%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU682^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:32:58 AM UTC 2026
% Result : Theorem 65.20s 9.40s
% Output : Refutation 65.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU682^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:08:15 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.20/1.04 % (2717676)Will run a generic schedule for satisfiability detection.
% 4.20/1.04 % (2717682)% WARNING: option uhcvi not known.
% 4.20/1.04 % (2717682)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3917204856:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.20/1.04 % (2717682)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.20/1.04 % (2717682)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.20/1.04 % (2717681)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2819106702_2999 on theBenchmark for (2999ds/0Mi)
% 4.20/1.04 % (2717683)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=441274968:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.20/1.04 % (2717684)dis+10_1_sil=32000:sp=arity:random_seed=2071163361:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.20/1.04 % (2717685)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=62548767:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.20/1.04 % (2717685)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.20/1.04 % Exception at run slice level
% 4.20/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.20/1.04 % (2717686)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3115920450:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.20/1.04 % (2717687)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3358263790:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.20/1.04 % (2717693)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3029913065:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.20/1.04 % Exception at run slice level
% 4.20/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.20/1.04 % (2717697)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1335386208:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.20/1.04 % (2717684)Instruction limit reached!
% 4.20/1.04 % (2717684)------------------------------
% 4.20/1.05 % (2717684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.05 % (2717684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.05 % (2717684)CaDiCaL version: 2.1.3
% 4.20/1.05 % (2717684)Termination reason: Instruction limit
% 4.20/1.05 % (2717684)Termination phase: Saturation
% 4.20/1.05 % (2717684)Time elapsed: 0.050 s
% 4.20/1.05 % (2717684)Peak memory usage: 12 MB
% 4.20/1.05 % (2717684)Instructions burned: 104 (million)
% 4.20/1.05 % (2717685)Instruction limit reached!
% 4.20/1.05 % (2717685)------------------------------
% 4.20/1.05 % (2717685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.05 % (2717685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.05 % (2717685)CaDiCaL version: 2.1.3
% 4.20/1.05 % (2717685)Termination reason: Instruction limit
% 4.20/1.05 % (2717685)Termination phase: Saturation
% 4.20/1.05 % (2717685)Time elapsed: 0.056 s
% 4.20/1.05 % (2717685)Peak memory usage: 12 MB
% 4.20/1.05 % (2717685)Instructions burned: 116 (million)
% 4.20/1.05 % (2717699)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=423781060:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.20/1.05 % (2717699)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.20/1.05 % (2717699)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.20/1.05 % (2717700)ott-21_1_sil=16000:fs=off:random_seed=4239113393:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.20/1.05 % (2717686)Instruction limit reached!
% 4.20/1.05 % (2717686)------------------------------
% 4.20/1.05 % (2717686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.05 % (2717686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.05 % (2717686)CaDiCaL version: 2.1.3
% 4.20/1.05 % (2717686)Termination reason: Instruction limit
% 4.20/1.05 % (2717686)Termination phase: Saturation
% 4.20/1.05 % (2717686)Time elapsed: 0.064 s
% 4.20/1.05 % (2717686)Peak memory usage: 13 MB
% 4.20/1.05 % (2717686)Instructions burned: 131 (million)
% 4.20/1.05 % (2717703)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2036589902:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 29.01/4.32 % (2717697)Instruction limit reached!
% 29.01/4.32 % (2717697)------------------------------
% 29.01/4.32 % (2717697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.01/4.32 % (2717697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.01/4.32 % (2717697)CaDiCaL version: 2.1.3
% 29.01/4.32 % (2717697)Termination reason: Instruction limit
% 29.01/4.32 % (2717697)Termination phase: Saturation
% 29.01/4.32 % (2717697)Time elapsed: 0.065 s
% 29.01/4.32 % (2717697)Peak memory usage: 12 MB
% 29.01/4.32 % (2717697)Instructions burned: 132 (million)
% 29.01/4.32 % (2717687)Instruction limit reached!
% 29.01/4.32 % (2717687)------------------------------
% 29.01/4.32 % (2717687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.01/4.32 % (2717687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.01/4.32 % (2717687)CaDiCaL version: 2.1.3
% 29.01/4.32 % (2717687)Termination reason: Instruction limit
% 29.01/4.32 % (2717687)Termination phase: Saturation
% 29.01/4.32 % (2717687)Time elapsed: 0.094 s
% 29.01/4.32 % (2717687)Peak memory usage: 12 MB
% 29.01/4.32 % (2717687)Instructions burned: 159 (million)
% 29.01/4.32 % (2717707)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1976867637:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 29.01/4.32 % Exception at run slice level
% 29.01/4.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.01/4.32 % (2717709)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1182809841:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 29.01/4.32 % (2717717)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3002933252:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 29.01/4.32 % Exception at run slice level
% 29.01/4.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.01/4.32 % (2717700)Instruction limit reached!
