%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU768^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:33:20 AM UTC 2026
% Result : Theorem 53.31s 7.98s
% Output : Refutation 53.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU768^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n006.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:23:25 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.72/1.26 % (798334)Will run a generic schedule for satisfiability detection.
% 6.72/1.26 % (798340)% WARNING: option uhcvi not known.
% 6.72/1.26 % (798343)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1229483610:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.72/1.26 % (798343)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.72/1.26 % (798339)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1908169539_2999 on theBenchmark for (2999ds/0Mi)
% 6.72/1.26 % (798342)dis+10_1_sil=32000:sp=arity:random_seed=4235115163:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.72/1.26 % (798340)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=88406127:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.72/1.26 % (798344)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1641296944:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.72/1.26 % (798341)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=462084445:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.72/1.26 % (798340)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.72/1.26 % Exception at run slice level
% 6.72/1.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.72/1.26 % (798340)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.72/1.26 % (798345)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3461663008:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.72/1.26 % (798352)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1051113149:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.72/1.26 % Exception at run slice level
% 6.72/1.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.72/1.26 % (798355)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2893459364:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.72/1.26 % (798343)Instruction limit reached!
% 6.72/1.26 % (798343)------------------------------
% 6.72/1.26 % (798343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.72/1.26 % (798343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/1.26 % (798343)CaDiCaL version: 2.1.3
% 6.72/1.26 % (798343)Termination reason: Instruction limit
% 6.72/1.26 % (798343)Termination phase: Saturation
% 6.72/1.26 % (798343)Time elapsed: 0.050 s
% 6.72/1.26 % (798343)Peak memory usage: 12 MB
% 6.72/1.26 % (798343)Instructions burned: 117 (million)
% 6.72/1.26 % (798342)Instruction limit reached!
% 6.72/1.26 % (798342)------------------------------
% 6.72/1.26 % (798342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.72/1.26 % (798342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/1.26 % (798342)CaDiCaL version: 2.1.3
% 6.72/1.26 % (798342)Termination reason: Instruction limit
% 6.72/1.26 % (798342)Termination phase: Saturation
% 6.72/1.26 % (798342)Time elapsed: 0.050 s
% 6.72/1.26 % (798342)Peak memory usage: 12 MB
% 6.72/1.26 % (798342)Instructions burned: 104 (million)
% 6.72/1.26 % (798344)Instruction limit reached!
% 6.72/1.26 % (798344)------------------------------
% 6.72/1.26 % (798344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.72/1.26 % (798344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/1.26 % (798344)CaDiCaL version: 2.1.3
% 6.72/1.26 % (798344)Termination reason: Instruction limit
% 6.72/1.26 % (798344)Termination phase: Saturation
% 6.72/1.26 % (798344)Time elapsed: 0.066 s
% 6.72/1.26 % (798344)Peak memory usage: 13 MB
% 6.72/1.26 % (798344)Instructions burned: 133 (million)
% 6.72/1.26 % (798357)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=3690455904:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.72/1.26 % (798357)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.72/1.26 % (798357)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.72/1.26 % (798358)ott-21_1_sil=16000:fs=off:random_seed=2204692057:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 6.72/1.26 % (798360)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2331626159:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 19.94/3.07 % (798355)Instruction limit reached!
% 19.94/3.07 % (798355)------------------------------
% 19.94/3.07 % (798355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.94/3.07 % (798355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.94/3.07 % (798355)CaDiCaL version: 2.1.3
% 19.94/3.07 % (798355)Termination reason: Instruction limit
% 19.94/3.07 % (798355)Termination phase: Saturation
% 19.94/3.07 % (798355)Time elapsed: 0.065 s
% 19.94/3.07 % (798355)Peak memory usage: 12 MB
% 19.94/3.07 % (798355)Instructions burned: 131 (million)
% 19.94/3.07 % (798363)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=471382143:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 19.94/3.07 % Exception at run slice level
% 19.94/3.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.94/3.07 % (798365)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=769625310:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 19.94/3.07 % (798358)Instruction limit reached!
% 19.94/3.07 % (798358)------------------------------
% 19.94/3.07 % (798358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.94/3.07 % (798358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.94/3.07 % (798358)CaDiCaL version: 2.1.3
% 19.94/3.07 % (798358)Termination reason: Instruction limit
% 19.94/3.07 % (798358)Termination phase: Saturation
% 19.94/3.07 % (798358)Time elapsed: 0.085 s
% 19.94/3.07 % (798358)Peak memory usage: 12 MB
% 19.94/3.07 % (798358)Instructions burned: 180 (million)
% 19.94/3.07 % (798345)Instruction limit reached!
% 19.94/3.07 % (798345)------------------------------
% 19.94/3.07 % (798345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.94/3.07 % (798345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.94/3.07 % (798345)CaDiCaL version: 2.1.3
% 19.94/3.07 % (798345)Termination reason: Instruction limit
% 19.94/3.07 % (798345)Termination phase: Saturation
% 19.94/3.07 % (798345)Time elapsed: 0.143 s
% 19.94/3.07 % (798345)Peak memory usage: 12 MB
% 19.94/3.07 % (798345)Instructions burned: 162 (million)
% 19.94/3.07 % (798367)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1570900411:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 19.94/3.07 % Exception at run slice level
% 19.94/3.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 19.94/3.07 % (798368)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=861292359:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 19.94/3.07 % (798368)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 19.94/3.07 % (798370)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3253898390:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 19.94/3.07 % (798370)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 19.94/3.07 % (798360)Instruction limit reached!
% 19.94/3.07 % (798360)------------------------------
% 19.94/3.07 % (798360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.94/3.07 % (798360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.94/3.07 % (798360)CaDiCaL version: 2.1.3
% 19.94/3.07 % (798360)Termination reason: Instruction limit
% 19.94/3.07 % (798360)Termination phase: Saturation
% 19.94/3.07 % (798360)Time elapsed: 0.245 s
% 19.94/3.07 % (798360)Peak memory usage: 14 MB
% 19.94/3.07 % (798360)Instructions burned: 479 (million)
% 19.94/3.07 % (798357)Instruction limit reached!
