)).
% 8.43/1.68 thf(func_def_152, type, db4: !>[X0: $tType]:(X0)).
% 8.43/1.68 thf(func_def_153, type, db5: !>[X0: $tType]:(X0)).
% 8.43/1.68 thf(func_def_154, type, sK84: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 8.43/1.68 thf(func_def_155, type, sK85: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 8.43/1.68 thf(func_def_156, type, sK86: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(func_def_157, type, sK87: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 8.43/1.68 thf(f1,axiom,(
% 8.43/1.68 (ord_less @ extended_enat @ (extended_enat2 @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062enat_A_Ilength_Axss_H_J_A_060_Allength_Axss_092_060close_062)).
% 8.43/1.68 thf(f3,axiom,(
% 8.43/1.68 (ord_less @ extended_enat @ (extended_enat2 @ (suc @ n3)) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062enat_A_ISuc_An_H_J_A_060_Allength_A_Ilnth_Axss_A_Ilength_Axss_H_J_J_092_060close_062)).
% 8.43/1.68 thf(f5,axiom,(
% 8.43/1.68 (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) = ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ (suc @ n3))))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062lnth_A_Ilconcat_Axss_J_A_ISuc_An_J_A_061_Alnth_A_Ilnth_Axss_A_Ilength_Axss_H_J_J_A_ISuc_An_H_J_092_060close_062)).
% 8.43/1.68 thf(f6,axiom,(
% 8.43/1.68 (((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[X0 : nat] : ((coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0)))) @ (set_ord_lessThan @ nat @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))) @ (extended_enat2 @ (suc @ n3)))))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062enat_A_ISuc_An_J_A_061_A_I_092_060Sum_062i_060length_Axss_H_O_Allength_A_Ilnth_Axss_Ai_J_J_A_L_Aenat_A_ISuc_An_H_J_092_060close_062)).
% 8.43/1.68 thf(f15,axiom,(
% 8.43/1.68 (((groups15040474setsum @ nat @ extended_enat @ (^[X0 : nat] : ((coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0)))) @ (set_ord_lessThan @ nat @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)))) = zero_zero @ extended_enat)),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__092_060open_062_I_092_060Sum_062i_060length_Axss_H_O_Allength_A_Ilnth_Axss_Ai_J_J_A_061_A0_092_060close_062)).
% 8.43/1.68 thf(f35,axiom,(
% 8.43/1.68 ! [X0 : $tType] : ((monoid_add @ X0 @ type2 @ X0) => ! [X1 : X0] : (((plus_plus @ X0 @ zero_zero @ X0 @ X1)) = X1))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_add_Oleft__neutral)).
% 8.43/1.68 thf(f217,axiom,(
% 8.43/1.68 ! [X0 : $tType] : (coindu1213758845finite @ X0 = (^[X1 : coindu1593790203_llist @ X0] : (? [X2 : nat] : (((coindu1018505716length @ X0 @ X1)) = ((extended_enat2 @ X2))))))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_lfinite__conv__llength__enat)).
% 8.43/1.68 thf(f244,axiom,(
% 8.43/1.68 ! [X0 : $tType,X1 : list @ X0] : (((coindu1018505716length @ X0 @ (coindu1079202755ist_of @ X0 @ X1))) = ((extended_enat2 @ (size_size @ list @ X0 @ X1))))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_llength__llist__of)).
% 8.43/1.68 thf(f245,axiom,(
% 8.43/1.68 ! [X0 : $tType,X1 : list @ X0] : (coindu1213758845finite @ X0 @ (coindu1079202755ist_of @ X0 @ X1))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_lfinite__llist__of)).
% 8.43/1.68 thf(f288,axiom,(
% 8.43/1.68 (monoid_add @ extended_enat @ type2 @ extended_enat)),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Omonoid__add_18)).