% 29.01/4.32 % (2717700)------------------------------
% 29.01/4.32 % (2717700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.01/4.32 % (2717700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.01/4.32 % (2717700)CaDiCaL version: 2.1.3
% 29.01/4.32 % (2717700)Termination reason: Instruction limit
% 29.01/4.32 % (2717700)Termination phase: Saturation
% 29.01/4.32 % (2717700)Time elapsed: 0.085 s
% 29.01/4.32 % (2717700)Peak memory usage: 12 MB
% 29.01/4.32 % (2717700)Instructions burned: 181 (million)
% 29.01/4.32 % (2717726)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=2745452720:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 29.01/4.32 % (2717726)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.01/4.32 % (2717730)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4193537150:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 29.01/4.32 % (2717730)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.01/4.32 % (2717703)Instruction limit reached!
% 29.01/4.32 % (2717703)------------------------------
% 29.01/4.32 % (2717703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.01/4.32 % (2717703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.01/4.32 % (2717703)CaDiCaL version: 2.1.3
% 29.01/4.32 % (2717703)Termination reason: Instruction limit
% 29.01/4.32 % (2717703)Termination phase: Saturation
% 29.01/4.32 % (2717703)Time elapsed: 0.237 s
% 29.01/4.32 % (2717703)Peak memory usage: 13 MB
% 29.01/4.32 % (2717703)Instructions burned: 477 (million)
% 29.01/4.32 % (2717793)fmb+10_1_sil=64000:random_seed=3386590782:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 29.01/4.32 % (2717793)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 29.01/4.32 % Exception at run slice level
% 29.01/4.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.01/4.32 % (2717800)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3511496591:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 29.01/4.32 % Exception at run slice level
% 29.01/4.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.49/8.63 % (2717699)Instruction limit reached!
% 59.49/8.63 % (2717699)------------------------------
% 59.49/8.63 % (2717699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.49/8.63 % (2717699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.49/8.63 % (2717699)CaDiCaL version: 2.1.3
% 59.49/8.63 % (2717699)Termination reason: Instruction limit
% 59.49/8.63 % (2717699)Termination phase: Saturation
% 59.49/8.63 % (2717699)Time elapsed: 0.320 s
% 59.49/8.63 % (2717699)Peak memory usage: 14 MB
% 59.49/8.63 % (2717699)Instructions burned: 685 (million)
% 59.49/8.63 % (2717802)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2911742147:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 59.49/8.63 % Exception at run slice level
% 59.49/8.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.49/8.63 % (2717803)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=364766916:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 59.49/8.63 % (2717803)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 59.49/8.63 % (2717809)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3854242283:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 59.49/8.63 % (2717809)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 59.49/8.63 % (2717809)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 59.49/8.63 % (2717726)Instruction limit reached!
% 59.49/8.63 % (2717726)------------------------------
% 59.49/8.63 % (2717726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.49/8.63 % (2717726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.49/8.63 % (2717726)CaDiCaL version: 2.1.3
% 59.49/8.63 % (2717726)Termination reason: Instruction limit
% 59.49/8.63 % (2717726)Termination phase: Saturation
% 59.49/8.63 % (2717726)Time elapsed: 0.344 s
% 59.49/8.63 % (2717726)Peak memory usage: 15 MB
% 59.49/8.63 % (2717726)Instructions burned: 693 (million)
% 59.49/8.63 % (2717836)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2038588955:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 59.49/8.63 % Exception at run slice level
% 59.49/8.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.49/8.63 % (2717844)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2808131760:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 59.49/8.63 % Exception at run slice level
% 59.49/8.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.49/8.63 % (2717850)ott-2_1_sil=16000:newcnf=on:random_seed=1168187147:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 59.49/8.63 % (2717850)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 59.49/8.63 % (2717730)Instruction limit reached!
% 59.49/8.63 % (2717730)------------------------------
% 59.49/8.63 % (2717730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.49/8.63 % (2717730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.49/8.63 % (2717730)CaDiCaL version: 2.1.3
% 59.49/8.63 % (2717730)Termination reason: Instruction limit
% 59.49/8.63 % (2717730)Termination phase: Saturation
% 59.49/8.63 % (2717730)Time elapsed: 0.431 s
% 59.49/8.63 % (2717730)Peak memory usage: 15 MB
% 59.49/8.63 % (2717730)Instructions burned: 879 (million)
% 59.49/8.63 % (2717858)ott+10_1_sil=32000:tgt=ground:random_seed=1738974432:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 59.49/8.63 % (2717709)Instruction limit reached!
% 59.49/8.63 % (2717709)------------------------------
% 59.49/8.63 % (2717709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.49/8.63 % (2717709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.49/8.63 % (2717709)CaDiCaL version: 2.1.3
% 59.49/8.63 % (2717709)Termination reason: Instruction limit
% 59.49/8.63 % (2717709)Termination phase: Saturation
% 59.49/8.63 % (2717709)Time elapsed: 0.620 s
% 59.49/8.63 % (2717709)Peak memory usage: 16 MB
% 59.49/8.63 % (2717709)Instructions burned: 1179 (million)
% 59.49/8.63 % (2717892)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1558813127:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 59.49/8.63 % Exception at run slice level
% 64.45/9.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 64.45/9.40 % (2717902)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3054005018:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 64.45/9.40 % (2717902)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 64.45/9.40 % (2717850)Instruction limit reached!