% 19.94/3.07 % (798357)------------------------------
% 19.94/3.07 % (798357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.94/3.07 % (798357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.94/3.07 % (798357)CaDiCaL version: 2.1.3
% 19.94/3.07 % (798357)Termination reason: Instruction limit
% 19.94/3.07 % (798357)Termination phase: Saturation
% 19.94/3.07 % (798357)Time elapsed: 0.281 s
% 19.94/3.07 % (798357)Peak memory usage: 14 MB
% 19.94/3.07 % (798357)Instructions burned: 686 (million)
% 19.94/3.07 % (798373)fmb+10_1_sil=64000:random_seed=409440926:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 19.94/3.07 % (798373)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 39.59/5.93 % Exception at run slice level
% 39.59/5.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.59/5.93 % (798374)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3043045674:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 39.59/5.93 % Exception at run slice level
% 39.59/5.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.59/5.93 % (798378)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2166579184:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 39.59/5.93 % (798378)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 39.59/5.93 % (798376)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1442125667:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 39.59/5.93 % Exception at run slice level
% 39.59/5.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.59/5.93 % (798381)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2054732374:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 39.59/5.93 % (798381)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 39.59/5.93 % (798381)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 39.59/5.93 % (798368)Instruction limit reached!
% 39.59/5.93 % (798368)------------------------------
% 39.59/5.93 % (798368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.59/5.93 % (798368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.59/5.93 % (798368)CaDiCaL version: 2.1.3
% 39.59/5.93 % (798368)Termination reason: Instruction limit
% 39.59/5.93 % (798368)Termination phase: Saturation
% 39.59/5.93 % (798368)Time elapsed: 0.318 s
% 39.59/5.93 % (798368)Peak memory usage: 15 MB
% 39.59/5.93 % (798368)Instructions burned: 692 (million)
% 39.59/5.93 % (798383)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3681429070:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 39.59/5.93 % Exception at run slice level
% 39.59/5.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.59/5.93 % (798385)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1653199267:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 39.59/5.93 % Exception at run slice level
% 39.59/5.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.59/5.93 % (798387)ott-2_1_sil=16000:newcnf=on:random_seed=3460157827:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 39.59/5.93 % (798387)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 39.59/5.93 % (798365)Instruction limit reached!
% 39.59/5.93 % (798365)------------------------------
% 39.59/5.93 % (798365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.59/5.93 % (798365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.59/5.93 % (798365)CaDiCaL version: 2.1.3
% 39.59/5.93 % (798365)Termination reason: Instruction limit
% 39.59/5.93 % (798365)Termination phase: Saturation
% 39.59/5.93 % (798365)Time elapsed: 0.550 s
% 39.59/5.93 % (798365)Peak memory usage: 15 MB
% 39.59/5.93 % (798365)Instructions burned: 1179 (million)
% 39.59/5.93 % (798389)ott+10_1_sil=32000:tgt=ground:random_seed=4147522808:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 39.59/5.93 % (798370)Instruction limit reached!
% 39.59/5.93 % (798370)------------------------------
% 39.59/5.93 % (798370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.59/5.93 % (798370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.59/5.93 % (798370)CaDiCaL version: 2.1.3
% 39.59/5.93 % (798370)Termination reason: Instruction limit
% 39.59/5.93 % (798370)Termination phase: Saturation
% 39.59/5.93 % (798370)Time elapsed: 0.750 s
% 39.59/5.93 % (798370)Peak memory usage: 16 MB
% 39.59/5.93 % (798370)Instructions burned: 880 (million)
% 39.59/5.93 % (798387)Instruction limit reached!
% 39.59/5.93 % (798387)------------------------------
% 39.59/5.93 % (798387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.59/5.93 % (798387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.59/5.93 % (798387)CaDiCaL version: 2.1.3
% 39.59/5.93 % (798387)Termination reason: Instruction limit
% 53.31/7.98 % (798387)Termination phase: Saturation
% 53.31/7.98 % (798387)Time elapsed: 0.398 s
% 53.31/7.98 % (798387)Peak memory usage: 15 MB
% 53.31/7.98 % (798387)Instructions burned: 874 (million)
% 53.31/7.98 % (798391)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=207469905:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 53.31/7.98 % Exception at run slice level
% 53.31/7.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 53.31/7.98 % (798392)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3794196178:i=3512:aac=none_2989 on theBenchmark for (2989ds/3512Mi)
% 53.31/7.98 % (798392)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 53.31/7.98 % (798394)dis+21_1_sil=32000:sas=cadical:random_seed=596037650:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 53.31/7.98 % (798381)Instruction limit reached!
% 53.31/7.98 % (798381)------------------------------
% 53.31/7.98 % (798381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798381)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798381)Termination reason: Instruction limit
% 53.31/7.98 % (798381)Termination phase: Saturation
% 53.31/7.98 % (798381)Time elapsed: 0.681 s
% 53.31/7.98 % (798381)Peak memory usage: 14 MB
% 53.31/7.98 % (798381)Instructions burned: 1474 (million)
% 53.31/7.98 % (798397)ott+11_1_sil=16000:gs=on:random_seed=1432458983:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 53.31/7.98 % (798397)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 53.31/7.98 % (798378)Instruction limit reached!