% 8.43/1.68 thf(f292,conjecture,(
% 8.43/1.68 ? [X0 : nat,X1 : nat] : ((((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[X2 : nat] : ((coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X2)))) @ (set_ord_lessThan @ nat @ X0)) @ (extended_enat2 @ X1)))) & (ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa)) & (ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0))) & (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) = ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0) @ X1))))),
% 8.43/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 8.43/1.68 thf(f293,negated_conjecture,(
% 8.43/1.68 ~ ? [X0 : nat,X1 : nat] : ((((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[X2 : nat] : ((coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X2)))) @ (set_ord_lessThan @ nat @ X0)) @ (extended_enat2 @ X1)))) & (ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa)) & (ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0))) & (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) = ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0) @ X1))))),
% 8.43/1.68 inference(negated_conjecture,[status(cth)],[f292])).
% 8.43/1.68 thf(f294,plain,(
% 8.43/1.68 (ord_less @ extended_enat @ (extended_enat2 @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))),
% 8.43/1.68 inference(rectify,[],[f1])).
% 8.43/1.68 thf(f295,plain,(
% 8.43/1.68 (((ord_less @ extended_enat @ (extended_enat2 @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))) = $true)),
% 8.43/1.68 inference(fool_elimination,[],[f294])).
% 8.43/1.68 thf(f298,plain,(
% 8.43/1.68 (ord_less @ extended_enat @ (extended_enat2 @ (suc @ n3)) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))))),
% 8.43/1.68 inference(rectify,[],[f3])).
% 8.43/1.68 thf(f299,plain,(
% 8.43/1.68 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n3)) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))))) = $true)),
% 8.43/1.68 inference(fool_elimination,[],[f298])).
% 8.43/1.68 thf(f302,plain,(
% 8.43/1.68 (((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[X0 : nat] : ((coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0)))) @ (set_ord_lessThan @ nat @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))) @ (extended_enat2 @ (suc @ n3)))))),
% 8.43/1.68 inference(rectify,[],[f6])).
% 8.43/1.68 thf(f303,plain,(
% 8.43/1.68 (((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[Y0 : nat]: (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ Y0))) @ (set_ord_lessThan @ nat @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))) @ (extended_enat2 @ (suc @ n3)))))),
% 8.43/1.68 inference(fool_elimination,[],[f302])).
% 8.43/1.68 thf(f316,plain,(
% 8.43/1.68 (((groups15040474setsum @ nat @ extended_enat @ (^[X0 : nat] : ((coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0)))) @ (set_ord_lessThan @ nat @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)))) = zero_zero @ extended_enat)),
% 8.43/1.68 inference(rectify,[],[f15])).
% 8.43/1.68 thf(f317,plain,(
% 8.43/1.68 (zero_zero @ extended_enat = ((groups15040474setsum @ nat @ extended_enat @ (^[Y0 : nat]: (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ Y0))) @ (set_ord_lessThan @ nat @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)))))),
% 8.43/1.68 inference(fool_elimination,[],[f316])).
% 8.43/1.68 thf(f347,plain,(
% 8.43/1.68 ! [X0 : $tType] : ((monoid_add @ X0 @ type2 @ X0) => ! [X1 : X0] : (((plus_plus @ X0 @ zero_zero @ X0 @ X1)) = X1))),
% 8.43/1.68 inference(rectify,[],[f35])).
% 8.43/1.68 thf(f348,plain,(
% 8.43/1.68 ! [X0 : $tType] : ((((monoid_add @ X0 @ type2 @ X0)) = $true) => ! [X1 : X0] : (((plus_plus @ X0 @ zero_zero @ X0 @ X1)) = X1))),
% 8.43/1.68 inference(fool_elimination,[],[f347])).
% 8.43/1.68 thf(f627,plain,(
% 8.43/1.68 ! [X0 : $tType] : (coindu1213758845finite @ X0 = (^[Y0 : coindu1593790203_llist @ X0]: (?? @ nat @ (^[Y1 : nat]: ((extended_enat2 @ Y1) = (coindu1018505716length @ X0 @ Y0))))))),
% 8.43/1.68 inference(fool_elimination,[],[f217])).