% 64.45/9.40 % (2717850)------------------------------
% 64.45/9.40 % (2717850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.45/9.40 % (2717850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.45/9.40 % (2717850)CaDiCaL version: 2.1.3
% 64.45/9.40 % (2717850)Termination reason: Instruction limit
% 64.45/9.40 % (2717850)Termination phase: Saturation
% 64.45/9.40 % (2717850)Time elapsed: 0.629 s
% 64.45/9.40 % (2717850)Peak memory usage: 15 MB
% 64.45/9.40 % (2717850)Instructions burned: 871 (million)
% 64.45/9.40 % (2717961)dis+21_1_sil=32000:sas=cadical:random_seed=3949389474:i=3773:amm=off_2987 on theBenchmark for (2987ds/3773Mi)
% 64.45/9.40 % (2717809)Instruction limit reached!
% 64.45/9.40 % (2717809)------------------------------
% 64.45/9.40 % (2717809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.45/9.40 % (2717809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.45/9.40 % (2717809)CaDiCaL version: 2.1.3
% 64.45/9.40 % (2717809)Termination reason: Instruction limit
% 64.45/9.40 % (2717809)Termination phase: Saturation
% 64.45/9.40 % (2717809)Time elapsed: 1.112 s
% 64.45/9.40 % (2717809)Peak memory usage: 14 MB
% 64.45/9.40 % (2717809)Instructions burned: 1472 (million)
% 64.45/9.40 % (2717994)ott+11_1_sil=16000:gs=on:random_seed=3605979493:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2984 on theBenchmark for (2984ds/2251Mi)
% 64.45/9.40 % (2717994)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 64.45/9.40 % (2717994)Instruction limit reached!
% 64.45/9.40 % (2717994)------------------------------
% 64.45/9.40 % (2717994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.45/9.40 % (2717994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.45/9.40 % (2717994)CaDiCaL version: 2.1.3
% 64.45/9.40 % (2717994)Termination reason: Instruction limit
% 64.45/9.40 % (2717994)Termination phase: Saturation
% 64.45/9.40 % (2717994)Time elapsed: 1.554 s
% 64.45/9.40 % (2717994)Peak memory usage: 15 MB
% 64.45/9.40 % (2717994)Instructions burned: 2252 (million)
% 64.45/9.40 % (2718069)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3222610501:fmbsr=1.6:i=67534_2968 on theBenchmark for (2968ds/67534Mi)
% 64.45/9.40 % Exception at run slice level
% 64.45/9.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 64.45/9.40 % (2718071)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=2083164106:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2968 on theBenchmark for (2968ds/4591Mi)
% 64.45/9.40 % (2717902)Instruction limit reached!
% 64.45/9.40 % (2717902)------------------------------
% 64.45/9.40 % (2717902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.45/9.40 % (2717902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.45/9.40 % (2717902)CaDiCaL version: 2.1.3
% 64.45/9.40 % (2717902)Termination reason: Instruction limit
% 64.45/9.40 % (2717902)Termination phase: Saturation
% 64.45/9.40 % (2717902)Time elapsed: 2.707 s
% 64.45/9.40 % (2717902)Peak memory usage: 18 MB
% 64.45/9.40 % (2717902)Instructions burned: 3512 (million)
% 64.45/9.40 % (2718083)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=607995434:i=29340_2964 on theBenchmark for (2964ds/29340Mi)
% 64.45/9.40 % (2717961)Instruction limit reached!
% 64.45/9.40 % (2717961)------------------------------
% 64.45/9.40 % (2717961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.45/9.40 % (2717961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.45/9.40 % (2717961)CaDiCaL version: 2.1.3
% 64.45/9.40 % (2717961)Termination reason: Instruction limit
% 64.45/9.40 % (2717961)Termination phase: Saturation
% 64.45/9.40 % (2717961)Time elapsed: 2.810 s
% 64.45/9.40 % (2717961)Peak memory usage: 19 MB
% 64.45/9.40 % (2717961)Instructions burned: 3774 (million)
% 64.45/9.40 % (2718107)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=2585645775:i=5211_2959 on theBenchmark for (2959ds/5211Mi)
% 65.20/9.40 % (2717803)Instruction limit reached!
% 65.20/9.40 % (2717803)------------------------------
% 65.20/9.40 % (2717803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.20/9.40 % (2717803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.20/9.40 % (2717803)CaDiCaL version: 2.1.3
% 65.20/9.40 % (2717803)Termination reason: Instruction limit
% 65.20/9.40 % (2717803)Termination phase: Saturation
% 65.20/9.40 % (2717803)Time elapsed: 3.663 s
% 65.20/9.40 % (2717803)Peak memory usage: 20 MB
% 65.20/9.40 % (2717803)Instructions burned: 5132 (million)
% 65.20/9.40 % (2718110)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=3285257071:i=5497:nm=2_2958 on theBenchmark for (2958ds/5497Mi)
% 65.20/9.40 % Exception at run slice level
% 65.20/9.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 65.20/9.40 % (2718114)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=344593060:fmbsr=2:i=46332_2958 on theBenchmark for (2958ds/46332Mi)
% 65.20/9.40 % Exception at run slice level
% 65.20/9.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 65.20/9.40 % (2718117)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=1463123653:i=14071_2958 on theBenchmark for (2958ds/14071Mi)
% 65.20/9.40 % Exception at run slice level
% 65.20/9.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 65.20/9.40 % (2718119)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2678927178:i=22565:add=on:rawr=on_2957 on theBenchmark for (2957ds/22565Mi)
% 65.20/9.40 % (2717858)Instruction limit reached!