% 53.31/7.98 % (798378)------------------------------
% 53.31/7.98 % (798378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798378)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798378)Termination reason: Instruction limit
% 53.31/7.98 % (798378)Termination phase: Saturation
% 53.31/7.98 % (798378)Time elapsed: 1.277 s
% 53.31/7.98 % (798378)Peak memory usage: 20 MB
% 53.31/7.98 % (798378)Instructions burned: 5133 (million)
% 53.31/7.98 % (798399)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=261996066:fmbsr=1.6:i=67534_2983 on theBenchmark for (2983ds/67534Mi)
% 53.31/7.98 % Exception at run slice level
% 53.31/7.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 53.31/7.98 % (798401)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=751256634:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2982 on theBenchmark for (2982ds/4591Mi)
% 53.31/7.98 % (798397)Instruction limit reached!
% 53.31/7.98 % (798397)------------------------------
% 53.31/7.98 % (798397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798397)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798397)Termination reason: Instruction limit
% 53.31/7.98 % (798397)Termination phase: Saturation
% 53.31/7.98 % (798397)Time elapsed: 0.925 s
% 53.31/7.98 % (798397)Peak memory usage: 15 MB
% 53.31/7.98 % (798397)Instructions burned: 2254 (million)
% 53.31/7.98 % (798403)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=1948311855:i=29340_2979 on theBenchmark for (2979ds/29340Mi)
% 53.31/7.98 % (798392)Instruction limit reached!
% 53.31/7.98 % (798392)------------------------------
% 53.31/7.98 % (798392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798392)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798392)Termination reason: Instruction limit
% 53.31/7.98 % (798392)Termination phase: Saturation
% 53.31/7.98 % (798392)Time elapsed: 1.679 s
% 53.31/7.98 % (798392)Peak memory usage: 18 MB
% 53.31/7.98 % (798392)Instructions burned: 3513 (million)
% 53.31/7.98 % (798405)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=1401537443:i=5211_2972 on theBenchmark for (2972ds/5211Mi)
% 53.31/7.98 % (798401)Instruction limit reached!
% 53.31/7.98 % (798401)------------------------------
% 53.31/7.98 % (798401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798401)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798401)Termination reason: Instruction limit
% 53.31/7.98 % (798401)Termination phase: Saturation
% 53.31/7.98 % (798401)Time elapsed: 1.103 s
% 53.31/7.98 % (798401)Peak memory usage: 18 MB
% 53.31/7.98 % (798401)Instructions burned: 4593 (million)
% 53.31/7.98 % (798407)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=4175463228:i=5497:nm=2_2971 on theBenchmark for (2971ds/5497Mi)
% 53.31/7.98 % Exception at run slice level
% 53.31/7.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 53.31/7.98 % (798409)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=750526188:fmbsr=2:i=46332_2971 on theBenchmark for (2971ds/46332Mi)
% 53.31/7.98 % Exception at run slice level
% 53.31/7.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 53.31/7.98 % (798411)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=256439069:i=14071_2971 on theBenchmark for (2971ds/14071Mi)
% 53.31/7.98 % Exception at run slice level
% 53.31/7.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 53.31/7.98 % (798413)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2507540144:i=22565:add=on:rawr=on_2971 on theBenchmark for (2971ds/22565Mi)
% 53.31/7.98 % (798389)Instruction limit reached!
% 53.31/7.98 % (798389)------------------------------
% 53.31/7.98 % (798389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798389)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798389)Termination reason: Instruction limit
% 53.31/7.98 % (798389)Termination phase: Saturation
% 53.31/7.98 % (798389)Time elapsed: 2.278 s
% 53.31/7.98 % (798389)Peak memory usage: 24 MB
% 53.31/7.98 % (798389)Instructions burned: 5120 (million)
% 53.31/7.98 % (798415)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=579827248:i=8173:av=off_2969 on theBenchmark for (2969ds/8173Mi)
% 53.31/7.98 % (798394)Instruction limit reached!
% 53.31/7.98 % (798394)------------------------------
% 53.31/7.98 % (798394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798394)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798394)Termination reason: Instruction limit
% 53.31/7.98 % (798394)Termination phase: Saturation
% 53.31/7.98 % (798394)Time elapsed: 2.370 s
% 53.31/7.98 % (798394)Peak memory usage: 19 MB
% 53.31/7.98 % (798394)Instructions burned: 3773 (million)
% 53.31/7.98 % (798417)dis+10_16:1_sil=16000:random_seed=1911553401:i=9155:fsr=off_2965 on theBenchmark for (2965ds/9155Mi)
% 53.31/7.98 % (798405)Instruction limit reached!
% 53.31/7.98 % (798405)------------------------------
% 53.31/7.98 % (798405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798405)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798405)Termination reason: Instruction limit
% 53.31/7.98 % (798405)Termination phase: Saturation
% 53.31/7.98 % (798405)Time elapsed: 2.520 s
% 53.31/7.98 % (798405)Peak memory usage: 26 MB
% 53.31/7.98 % (798405)Instructions burned: 5213 (million)
% 53.31/7.98 % (798420)ott-3_8_sil=64000:random_seed=1563795556:i=20139:bs=on_2947 on theBenchmark for (2947ds/20139Mi)
% 53.31/7.98 % (798417)Instruction limit reached!
% 53.31/7.98 % (798417)------------------------------
% 53.31/7.98 % (798417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798417)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798417)Termination reason: Instruction limit
% 53.31/7.98 % (798417)Termination phase: Saturation
% 53.31/7.98 % (798417)Time elapsed: 2.232 s
% 53.31/7.98 % (798417)Peak memory usage: 25 MB
% 53.31/7.98 % (798417)Instructions burned: 9157 (million)
% 53.31/7.98 % (798422)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=3915899107:fmbsr=2:i=32576_2943 on theBenchmark for (2943ds/32576Mi)
% 53.31/7.98 % Exception at run slice level
% 53.31/7.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 53.31/7.98 % (798424)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=2160828273:i=11404_2943 on theBenchmark for (2943ds/11404Mi)
% 53.31/7.98 % (798415)Instruction limit reached!