% 8.43/1.68 thf(f661,plain,(
% 8.43/1.68 ! [X0 : $tType,X1 : list @ X0] : (coindu1213758845finite @ X0 @ (coindu1079202755ist_of @ X0 @ X1))),
% 8.43/1.68 inference(rectify,[],[f245])).
% 8.43/1.68 thf(f662,plain,(
% 8.43/1.68 ! [X0 : $tType,X1 : list @ X0] : (((coindu1213758845finite @ X0 @ (coindu1079202755ist_of @ X0 @ X1))) = $true)),
% 8.43/1.68 inference(fool_elimination,[],[f661])).
% 8.43/1.68 thf(f743,plain,(
% 8.43/1.68 (monoid_add @ extended_enat @ type2 @ extended_enat)),
% 8.43/1.68 inference(rectify,[],[f288])).
% 8.43/1.68 thf(f744,plain,(
% 8.43/1.68 (((monoid_add @ extended_enat @ type2 @ extended_enat)) = $true)),
% 8.43/1.68 inference(fool_elimination,[],[f743])).
% 8.43/1.68 thf(f751,plain,(
% 8.43/1.68 ~ ? [X0 : nat,X1 : nat] : ((((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[X2 : nat] : ((coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X2)))) @ (set_ord_lessThan @ nat @ X0)) @ (extended_enat2 @ X1)))) & (ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa)) & (ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0))) & (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) = ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0) @ X1))))),
% 8.43/1.68 inference(rectify,[],[f293])).
% 8.43/1.68 thf(f752,plain,(
% 8.43/1.68 ~ ? [X0 : nat,X1 : nat] : ((((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[Y0 : nat]: (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ Y0))) @ (set_ord_lessThan @ nat @ X0)) @ (extended_enat2 @ X1)))) & (((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))) = $true) & (((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0)))) = $true) & (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) = ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0) @ X1))))),
% 8.43/1.68 inference(fool_elimination,[],[f751])).
% 8.43/1.68 thf(f796,plain,(
% 8.43/1.68 ! [X0 : $tType] : (! [X1 : X0] : (((plus_plus @ X0 @ zero_zero @ X0 @ X1)) = X1) | (((monoid_add @ X0 @ type2 @ X0)) != $true))),
% 8.43/1.68 inference(ennf_transformation,[],[f348])).
% 8.43/1.68 thf(f963,plain,(
% 8.43/1.68 ! [X0 : nat,X1 : nat] : ((((extended_enat2 @ (suc @ na))) != ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[Y0 : nat]: (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ Y0))) @ (set_ord_lessThan @ nat @ X0)) @ (extended_enat2 @ X1)))) | (((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))) != $true) | (((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0)))) != $true) | (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) != ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0) @ X1))))),
% 8.43/1.68 inference(ennf_transformation,[],[f752])).
% 8.43/1.68 thf(f1021,plain,(
% 8.43/1.68 (((ord_less @ extended_enat @ (extended_enat2 @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))) = $true)),
% 8.43/1.68 inference(cnf_transformation,[],[f295])).
% 8.43/1.68 thf(f1023,plain,(
% 8.43/1.68 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n3)) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))))) = $true)),
% 8.43/1.68 inference(cnf_transformation,[],[f299])).
% 8.43/1.68 thf(f1025,plain,(
% 8.43/1.68 (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) = ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ (suc @ n3))))),
% 8.43/1.68 inference(cnf_transformation,[],[f5])).
% 8.43/1.68 thf(f1026,plain,(
% 8.43/1.68 (((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[Y0 : nat]: (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ Y0))) @ (set_ord_lessThan @ nat @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))) @ (extended_enat2 @ (suc @ n3)))))),
% 8.43/1.68 inference(cnf_transformation,[],[f303])).