% 65.20/9.40 % (2717858)------------------------------
% 65.20/9.40 % (2717858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.20/9.40 % (2717858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.20/9.40 % (2717858)CaDiCaL version: 2.1.3
% 65.20/9.40 % (2717858)Termination reason: Instruction limit
% 65.20/9.40 % (2717858)Termination phase: Saturation
% 65.20/9.40 % (2717858)Time elapsed: 3.771 s
% 65.20/9.40 % (2717858)Peak memory usage: 24 MB
% 65.20/9.40 % (2717858)Instructions burned: 5115 (million)
% 65.20/9.40 % (2718127)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=4171496419:i=8173:av=off_2955 on theBenchmark for (2955ds/8173Mi)
% 65.20/9.40 % (2718071)Instruction limit reached!
% 65.20/9.40 % (2718071)------------------------------
% 65.20/9.40 % (2718071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.20/9.40 % (2718071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.20/9.40 % (2718071)CaDiCaL version: 2.1.3
% 65.20/9.40 % (2718071)Termination reason: Instruction limit
% 65.20/9.40 % (2718071)Termination phase: Saturation
% 65.20/9.40 % (2718071)Time elapsed: 2.685 s
% 65.20/9.40 % (2718071)Peak memory usage: 18 MB
% 65.20/9.40 % (2718071)Instructions burned: 4591 (million)
% 65.20/9.40 % (2718304)dis+10_16:1_sil=16000:random_seed=2395119240:i=9155:fsr=off_2941 on theBenchmark for (2941ds/9155Mi)
% 65.20/9.40 % (2718107)Instruction limit reached!
% 65.20/9.40 % (2718107)------------------------------
% 65.20/9.40 % (2718107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.20/9.40 % (2718107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.20/9.40 % (2718107)CaDiCaL version: 2.1.3
% 65.20/9.40 % (2718107)Termination reason: Instruction limit
% 65.20/9.40 % (2718107)Termination phase: Saturation
% 65.20/9.40 % (2718107)Time elapsed: 2.795 s
% 65.20/9.40 % (2718107)Peak memory usage: 23 MB
% 65.20/9.40 % (2718107)Instructions burned: 5211 (million)
% 65.20/9.40 % (2718306)ott-3_8_sil=64000:random_seed=1103617772:i=20139:bs=on_2931 on theBenchmark for (2931ds/20139Mi)
% 65.20/9.40 % (2718127)Instruction limit reached!
% 65.20/9.40 % (2718127)------------------------------
% 65.20/9.40 % (2718127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.20/9.40 % (2718127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.20/9.40 % (2718127)CaDiCaL version: 2.1.3
% 65.20/9.40 % (2718127)Termination reason: Instruction limit
% 65.20/9.40 % (2718127)Termination phase: Saturation
% 65.20/9.40 % (2718127)Time elapsed: 3.914 s
% 65.20/9.40 % (2718127)Peak memory usage: 30 MB
% 65.20/9.40 % (2718127)Instructions burned: 8173 (million)
% 65.20/9.40 % (2718308)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=2416450644:fmbsr=2:i=32576_2916 on theBenchmark for (2916ds/32576Mi)
% 65.20/9.40 % Exception at run slice level
% 65.20/9.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 65.20/9.40 % (2718310)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=3826465676:i=11404_2915 on theBenchmark for (2915ds/11404Mi)
% 65.20/9.40 % (2718306) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2717676-2718306"...
% 65.20/9.40 % (2718306)...printing done.
% 65.20/9.40 % (2718306)Refutation found. Thanks to Tanya!
% 65.20/9.40 % SZS status Theorem for theBenchmark
% 65.20/9.40 % SZS output start Proof for theBenchmark
% 65.20/9.40 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 65.20/9.40 thf(func_def_0, type, in: ($i > $i > $o)).
% 65.20/9.40 thf(func_def_1, type, subset: ($i > $i > $o)).
% 65.20/9.40 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 65.20/9.40 thf(func_def_3, type, cartprod: ($i > $i > $i)).
% 65.20/9.40 thf(func_def_4, type, breln: ($i > $i > $i > $o)).
% 65.20/9.40 thf(func_def_6, type, brelnall1: $o).
% 65.20/9.40 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 65.20/9.40 thf(func_def_8, type, db2: !>[X0: $tType]:(X0)).
% 65.20/9.40 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 65.20/9.40 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 65.20/9.40 thf(func_def_11, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 65.20/9.40 thf(func_def_12, type, vIMP: ($o > $o > $o)).
% 65.20/9.40 thf(func_def_13, type, db4: !>[X0: $tType]:(X0)).
% 65.20/9.40 thf(func_def_14, type, db5: !>[X0: $tType]:(X0)).
% 65.20/9.40 thf(func_def_20, type, sK3: ($i > $o)).
% 65.20/9.40 thf(func_def_22, type, vNOT: ($o > $o)).
% 65.20/9.40 thf(func_def_23, type, sK5: ($i > $i > ($i > $o) > $i > $i)).
% 65.20/9.40 thf(func_def_24, type, sK6: ($i > $i > $i > ($i > $o) > $i)).