% 53.31/7.98 % (798415)------------------------------
% 53.31/7.98 % (798415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798415)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798415)Termination reason: Instruction limit
% 53.31/7.98 % (798415)Termination phase: Saturation
% 53.31/7.98 % (798415)Time elapsed: 3.721 s
% 53.31/7.98 % (798415)Peak memory usage: 30 MB
% 53.31/7.98 % (798415)Instructions burned: 8173 (million)
% 53.31/7.98 % (798426)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=1719972459:i=14134_2932 on theBenchmark for (2932ds/14134Mi)
% 53.31/7.98 % (798426)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 53.31/7.98 % (798420) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-798334-798420"...
% 53.31/7.98 % (798420)...printing done.
% 53.31/7.98 % (798420)Refutation found. Thanks to Tanya!
% 53.31/7.98 % SZS status Theorem for theBenchmark
% 53.31/7.98 % SZS output start Proof for theBenchmark
% 53.31/7.98 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 53.31/7.98 thf(func_def_0, type, in: ($i > $i > $o)).
% 53.31/7.98 thf(func_def_1, type, subset: ($i > $i > $o)).
% 53.31/7.98 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 53.31/7.98 thf(func_def_3, type, cartprod: ($i > $i > $i)).
% 53.31/7.98 thf(func_def_4, type, breln: ($i > $i > $i > $o)).
% 53.31/7.98 thf(func_def_6, type, brelnall2: $o).
% 53.31/7.98 thf(func_def_7, type, breln1: ($i > $i > $o)).
% 53.31/7.98 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 53.31/7.98 thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
% 53.31/7.98 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 53.31/7.98 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 53.31/7.98 thf(func_def_12, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 53.31/7.98 thf(func_def_13, type, vIMP: ($o > $o > $o)).
% 53.31/7.98 thf(func_def_14, type, db4: !>[X0: $tType]:(X0)).
% 53.31/7.98 thf(func_def_15, type, db5: !>[X0: $tType]:(X0)).
% 53.31/7.98 thf(func_def_20, type, sK2: ($i > $o)).
% 53.31/7.98 thf(func_def_22, type, vNOT: ($o > $o)).
% 53.31/7.98 thf(func_def_23, type, sK4: ($i > $i > ($i > $o) > $i > $i)).
% 53.31/7.98 thf(func_def_24, type, sK5: ($i > $i > $i > ($i > $o) > $i)).
% 53.31/7.98 thf(func_def_26, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 53.31/7.98 thf(f1,axiom,(
% 53.31/7.98 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 53.31/7.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 53.31/7.98 thf(f2,axiom,(
% 53.31/7.98 (brelnall2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4)))))),
% 53.31/7.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2)).
% 53.31/7.98 thf(f3,axiom,(
% 53.31/7.98 (breln1 = (^[X0 : $i, X1 : $i] : ((breln @ X0 @ X0 @ X1))))),
% 53.31/7.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1)).
% 53.31/7.98 thf(f4,conjecture,(
% 53.31/7.98 brelnall2 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X3 : $i] : ((in @ X3 @ X1) => (X2 @ X3))))),
% 53.31/7.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all2)).
% 53.31/7.98 thf(f5,negated_conjecture,(
% 53.31/7.98 ~(brelnall2 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X3 : $i] : ((in @ X3 @ X1) => (X2 @ X3)))))),
% 53.31/7.98 inference(negated_conjecture,[status(cth)],[f4])).
% 53.31/7.98 thf(f6,plain,(
% 53.31/7.98 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 53.31/7.98 inference(fool_elimination,[],[f1])).
% 53.31/7.98 thf(f7,plain,(
% 53.31/7.98 (brelnall2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X2) => (X3 @ X6)))))),
% 53.31/7.98 inference(rectify,[],[f2])).
% 53.31/7.98 thf(f8,plain,(
% 53.31/7.98 (brelnall2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (Y3 @ Y4))))))))))))))))),
% 53.31/7.98 inference(fool_elimination,[],[f7])).
% 53.31/7.98 thf(f9,plain,(
% 53.31/7.98 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 53.31/7.98 inference(fool_elimination,[],[f3])).
% 53.31/7.98 thf(f10,plain,(
% 53.31/7.98 ~(brelnall2 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X1) => (X2 @ X5)))))),
% 53.31/7.98 inference(rectify,[],[f5])).
% 53.31/7.98 thf(f11,plain,(
% 53.31/7.98 ~((brelnall2 = $true) => ! [X0 : $i,X1 : $i] : ((((breln1 @ X0 @ X1)) = $true) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((in @ (kpair @ X3 @ X4) @ X1)) = $true) => (((X2 @ (kpair @ X3 @ X4))) = $true)))) => ! [X5 : $i] : ((((in @ X5 @ X1)) = $true) => (((X2 @ X5)) = $true)))))),
% 53.31/7.98 inference(fool_elimination,[],[f10])).
% 53.31/7.98 thf(f12,plain,(
% 53.31/7.98 ? [X0 : $i,X1 : $i] : (? [X2 : ($i > $o)] : (? [X5 : $i] : ((((X2 @ X5)) != $true) & (((in @ X5 @ X1)) = $true)) & ! [X3 : $i] : (! [X4 : $i] : (((((X2 @ (kpair @ X3 @ X4))) = $true) | (((in @ (kpair @ X3 @ X4) @ X1)) != $true)) | (((in @ X4 @ X0)) != $true)) | (((in @ X3 @ X0)) != $true))) & (((breln1 @ X0 @ X1)) = $true)) & (brelnall2 = $true)),
% 53.31/7.98 inference(ennf_transformation,[],[f11])).