% 8.43/1.68 thf(f1038,plain,(
% 8.43/1.68 (zero_zero @ extended_enat = ((groups15040474setsum @ nat @ extended_enat @ (^[Y0 : nat]: (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ Y0))) @ (set_ord_lessThan @ nat @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)))))),
% 8.43/1.68 inference(cnf_transformation,[],[f317])).
% 8.43/1.68 thf(f1058,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : X0] : ((((monoid_add @ X0 @ type2 @ X0)) != $true) | (((plus_plus @ X0 @ zero_zero @ X0 @ X1)) = X1)) )),
% 8.43/1.68 inference(cnf_transformation,[],[f796])).
% 8.43/1.68 thf(f1280,plain,(
% 8.43/1.68 ( ! [X0 : $tType] : ((coindu1213758845finite @ X0 = (^[Y0 : coindu1593790203_llist @ X0]: (?? @ nat @ (^[Y1 : nat]: ((extended_enat2 @ Y1) = (coindu1018505716length @ X0 @ Y0))))))) )),
% 8.43/1.68 inference(cnf_transformation,[],[f627])).
% 8.43/1.68 thf(f1320,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : list @ X0] : ((((coindu1018505716length @ X0 @ (coindu1079202755ist_of @ X0 @ X1))) = ((extended_enat2 @ (size_size @ list @ X0 @ X1))))) )),
% 8.43/1.68 inference(cnf_transformation,[],[f244])).
% 8.43/1.68 thf(f1321,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : list @ X0] : ((((coindu1213758845finite @ X0 @ (coindu1079202755ist_of @ X0 @ X1))) = $true)) )),
% 8.43/1.68 inference(cnf_transformation,[],[f662])).
% 8.43/1.68 thf(f1364,plain,(
% 8.43/1.68 (((monoid_add @ extended_enat @ type2 @ extended_enat)) = $true)),
% 8.43/1.68 inference(cnf_transformation,[],[f744])).
% 8.43/1.68 thf(f1368,plain,(
% 8.43/1.68 ( ! [X0 : nat,X1 : nat] : ((((extended_enat2 @ (suc @ na))) != ((plus_plus @ extended_enat @ (groups15040474setsum @ nat @ extended_enat @ (^[Y0 : nat]: (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ Y0))) @ (set_ord_lessThan @ nat @ X0)) @ (extended_enat2 @ X1)))) | (((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))) != $true) | (((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0)))) != $true) | (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) != ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ X0) @ X1)))) )),
% 8.43/1.68 inference(cnf_transformation,[],[f963])).
% 8.43/1.68 thf(f1370,definition,(
% 8.43/1.68 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 8.43/1.68 introduced(theory,[fool_exhaustiveness_axiom])).
% 8.43/1.68 thf(f1405,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : list @ X0] : (($true = (((^[Y0 : coindu1593790203_llist @ X0]: (?? @ nat @ (^[Y1 : nat]: ((extended_enat2 @ Y1) = (coindu1018505716length @ X0 @ Y0))))) @ (coindu1079202755ist_of @ X0 @ X1))))) )),
% 8.43/1.68 inference(definition_unfolding,[],[f1321,f1280])).
% 8.43/1.68 thf(f1424,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : list @ X0] : (($true = ((?? @ nat @ (^[Y0 : nat]: ((extended_enat2 @ Y0) = (coindu1018505716length @ X0 @ (coindu1079202755ist_of @ X0 @ X1)))))))) )),
% 8.43/1.68 inference(beta-eta_normalization,[],[f1405])).
% 8.43/1.68 thf(f1425,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : list @ X0] : (($true = (((^[Y0 : nat]: ((extended_enat2 @ Y0) = (coindu1018505716length @ X0 @ (coindu1079202755ist_of @ X0 @ X1)))) @ (sK62 @ X0 @ X1))))) )),
% 8.43/1.68 inference(sigma_proxy_clausification,[],[f1424])).