% 65.20/9.40 thf(func_def_26, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 65.20/9.40 thf(f1,axiom,(
% 65.20/9.40 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 65.20/9.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 65.20/9.40 thf(f2,axiom,(
% 65.20/9.40 (brelnall1 = ! [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)))))),
% 65.20/9.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1)).
% 65.20/9.40 thf(f3,conjecture,(
% 65.20/9.40 brelnall1 => ! [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))))),
% 65.20/9.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2)).
% 65.20/9.40 thf(f4,negated_conjecture,(
% 65.20/9.40 ~(brelnall1 => ! [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)))))),
% 65.20/9.40 inference(negated_conjecture,[status(cth)],[f3])).
% 65.20/9.40 thf(f5,plain,(
% 65.20/9.40 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 65.20/9.40 inference(fool_elimination,[],[f1])).
% 65.20/9.40 thf(f6,plain,(
% 65.20/9.40 (brelnall1 = ! [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)))))),
% 65.20/9.40 inference(rectify,[],[f2])).
% 65.20/9.40 thf(f7,plain,(
% 65.20/9.40 (brelnall1 = ((!! @ $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))))))))))))))))),
% 65.20/9.40 inference(fool_elimination,[],[f6])).
% 65.20/9.40 thf(f8,plain,(
% 65.20/9.40 ~(brelnall1 => ! [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)))))),
% 65.20/9.40 inference(rectify,[],[f4])).
% 65.20/9.40 thf(f9,plain,(
% 65.20/9.40 ~((brelnall1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X0 @ X1 @ X2)) = $true) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ! [X5 : $i] : ((((in @ X5 @ X1)) = $true) => ((((in @ (kpair @ X4 @ X5) @ X2)) = $true) => (((X3 @ (kpair @ X4 @ X5))) = $true)))) => ! [X6 : $i] : ((((in @ X6 @ X2)) = $true) => (((X3 @ X6)) = $true)))))),
% 65.20/9.40 inference(fool_elimination,[],[f8])).
% 65.20/9.40 thf(f10,plain,(
% 65.20/9.40 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : ($i > $o)] : (? [X6 : $i] : ((((X3 @ X6)) != $true) & (((in @ X6 @ X2)) = $true)) & ! [X4 : $i] : (! [X5 : $i] : (((((X3 @ (kpair @ X4 @ X5))) = $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true)) | (((in @ X5 @ X1)) != $true)) | (((in @ X4 @ X0)) != $true))) & (((breln @ X0 @ X1 @ X2)) = $true)) & (brelnall1 = $true)),
% 65.20/9.40 inference(ennf_transformation,[],[f9])).
% 65.20/9.40 thf(f11,plain,(
% 65.20/9.40 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : ($i > $o)] : (? [X6 : $i] : ((((X3 @ X6)) != $true) & (((in @ X6 @ X2)) = $true)) & ! [X4 : $i] : (! [X5 : $i] : ((((X3 @ (kpair @ X4 @ X5))) = $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true) | (((in @ X5 @ X1)) != $true)) | (((in @ X4 @ X0)) != $true))) & (((breln @ X0 @ X1 @ X2)) = $true)) & (brelnall1 = $true)),
% 65.20/9.40 inference(flattening,[],[f10])).
% 65.20/9.40 thf(f12,plain,(
% 65.20/9.40 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : ($i > $o)] : (? [X4 : $i] : ((((X3 @ X4)) != $true) & (((in @ X4 @ X2)) = $true)) & ! [X5 : $i] : (! [X6 : $i] : (($true = ((X3 @ (kpair @ X5 @ X6)))) | ($true != ((in @ (kpair @ X5 @ X6) @ X2))) | ($true != ((in @ X6 @ X1)))) | ($true != ((in @ X5 @ X0))))) & (((breln @ X0 @ X1 @ X2)) = $true)) & (brelnall1 = $true)),
% 65.20/9.40 inference(rectify,[],[f11])).
% 65.20/9.40 thf(f13,plain,(
% 65.20/9.40 (((($true != ((sK3 @ sK4))) & ($true = ((in @ sK4 @ sK2)))) & ! [X5 : $i] : (! [X6 : $i] : (($true = ((sK3 @ (kpair @ X5 @ X6)))) | ($true != ((in @ (kpair @ X5 @ X6) @ sK2))) | ($true != ((in @ X6 @ sK1)))) | ($true != ((in @ X5 @ sK0))))) & ($true = ((breln @ sK0 @ sK1 @ sK2)))) & (brelnall1 = $true)),
% 65.20/9.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f12])).
% 65.20/9.40 thf(f14,plain,(
% 65.20/9.40 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 65.20/9.40 inference(cnf_transformation,[],[f5])).
% 65.20/9.40 thf(f15,plain,(
% 65.20/9.40 (brelnall1 = ((!! @ $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))))))))))))))))),
% 65.20/9.40 inference(cnf_transformation,[],[f7])).
% 65.20/9.40 thf(f16,plain,(
% 65.20/9.40 (brelnall1 = $true)),
% 65.20/9.40 inference(cnf_transformation,[],[f13])).
% 65.20/9.40 thf(f17,plain,(
% 65.20/9.40 ($true = ((breln @ sK0 @ sK1 @ sK2)))),
% 65.20/9.40 inference(cnf_transformation,[],[f13])).