% 53.31/7.98 thf(f13,plain,(
% 53.31/7.98 ? [X0 : $i,X1 : $i] : (? [X2 : ($i > $o)] : (? [X5 : $i] : ((((X2 @ X5)) != $true) & (((in @ X5 @ X1)) = $true)) & ! [X3 : $i] : (! [X4 : $i] : ((((X2 @ (kpair @ X3 @ X4))) = $true) | (((in @ (kpair @ X3 @ X4) @ X1)) != $true) | (((in @ X4 @ X0)) != $true)) | (((in @ X3 @ X0)) != $true))) & (((breln1 @ X0 @ X1)) = $true)) & (brelnall2 = $true)),
% 53.31/7.98 inference(flattening,[],[f12])).
% 53.31/7.98 thf(f14,plain,(
% 53.31/7.98 ? [X0 : $i,X1 : $i] : (? [X2 : ($i > $o)] : (? [X3 : $i] : ((((X2 @ X3)) != $true) & (((in @ X3 @ X1)) = $true)) & ! [X4 : $i] : (! [X5 : $i] : (($true = ((X2 @ (kpair @ X4 @ X5)))) | ($true != ((in @ (kpair @ X4 @ X5) @ X1))) | ($true != ((in @ X5 @ X0)))) | (((in @ X4 @ X0)) != $true))) & (((breln1 @ X0 @ X1)) = $true)) & (brelnall2 = $true)),
% 53.31/7.98 inference(rectify,[],[f13])).
% 53.31/7.98 thf(f15,plain,(
% 53.31/7.98 (((($true != ((sK2 @ sK3))) & ($true = ((in @ sK3 @ sK1)))) & ! [X4 : $i] : (! [X5 : $i] : (($true = ((sK2 @ (kpair @ X4 @ X5)))) | ($true != ((in @ (kpair @ X4 @ X5) @ sK1))) | ($true != ((in @ X5 @ sK0)))) | ($true != ((in @ X4 @ sK0))))) & ($true = ((breln1 @ sK0 @ sK1)))) & (brelnall2 = $true)),
% 53.31/7.98 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f14])).
% 53.31/7.98 thf(f16,plain,(
% 53.31/7.98 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 53.31/7.98 inference(cnf_transformation,[],[f6])).
% 53.31/7.98 thf(f17,plain,(
% 53.31/7.98 (brelnall2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (Y3 @ Y4))))))))))))))))),
% 53.31/7.98 inference(cnf_transformation,[],[f8])).
% 53.31/7.98 thf(f18,plain,(
% 53.31/7.98 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 53.31/7.98 inference(cnf_transformation,[],[f9])).
% 53.31/7.98 thf(f19,plain,(
% 53.31/7.98 (brelnall2 = $true)),
% 53.31/7.98 inference(cnf_transformation,[],[f15])).
% 53.31/7.98 thf(f20,plain,(
% 53.31/7.98 ($true = ((breln1 @ sK0 @ sK1)))),
% 53.31/7.98 inference(cnf_transformation,[],[f15])).
% 53.31/7.98 thf(f21,plain,(
% 53.31/7.98 ( ! [X4 : $i,X5 : $i] : (($true != ((in @ X5 @ sK0))) | ($true != ((in @ (kpair @ X4 @ X5) @ sK1))) | ($true = ((sK2 @ (kpair @ X4 @ X5)))) | ($true != ((in @ X4 @ sK0)))) )),
% 53.31/7.98 inference(cnf_transformation,[],[f15])).
% 53.31/7.98 thf(f22,plain,(
% 53.31/7.98 ($true = ((in @ sK3 @ sK1)))),
% 53.31/7.98 inference(cnf_transformation,[],[f15])).
% 53.31/7.98 thf(f23,plain,(
% 53.31/7.98 ($true != ((sK2 @ sK3)))),
% 53.31/7.98 inference(cnf_transformation,[],[f15])).
% 53.31/7.98 thf(f25,definition,(
% 53.31/7.98 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 53.31/7.98 introduced(theory,[fool_exhaustiveness_axiom])).
% 53.31/7.98 thf(f26,plain,(
% 53.31/7.98 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 53.31/7.98 inference(definition_unfolding,[],[f18,f16])).
% 53.31/7.98 thf(f27,plain,(
% 53.31/7.98 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (Y3 @ Y4))))))))))))))))),
% 53.31/7.98 inference(definition_unfolding,[],[f17,f19,f16])).
% 53.31/7.98 thf(f28,plain,(
% 53.31/7.98 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ sK1)))),
% 53.31/7.98 inference(definition_unfolding,[],[f20,f26])).
% 53.31/7.98 thf(f29,plain,(
% 53.31/7.98 ($true = ((subset @ sK1 @ (cartprod @ sK0 @ sK0))))),
% 53.31/7.98 inference(beta-eta_normalization,[],[f28])).
% 53.31/7.98 thf(f30,plain,(
% 53.31/7.98 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y1 @ Y0) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (Y3 @ Y4))))))))))))) @ X1)))) )),
% 53.31/7.98 inference(pi_proxy_clausification,[],[f27])).
% 53.31/7.98 thf(f31,plain,(
% 53.31/7.98 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ (cartprod @ Y1 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => (Y2 @ Y3))))))))))))))) )),
% 53.31/7.98 inference(beta-eta_normalization,[],[f30])).
% 53.31/7.98 thf(f32,plain,(
% 53.31/7.98 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ (cartprod @ Y1 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => (Y2 @ Y3))))))))))) @ X2)))) )),
% 53.31/7.98 inference(pi_proxy_clausification,[],[f31])).
% 53.31/7.98 thf(f33,plain,(
% 53.31/7.98 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ X2)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (Y1 @ Y2))))))))))))) )),
% 53.31/7.98 inference(beta-eta_normalization,[],[f32])).
% 53.31/7.98 thf(f34,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ X2)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (Y1 @ Y2))))))))) @ X3)))) )),
% 53.31/7.98 inference(pi_proxy_clausification,[],[f33])).
% 53.31/7.98 thf(f35,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((subset @ X1 @ (cartprod @ X3 @ X2)) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (Y0 @ Y1))))))))))) )),
% 53.31/7.98 inference(beta-eta_normalization,[],[f34])).