% 8.43/1.68 thf(f1426,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : list @ X0] : (($true = (((extended_enat2 @ (sK62 @ X0 @ X1)) = (coindu1018505716length @ X0 @ (coindu1079202755ist_of @ X0 @ X1)))))) )),
% 8.43/1.68 inference(beta-eta_normalization,[],[f1425])).
% 8.43/1.68 thf(f1427,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : list @ X0] : ((((coindu1018505716length @ X0 @ (coindu1079202755ist_of @ X0 @ X1))) = ((extended_enat2 @ (sK62 @ X0 @ X1))))) )),
% 8.43/1.68 inference(equality_proxy_clausification,[],[f1426])).
% 8.43/1.68 thf(f2521,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (((plus_plus @ X0 @ zero_zero @ X0 @ X1)) = X1) | (((monoid_add @ X0 @ type2 @ X0)) = $false)) )),
% 8.43/1.68 inference(constrained_superposition,[],[f1058,f1370])).
% 8.43/1.68 thf(f2522,plain,(
% 8.43/1.68 ( ! [X0 : extended_enat] : (($true != $true) | (((plus_plus @ extended_enat @ zero_zero @ extended_enat @ X0)) = X0)) )),
% 8.43/1.68 inference(constrained_superposition,[],[f1058,f1364])).
% 8.43/1.68 thf(f2525,plain,(
% 8.43/1.68 ( ! [X0 : extended_enat] : ((((plus_plus @ extended_enat @ zero_zero @ extended_enat @ X0)) = X0)) )),
% 8.43/1.68 inference(trivial_inequality_removal,[],[f2522])).
% 8.43/1.68 thf(f2526,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : X0] : ((((plus_plus @ X0 @ zero_zero @ X0 @ X1)) = X1) | (((monoid_add @ X0 @ type2 @ X0)) = $false)) )),
% 8.43/1.68 inference(trivial_inequality_removal,[],[f2521])).
% 8.43/1.68 thf(f2806,plain,(
% 8.43/1.68 ( ! [X0 : $tType,X1 : list @ X0] : ((((extended_enat2 @ (size_size @ list @ X0 @ X1))) = ((extended_enat2 @ (sK62 @ X0 @ X1))))) )),
% 8.43/1.68 inference(forward_demodulation,[],[f1320,f1427])).
% 8.43/1.68 thf(f5224,plain,(
% 8.43/1.68 ($true = ((ord_less @ extended_enat @ (extended_enat2 @ (sK62 @ coindu1593790203_llist @ a @ xss2)) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))))),
% 8.43/1.68 inference(forward_demodulation,[],[f1021,f2806])).
% 8.43/1.68 thf(f12882,plain,(
% 8.43/1.68 ( ! [X0 : nat] : ((((extended_enat2 @ (suc @ na))) != ((plus_plus @ extended_enat @ zero_zero @ extended_enat @ (extended_enat2 @ X0)))) | (((ord_less @ extended_enat @ (extended_enat2 @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))) != $true) | ($true != ((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)))))) | (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) != ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ X0)))) )),
% 8.43/1.68 inference(constrained_superposition,[],[f1368,f1038])).
% 8.43/1.68 thf(f12889,plain,(
% 8.43/1.68 ( ! [X0 : nat] : ((((extended_enat2 @ (suc @ na))) != ((extended_enat2 @ X0))) | (((ord_less @ extended_enat @ (extended_enat2 @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa))) != $true) | ($true != ((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)))))) | (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) != ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ X0)))) )),
% 8.43/1.68 inference(forward_demodulation,[],[f12882,f2525])).
% 8.43/1.68 thf(f12892,plain,(
% 8.43/1.68 ( ! [X0 : nat] : (($true != ((ord_less @ extended_enat @ (extended_enat2 @ (sK62 @ coindu1593790203_llist @ a @ xss2)) @ (coindu1018505716length @ coindu1593790203_llist @ a @ xssa)))) | (((extended_enat2 @ (suc @ na))) != ((extended_enat2 @ X0))) | ($true != ((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)))))) | (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) != ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ X0)))) )),
% 8.43/1.68 inference(forward_demodulation,[],[f12889,f2806])).