% 65.20/9.40 thf(f18,plain,(
% 65.20/9.40 ( ! [X6 : $i,X5 : $i] : (($true != ((in @ X6 @ sK1))) | ($true != ((in @ (kpair @ X5 @ X6) @ sK2))) | ($true = ((sK3 @ (kpair @ X5 @ X6)))) | ($true != ((in @ X5 @ sK0)))) )),
% 65.20/9.40 inference(cnf_transformation,[],[f13])).
% 65.20/9.40 thf(f19,plain,(
% 65.20/9.40 ($true = ((in @ sK4 @ sK2)))),
% 65.20/9.40 inference(cnf_transformation,[],[f13])).
% 65.20/9.40 thf(f20,plain,(
% 65.20/9.40 ($true != ((sK3 @ sK4)))),
% 65.20/9.40 inference(cnf_transformation,[],[f13])).
% 65.20/9.40 thf(f22,definition,(
% 65.20/9.40 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 65.20/9.40 introduced(theory,[fool_exhaustiveness_axiom])).
% 65.20/9.40 thf(f23,plain,(
% 65.20/9.40 ($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 : $i]: ((in @ Y4 @ Y0) => (Y3 @ Y4))))))))))))))))),
% 65.20/9.40 inference(definition_unfolding,[],[f15,f16,f14])).
% 65.20/9.40 thf(f24,plain,(
% 65.20/9.40 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK0 @ sK1 @ sK2)))),
% 65.20/9.40 inference(definition_unfolding,[],[f17,f14])).
% 65.20/9.40 thf(f25,plain,(
% 65.20/9.40 ($true = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))),
% 65.20/9.40 inference(beta-eta_normalization,[],[f24])).
% 65.20/9.40 thf(f26,plain,(
% 65.20/9.40 ( ! [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)))) )),
% 65.20/9.40 inference(pi_proxy_clausification,[],[f23])).
% 65.20/9.40 thf(f27,plain,(
% 65.20/9.40 ( ! [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))))))))))))))) )),
% 65.20/9.40 inference(beta-eta_normalization,[],[f26])).
% 65.20/9.40 thf(f28,plain,(
% 65.20/9.40 ( ! [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)))) )),
% 65.20/9.40 inference(pi_proxy_clausification,[],[f27])).
% 65.20/9.40 thf(f29,plain,(
% 65.20/9.40 ( ! [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))))))))))))) )),
% 65.20/9.40 inference(beta-eta_normalization,[],[f28])).
% 65.20/9.40 thf(f30,plain,(
% 65.20/9.40 ( ! [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)))) )),
% 65.20/9.40 inference(pi_proxy_clausification,[],[f29])).
% 65.20/9.40 thf(f31,plain,(
% 65.20/9.40 ( ! [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))))))))))) )),
% 65.20/9.40 inference(beta-eta_normalization,[],[f30])).
% 65.20/9.40 thf(f32,plain,(
% 65.20/9.40 ( ! [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)))))))))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f31])).
% 65.20/9.40 thf(f33,plain,(
% 65.20/9.40 ( ! [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)))) )),
% 65.20/9.40 inference(pi_proxy_clausification,[],[f32])).
% 65.20/9.40 thf(f34,plain,(
% 65.20/9.40 ( ! [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)))))))) )),
% 65.20/9.40 inference(beta-eta_normalization,[],[f33])).
% 65.20/9.40 thf(f35,plain,(
% 65.20/9.40 ( ! [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))))))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f34])).
% 65.20/9.40 thf(f36,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o)] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (X4 @ (kpair @ Y0 @ Y1)))))))) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (X4 @ Y0))))))) )),
% 65.20/9.40 inference(sigma_proxy_clausification,[],[f35])).
% 65.20/9.40 thf(f37,plain,(
% 65.20/9.40 ( ! [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 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (X4 @ (kpair @ Y0 @ Y1)))))))) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X1) => (X4 @ Y0))) @ X5)))) )),
% 65.20/9.40 inference(pi_proxy_clausification,[],[f36])).
% 65.20/9.40 thf(f38,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X1) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0))))))))) | ($true = (((in @ X5 @ X1) => (X4 @ X5))))) )),
% 65.20/9.40 inference(beta-eta_normalization,[],[f37])).
% 65.20/9.40 thf(f39,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X1) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) | ($true = (((in @ X5 @ X1) => (X4 @ X5))))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f38])).
% 65.20/9.40 thf(f40,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = ((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X3))) | ($true = (((in @ X5 @ X1) => (X4 @ X5))))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f38])).
% 65.20/9.40 thf(f41,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ X5))) | (((in @ X5 @ X1)) = $false) | ($true = ((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X3))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f40])).
% 65.20/9.40 thf(f42,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X1) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0))))) @ (sK6 @ X1 @ X2 @ X3 @ X4)))) | ($true = (((in @ X5 @ X1) => (X4 @ X5))))) )),
% 65.20/9.40 inference(sigma_proxy_clausification,[],[f39])).
% 65.20/9.40 thf(f43,plain,(
% 65.20/9.40 ( ! [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 @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X1) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0))))) @ (sK6 @ X1 @ X2 @ X3 @ X4)))) | (((in @ X5 @ X1)) = $false) | ($true = ((X4 @ X5)))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f42])).