% 53.31/7.98 thf(f36,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (Y0 @ Y1)))))))))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f35])).
% 53.31/7.98 thf(f37,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o)] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (Y0 @ Y1)))))) @ X4)))) )),
% 53.31/7.98 inference(pi_proxy_clausification,[],[f36])).
% 53.31/7.98 thf(f38,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o)] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (X4 @ (kpair @ Y0 @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (X4 @ Y0)))))))) )),
% 53.31/7.98 inference(beta-eta_normalization,[],[f37])).
% 53.31/7.98 thf(f39,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o)] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (X4 @ (kpair @ Y0 @ Y1))))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (X4 @ Y0))))))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f38])).
% 53.31/7.98 thf(f40,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o)] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (X4 @ (kpair @ Y0 @ Y1)))))))) @ (sK4 @ X3 @ X1 @ X4 @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (X4 @ Y0))))))) )),
% 53.31/7.98 inference(sigma_proxy_clausification,[],[f39])).
% 53.31/7.98 thf(f41,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (X4 @ (kpair @ Y0 @ Y1)))))))) @ (sK4 @ X3 @ X1 @ X4 @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X1) => (X4 @ Y0))) @ X5)))) )),
% 53.31/7.98 inference(pi_proxy_clausification,[],[f40])).
% 53.31/7.98 thf(f42,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((in @ (sK4 @ X3 @ X1 @ X4 @ X2) @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X1) => (X4 @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ Y0))))))))) | ($true = (((in @ X5 @ X1) => (X4 @ X5))))) )),
% 53.31/7.98 inference(beta-eta_normalization,[],[f41])).
% 53.31/7.98 thf(f43,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X1) => (X4 @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) | ($true = (((in @ X5 @ X1) => (X4 @ X5))))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f42])).
% 53.31/7.98 thf(f44,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = ((in @ (sK4 @ X3 @ X1 @ X4 @ X2) @ X3))) | ($true = (((in @ X5 @ X1) => (X4 @ X5))))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f42])).
% 53.31/7.98 thf(f45,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ X5))) | (((in @ X5 @ X1)) = $false) | ($true = ((in @ (sK4 @ X3 @ X1 @ X4 @ X2) @ X3))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f44])).
% 53.31/7.98 thf(f46,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X1) => (X4 @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ Y0))))) @ (sK5 @ X1 @ X2 @ X3 @ X4)))) | ($true = (((in @ X5 @ X1) => (X4 @ X5))))) )),
% 53.31/7.98 inference(sigma_proxy_clausification,[],[f43])).
% 53.31/7.98 thf(f47,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X1) => (X4 @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ Y0))))) @ (sK5 @ X1 @ X2 @ X3 @ X4)))) | (((in @ X5 @ X1)) = $false) | ($true = ((X4 @ X5)))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f46])).
% 53.31/7.98 thf(f48,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((in @ (sK5 @ X1 @ X2 @ X3 @ X4) @ X2) => ((in @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ (sK5 @ X1 @ X2 @ X3 @ X4)) @ X1) => (X4 @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ (sK5 @ X1 @ X2 @ X3 @ X4))))))) | (((in @ X5 @ X1)) = $false) | ($true = ((X4 @ X5)))) )),
% 53.31/7.98 inference(beta-eta_normalization,[],[f47])).
% 53.31/7.98 thf(f49,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((in @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ (sK5 @ X1 @ X2 @ X3 @ X4)) @ X1) => (X4 @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ (sK5 @ X1 @ X2 @ X3 @ X4)))))) | (((in @ X5 @ X1)) = $false) | ($true = ((X4 @ X5)))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f48])).
% 53.31/7.98 thf(f50,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ X5))) | (((in @ X5 @ X1)) = $false) | ($true = ((in @ (sK5 @ X1 @ X2 @ X3 @ X4) @ X2))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f48])).
% 53.31/7.98 thf(f51,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ X5))) | (((in @ X5 @ X1)) = $false) | ($false = ((X4 @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ (sK5 @ X1 @ X2 @ X3 @ X4))))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f49])).
% 53.31/7.98 thf(f52,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ X5))) | (((in @ X5 @ X1)) = $false) | ($true = ((in @ (kpair @ (sK4 @ X3 @ X1 @ X4 @ X2) @ (sK5 @ X1 @ X2 @ X3 @ X4)) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 53.31/7.98 inference(imp_proxy_clausification,[],[f49])).
% 53.31/7.98 thf(f65,plain,(
% 53.31/7.98 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != ((in @ (kpair @ X1 @ X0) @ sK1))) | ($true = ((sK2 @ (kpair @ X1 @ X0)))) | ($true != ((in @ X1 @ sK0))) | ($false = ((in @ X0 @ sK0)))) )),
% 53.31/7.98 inference(constrained_superposition,[],[f21,f25])).
% 53.31/7.98 thf(f66,plain,(
% 53.31/7.98 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK0))) | ($true = ((sK2 @ (kpair @ X1 @ X0)))) | ($true != ((in @ (kpair @ X1 @ X0) @ sK1))) | ($false = ((in @ X0 @ sK0)))) )),
% 53.31/7.98 inference(trivial_inequality_removal,[],[f65])).
% 53.31/7.98 thf(f102,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o),X4 : $i] : (($true != $true) | ($true = ((sK2 @ (kpair @ (sK4 @ sK0 @ X0 @ X1 @ X2) @ X3)))) | ($true != ((in @ (kpair @ (sK4 @ sK0 @ X0 @ X1 @ X2) @ X3) @ sK1))) | ($false = ((in @ X3 @ sK0))) | ($true = ((X1 @ X4))) | (((in @ X4 @ X0)) = $false) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ X2))))) )),
% 53.31/7.98 inference(constrained_superposition,[],[f66,f45])).