% 8.43/1.68 thf(f12893,plain,(
% 8.43/1.68 ( ! [X0 : nat] : ((((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) != ((coindu749330388e_lnth @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)) @ X0))) | ($true != ((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2)))))) | (((extended_enat2 @ (suc @ na))) != ((extended_enat2 @ X0)))) )),
% 8.43/1.68 inference(forward_subsumption_resolution,[],[f12892,f5224])).
% 8.43/1.68 thf(f14710,plain,(
% 8.43/1.68 (((extended_enat2 @ (suc @ na))) = ((plus_plus @ extended_enat @ zero_zero @ extended_enat @ (extended_enat2 @ (suc @ n3)))))),
% 8.43/1.68 inference(forward_demodulation,[],[f1026,f1038])).
% 8.43/1.68 thf(f22962,plain,(
% 8.43/1.68 (((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na))) != ((coindu749330388e_lnth @ a @ (coindu441856546concat @ a @ xssa) @ (suc @ na)))) | (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n3)) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))))) != $true) | (((extended_enat2 @ (suc @ n3))) != ((extended_enat2 @ (suc @ na))))),
% 8.43/1.68 inference(constrained_superposition,[],[f12893,f1025])).
% 8.43/1.68 thf(f22963,plain,(
% 8.43/1.68 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n3)) @ (coindu1018505716length @ a @ (coindu749330388e_lnth @ coindu1593790203_llist @ a @ xssa @ (size_size @ list @ coindu1593790203_llist @ a @ xss2))))) != $true) | (((extended_enat2 @ (suc @ n3))) != ((extended_enat2 @ (suc @ na))))),
% 8.43/1.68 inference(trivial_inequality_removal,[],[f22962])).
% 8.43/1.68 thf(f22964,plain,(
% 8.43/1.68 (((extended_enat2 @ (suc @ n3))) != ((extended_enat2 @ (suc @ na))))),
% 8.43/1.68 inference(forward_subsumption_resolution,[],[f22963,f1023])).
% 8.43/1.68 thf(f30861,plain,(
% 8.43/1.68 (((extended_enat2 @ (suc @ n3))) = ((extended_enat2 @ (suc @ na)))) | (((monoid_add @ extended_enat @ type2 @ extended_enat)) = $false)),
% 8.43/1.68 inference(constrained_superposition,[],[f14710,f2526])).
% 8.43/1.68 thf(f31106,plain,(
% 8.43/1.68 (((monoid_add @ extended_enat @ type2 @ extended_enat)) = $false)),
% 8.43/1.68 inference(forward_subsumption_resolution,[],[f30861,f22964])).
% 8.43/1.68 thf(f31854,plain,(
% 8.43/1.68 ($true = $false)),
% 8.43/1.68 inference(constrained_superposition,[],[f1364,f31106])).
% 8.43/1.68 thf(f31855,plain,(
% 8.43/1.68 $false),
% 8.43/1.68 inference(trivial_inequality_removal,[],[f31854])).
% 8.43/1.68 % SZS output end Proof for theBenchmark
% 8.43/1.68 % (152696)------------------------------
% 8.43/1.68 % (152696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.43/1.68 % (152696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/1.68 % (152696)CaDiCaL version: 2.1.3
% 8.43/1.68 % (152696)Termination reason: Refutation
% 8.43/1.68 % (152696)Time elapsed: 1.391 s
% 8.43/1.68 % (152696)Peak memory usage: 36 MB
% 8.43/1.68 % (152696)Instructions burned: 4911 (million)
% 8.43/1.68 % (152690)Success in time 1.447 s
% 8.43/1.68 % Vampire exiting
%------------------------------------------------------------------------------