% 65.20/9.40 thf(f44,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((in @ (sK6 @ X1 @ X2 @ X3 @ X4) @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X1) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4))))))) | (((in @ X5 @ X1)) = $false) | ($true = ((X4 @ X5)))) )),
% 65.20/9.40 inference(beta-eta_normalization,[],[f43])).
% 65.20/9.40 thf(f45,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = (((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X1) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)))))) | (((in @ X5 @ X1)) = $false) | ($true = ((X4 @ X5)))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f44])).
% 65.20/9.40 thf(f46,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ X5))) | (((in @ X5 @ X1)) = $false) | ($true = ((in @ (sK6 @ X1 @ X2 @ X3 @ X4) @ X2))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f44])).
% 65.20/9.40 thf(f47,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ X5))) | (((in @ X5 @ X1)) = $false) | ($false = ((X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4))))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f45])).
% 65.20/9.40 thf(f48,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ X5))) | (((in @ X5 @ X1)) = $false) | ($true = ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 65.20/9.40 inference(imp_proxy_clausification,[],[f45])).
% 65.20/9.40 thf(f61,plain,(
% 65.20/9.40 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != ((in @ (kpair @ X1 @ X0) @ sK2))) | ($true = ((sK3 @ (kpair @ X1 @ X0)))) | ($true != ((in @ X1 @ sK0))) | ($false = ((in @ X0 @ sK1)))) )),
% 65.20/9.40 inference(constrained_superposition,[],[f18,f22])).
% 65.20/9.40 thf(f62,plain,(
% 65.20/9.40 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK0))) | ($true = ((sK3 @ (kpair @ X1 @ X0)))) | ($true != ((in @ (kpair @ X1 @ X0) @ sK2))) | ($false = ((in @ X0 @ sK1)))) )),
% 65.20/9.40 inference(trivial_inequality_removal,[],[f61])).
% 65.20/9.40 thf(f98,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o),X4 : $i] : (($true != $true) | ($true = ((sK3 @ (kpair @ (sK5 @ sK0 @ X0 @ X1 @ X2) @ X3)))) | ($true != ((in @ (kpair @ (sK5 @ sK0 @ X0 @ X1 @ X2) @ X3) @ sK2))) | ($false = ((in @ X3 @ sK1))) | ($true = ((X1 @ X4))) | (((in @ X4 @ X0)) = $false) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ X2))))) )),
% 65.20/9.40 inference(constrained_superposition,[],[f62,f41])).
% 65.20/9.40 thf(f129,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o),X4 : $i] : (($true != ((in @ (kpair @ (sK5 @ sK0 @ X0 @ X1 @ X2) @ X3) @ sK2))) | ($true = ((sK3 @ (kpair @ (sK5 @ sK0 @ X0 @ X1 @ X2) @ X3)))) | ($false = ((in @ X3 @ sK1))) | ($true = ((X1 @ X4))) | (((in @ X4 @ X0)) = $false) | ($false = ((subset @ X0 @ (cartprod @ sK0 @ X2))))) )),
% 65.20/9.40 inference(trivial_inequality_removal,[],[f98])).
% 65.20/9.40 thf(f7361,plain,(
% 65.20/9.40 ( ! [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 @ (sK5 @ X1 @ X2 @ X0 @ X3) @ (sK6 @ X2 @ X3 @ X1 @ X0)))))) )),
% 65.20/9.40 inference(equality_factoring,[],[f47])).
% 65.20/9.40 thf(f7944,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X0 : ($i > $o),X1 : $i,X4 : $i] : (($true != ((X0 @ (kpair @ (sK5 @ X1 @ X2 @ X0 @ X3) @ (sK6 @ X2 @ X3 @ X1 @ X0))))) | (((in @ X4 @ X2)) = $false) | ($false = ((subset @ X2 @ (cartprod @ X1 @ X3)))) | ($true = ((X0 @ X4)))) )),
% 65.20/9.40 inference(forward_subsumption_resolution,[],[f7361,f22])).
% 65.20/9.40 thf(f13290,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($false = ((in @ X0 @ X1))) | ($true = ((in @ (kpair @ (sK5 @ X2 @ X1 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X3) @ (sK6 @ X1 @ X3 @ X2 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X3)))) | (sK4 != X0)) )),
% 65.20/9.40 inference(constrained_superposition,[],[f20,f48])).
% 65.20/9.40 thf(f13896,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = ((in @ X0 @ X1))) | ($true = ((in @ (kpair @ (sK5 @ X2 @ X1 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X3) @ (sK6 @ X1 @ X3 @ X2 @ (^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X3)))) | (sK4 != X0)) )),
% 65.20/9.40 inference(trivial_inequality_removal,[],[f13290])).
% 65.20/9.40 thf(f13897,plain,(
% 65.20/9.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((sK4 != X0) | ($true = ((in @ (kpair @ (sK5 @ X2 @ X1 @ sK3 @ X3) @ (sK6 @ X1 @ X3 @ X2 @ sK3)) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X2 @ X3)))) | ($false = ((in @ X0 @ X1)))) )),
% 65.20/9.40 inference(beta-eta_normalization,[],[f13896])).