% 53.31/7.98 thf(f133,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o),X4 : $i] : (($true != ((in @ (kpair @ (sK4 @ sK0 @ X0 @ X1 @ X2) @ X3) @ sK1))) | ($true = ((sK2 @ (kpair @ (sK4 @ sK0 @ X0 @ X1 @ X2) @ X3)))) | ($false = ((in @ X3 @ sK0))) | ($true = ((X1 @ X4))) | (((in @ X4 @ X0)) = $false) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ X2))))) )),
% 53.31/7.98 inference(trivial_inequality_removal,[],[f102])).
% 53.31/7.98 thf(f7365,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i,X4 : $i] : (($false != ((X0 @ X4))) | ($true = ((X0 @ X4))) | (((in @ X4 @ X2)) = $false) | ($false = ((subset @ X2 @ (cartprod @ X1 @ X3)))) | ($true != ((X0 @ (kpair @ (sK4 @ X1 @ X2 @ X0 @ X3) @ (sK5 @ X2 @ X3 @ X1 @ X0)))))) )),
% 53.31/7.98 inference(equality_factoring,[],[f51])).
% 53.31/7.98 thf(f7948,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i,X4 : $i] : (($true != ((X0 @ (kpair @ (sK4 @ X1 @ X2 @ X0 @ X3) @ (sK5 @ X2 @ X3 @ X1 @ X0))))) | (((in @ X4 @ X2)) = $false) | ($false = ((subset @ X2 @ (cartprod @ X1 @ X3)))) | ($true = ((X0 @ X4)))) )),
% 53.31/7.98 inference(forward_subsumption_resolution,[],[f7365,f25])).
% 53.31/7.98 thf(f13294,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($false = ((in @ X0 @ X1))) | ($true = ((in @ (kpair @ (sK4 @ X2 @ X1 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X3) @ (sK5 @ X1 @ X3 @ X2 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X3)))) | (sK3 != X0)) )),
% 53.31/7.98 inference(constrained_superposition,[],[f23,f52])).
% 53.31/7.98 thf(f13900,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = ((in @ X0 @ X1))) | ($true = ((in @ (kpair @ (sK4 @ X2 @ X1 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X3) @ (sK5 @ X1 @ X3 @ X2 @ (^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X3)))) | (sK3 != X0)) )),
% 53.31/7.98 inference(trivial_inequality_removal,[],[f13294])).
% 53.31/7.98 thf(f13901,plain,(
% 53.31/7.98 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((sK3 != X0) | ($true = ((in @ (kpair @ (sK4 @ X2 @ X1 @ sK2 @ X3) @ (sK5 @ X1 @ X3 @ X2 @ sK2)) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X3)))) | ($false = ((in @ X0 @ X1)))) )),
% 53.31/7.98 inference(beta-eta_normalization,[],[f13900])).
% 53.31/7.98 thf(f14183,plain,(
% 53.31/7.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (kpair @ (sK4 @ X0 @ X1 @ sK2 @ X2) @ (sK5 @ X1 @ X2 @ X0 @ sK2)) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X0 @ X2)))) | ($false = ((in @ sK3 @ X1)))) )),
% 53.31/7.98 inference(equality_resolution,[],[f13901])).
% 53.31/7.98 thf(f14264,plain,(
% 53.31/7.98 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((sK2 @ (kpair @ (sK4 @ sK0 @ sK1 @ sK2 @ X0) @ (sK5 @ sK1 @ X0 @ sK0 @ sK2))))) | ($false = ((in @ (sK5 @ sK1 @ X0 @ sK0 @ sK2) @ sK0))) | ($true = ((sK2 @ X1))) | ($false = ((in @ X1 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0)))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0)))) | (((in @ sK3 @ sK1)) = $false)) )),
% 53.31/7.98 inference(constrained_superposition,[],[f133,f14183])).
% 53.31/7.98 thf(f14307,plain,(
% 53.31/7.98 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((sK2 @ (kpair @ (sK4 @ sK0 @ sK1 @ sK2 @ X0) @ (sK5 @ sK1 @ X0 @ sK0 @ sK2))))) | ($false = ((in @ (sK5 @ sK1 @ X0 @ sK0 @ sK2) @ sK0))) | ($true = ((sK2 @ X1))) | ($false = ((in @ X1 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0)))) | (((in @ sK3 @ sK1)) = $false)) )),
% 53.31/7.98 inference(duplicate_literal_removal,[],[f14264])).
% 53.31/7.98 thf(f14308,plain,(
% 53.31/7.98 ( ! [X0 : $i,X1 : $i] : (($true = ((sK2 @ (kpair @ (sK4 @ sK0 @ sK1 @ sK2 @ X0) @ (sK5 @ sK1 @ X0 @ sK0 @ sK2))))) | ($false = ((in @ (sK5 @ sK1 @ X0 @ sK0 @ sK2) @ sK0))) | ($true = ((sK2 @ X1))) | ($false = ((in @ X1 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0)))) | (((in @ sK3 @ sK1)) = $false)) )),
% 53.31/7.98 inference(trivial_inequality_removal,[],[f14307])).
% 53.31/7.98 thf(f14394,plain,(
% 53.31/7.98 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (sK5 @ sK1 @ X0 @ sK0 @ sK2) @ sK0))) | ($true = ((sK2 @ X1))) | ($false = ((in @ X1 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0)))) | (((in @ sK3 @ sK1)) = $false)) )),
% 53.31/7.98 inference(forward_subsumption_resolution,[],[f14308,f7948])).
% 53.31/7.98 thf(f14427,plain,(
% 53.31/7.98 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (sK5 @ sK1 @ X0 @ sK0 @ sK2) @ sK0))) | ($true = ((sK2 @ X1))) | ($false = ((in @ X1 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0))))) )),
% 53.31/7.98 inference(forward_demodulation,[],[f14394,f22])).
% 53.31/7.98 thf(f14428,plain,(
% 53.31/7.98 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (sK5 @ sK1 @ X0 @ sK0 @ sK2) @ sK0))) | ($true = ((sK2 @ X1))) | ($false = ((in @ X1 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0))))) )),
% 53.31/7.98 inference(trivial_inequality_removal,[],[f14427])).
% 53.31/7.98 thf(f14430,definition,(
% 53.31/7.98 spl6_11 <=> ! [X1 : $i] : (($true = ((sK2 @ X1))) | ($false = ((in @ X1 @ sK1))))),
% 53.31/7.98 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 53.31/7.98 thf(f14431,plain,(
% 53.31/7.98 ( ! [X1 : $i] : (($false = ((in @ X1 @ sK1))) | ($true = ((sK2 @ X1)))) ) | ~spl6_11),
% 53.31/7.98 inference(avatar_component_clause,[],[f14430])).
% 53.31/7.98 thf(f14433,definition,(
% 53.31/7.98 spl6_12 <=> ! [X0 : $i] : (($false = ((in @ (sK5 @ sK1 @ X0 @ sK0 @ sK2) @ sK0))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0)))))),
% 53.31/7.98 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 53.31/7.98 thf(f14434,plain,(
% 53.31/7.98 ( ! [X0 : $i] : (($false = ((in @ (sK5 @ sK1 @ X0 @ sK0 @ sK2) @ sK0))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ X0))))) ) | ~spl6_12),
% 53.31/7.98 inference(avatar_component_clause,[],[f14433])).
% 53.31/7.98 thf(f14435,plain,(
% 53.31/7.98 spl6_11 | spl6_12),
% 53.31/7.98 inference(avatar_split_clause,[],[f14428,f14433,f14430])).
% 53.31/7.98 thf(f14578,plain,(
% 53.31/7.98 ($true = $false) | ($true = ((sK2 @ sK3))) | ~spl6_11),
% 53.31/7.98 inference(constrained_superposition,[],[f14431,f22])).
% 53.31/7.98 thf(f14765,plain,(
% 53.31/7.98 ($true = ((sK2 @ sK3))) | ~spl6_11),
% 53.31/7.98 inference(trivial_inequality_removal,[],[f14578])).
% 53.31/7.98 thf(f14811,plain,(
% 53.31/7.98 $false | ~spl6_11),
% 53.31/7.98 inference(forward_subsumption_resolution,[],[f14765,f23])).
% 53.31/7.98 thf(f14812,plain,(
% 53.31/7.98 ~spl6_11),
% 53.31/7.98 inference(avatar_contradiction_clause,[],[f14811])).
% 53.31/7.98 thf(f15025,plain,(
% 53.31/7.98 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK2 @ X0))) | ($false = ((in @ X0 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0)))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0))))) ) | ~spl6_12),
% 53.31/7.98 inference(constrained_superposition,[],[f50,f14434])).
% 53.31/7.98 thf(f15095,plain,(
% 53.31/7.98 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK2 @ X0))) | ($false = ((in @ X0 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0))))) ) | ~spl6_12),
% 53.31/7.98 inference(duplicate_literal_removal,[],[f15025])).
% 53.31/7.98 thf(f15096,plain,(
% 53.31/7.98 ( ! [X0 : $i] : (($true = ((sK2 @ X0))) | ($false = ((in @ X0 @ sK1))) | ($false = ((subset @ sK1 @ (cartprod @ sK0 @ sK0))))) ) | ~spl6_12),
% 53.31/7.98 inference(trivial_inequality_removal,[],[f15095])).
% 53.31/7.98 thf(f15126,plain,(
% 53.31/7.98 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK2 @ X0))) | ($false = ((in @ X0 @ sK1)))) ) | ~spl6_12),
% 53.31/7.98 inference(forward_demodulation,[],[f15096,f29])).
% 53.31/7.98 thf(f15127,plain,(
% 53.31/7.98 ( ! [X0 : $i] : (($true = ((sK2 @ X0))) | ($false = ((in @ X0 @ sK1)))) ) | ~spl6_12),
% 53.31/7.98 inference(trivial_inequality_removal,[],[f15126])).
% 53.31/7.98 thf(f15132,plain,(
% 53.31/7.98 spl6_11 | ~spl6_12),
% 53.31/7.98 inference(avatar_split_clause,[],[f15127,f14433,f14430])).
% 53.31/7.98 cnf(s8, plain, spl6_11 | spl6_12, inference(sat_conversion,[],[f14435])).
% 53.31/7.98 cnf(s10, plain, ~spl6_11, inference(sat_conversion,[],[f14812])).
% 53.31/7.98 cnf(s11, plain, spl6_11 | ~spl6_12, inference(sat_conversion,[],[f15132])).
% 53.31/7.98 cnf(s13, plain, ~spl6_12, inference(rat,[],[s11,s10])).
% 53.31/7.98 cnf(s14, plain, $false, inference(rat,[],[s8,s13,s10])).
% 53.31/7.98 thf(f15133,plain,(
% 53.31/7.98 $false),
% 53.31/7.98 inference(avatar_sat_refutation,[],[s14])).
% 53.31/7.98 % SZS output end Proof for theBenchmark
% 53.31/7.98 % (798420)------------------------------
% 53.31/7.98 % (798420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 53.31/7.98 % (798420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.31/7.98 % (798420)CaDiCaL version: 2.1.3
% 53.31/7.98 % (798420)Termination reason: Refutation
% 53.31/7.98 % (798420)Time elapsed: 2.450 s
% 53.31/7.98 % (798420)Peak memory usage: 21 MB
% 53.31/7.98 % (798420)Instructions burned: 5194 (million)
% 53.31/7.98 % (798334)Success in time 7.738 s
% 53.31/7.98 % Vampire exiting
%------------------------------------------------------------------------------