% 65.20/9.40 thf(f14179,plain,(
% 65.20/9.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (kpair @ (sK5 @ X0 @ X1 @ sK3 @ X2) @ (sK6 @ X1 @ X2 @ X0 @ sK3)) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X0 @ X2)))) | ($false = ((in @ sK4 @ X1)))) )),
% 65.20/9.40 inference(equality_resolution,[],[f13897])).
% 65.20/9.40 thf(f14260,plain,(
% 65.20/9.40 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((sK3 @ (kpair @ (sK5 @ sK0 @ sK2 @ sK3 @ X0) @ (sK6 @ sK2 @ X0 @ sK0 @ sK3))))) | ($false = ((in @ (sK6 @ sK2 @ X0 @ sK0 @ sK3) @ sK1))) | ($true = ((sK3 @ X1))) | ($false = ((in @ X1 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0)))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0)))) | (((in @ sK4 @ sK2)) = $false)) )),
% 65.20/9.40 inference(constrained_superposition,[],[f129,f14179])).
% 65.20/9.40 thf(f14303,plain,(
% 65.20/9.40 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((sK3 @ (kpair @ (sK5 @ sK0 @ sK2 @ sK3 @ X0) @ (sK6 @ sK2 @ X0 @ sK0 @ sK3))))) | ($false = ((in @ (sK6 @ sK2 @ X0 @ sK0 @ sK3) @ sK1))) | ($true = ((sK3 @ X1))) | ($false = ((in @ X1 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0)))) | (((in @ sK4 @ sK2)) = $false)) )),
% 65.20/9.40 inference(duplicate_literal_removal,[],[f14260])).
% 65.20/9.40 thf(f14304,plain,(
% 65.20/9.40 ( ! [X0 : $i,X1 : $i] : (($true = ((sK3 @ (kpair @ (sK5 @ sK0 @ sK2 @ sK3 @ X0) @ (sK6 @ sK2 @ X0 @ sK0 @ sK3))))) | ($false = ((in @ (sK6 @ sK2 @ X0 @ sK0 @ sK3) @ sK1))) | ($true = ((sK3 @ X1))) | ($false = ((in @ X1 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0)))) | (((in @ sK4 @ sK2)) = $false)) )),
% 65.20/9.40 inference(trivial_inequality_removal,[],[f14303])).
% 65.20/9.40 thf(f14390,plain,(
% 65.20/9.40 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (sK6 @ sK2 @ X0 @ sK0 @ sK3) @ sK1))) | ($true = ((sK3 @ X1))) | ($false = ((in @ X1 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0)))) | (((in @ sK4 @ sK2)) = $false)) )),
% 65.20/9.40 inference(forward_subsumption_resolution,[],[f14304,f7944])).
% 65.20/9.40 thf(f14427,plain,(
% 65.20/9.40 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (sK6 @ sK2 @ X0 @ sK0 @ sK3) @ sK1))) | ($true = ((sK3 @ X1))) | ($false = ((in @ X1 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0))))) )),
% 65.20/9.40 inference(forward_demodulation,[],[f14390,f19])).
% 65.20/9.40 thf(f14428,plain,(
% 65.20/9.40 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (sK6 @ sK2 @ X0 @ sK0 @ sK3) @ sK1))) | ($true = ((sK3 @ X1))) | ($false = ((in @ X1 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0))))) )),
% 65.20/9.40 inference(trivial_inequality_removal,[],[f14427])).
% 65.20/9.40 thf(f14430,definition,(
% 65.20/9.40 spl7_12 <=> ! [X1 : $i] : (($true = ((sK3 @ X1))) | ($false = ((in @ X1 @ sK2))))),
% 65.20/9.40 introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition])).
% 65.20/9.40 thf(f14431,plain,(
% 65.20/9.40 ( ! [X1 : $i] : (($false = ((in @ X1 @ sK2))) | ($true = ((sK3 @ X1)))) ) | ~spl7_12),
% 65.20/9.40 inference(avatar_component_clause,[],[f14430])).
% 65.20/9.40 thf(f14433,definition,(
% 65.20/9.40 spl7_13 <=> ! [X0 : $i] : (($false = ((in @ (sK6 @ sK2 @ X0 @ sK0 @ sK3) @ sK1))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0)))))),
% 65.20/9.40 introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition])).
% 65.20/9.40 thf(f14434,plain,(
% 65.20/9.40 ( ! [X0 : $i] : (($false = ((in @ (sK6 @ sK2 @ X0 @ sK0 @ sK3) @ sK1))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ X0))))) ) | ~spl7_13),
% 65.20/9.40 inference(avatar_component_clause,[],[f14433])).
% 65.20/9.40 thf(f14435,plain,(
% 65.20/9.40 spl7_12 | spl7_13),
% 65.20/9.40 inference(avatar_split_clause,[],[f14428,f14433,f14430])).
% 65.20/9.40 thf(f14758,plain,(
% 65.20/9.40 ($true = $false) | ($true = ((sK3 @ sK4))) | ~spl7_12),
% 65.20/9.40 inference(constrained_superposition,[],[f14431,f19])).
% 65.20/9.40 thf(f14947,plain,(
% 65.20/9.40 ($true = ((sK3 @ sK4))) | ~spl7_12),
% 65.20/9.40 inference(trivial_inequality_removal,[],[f14758])).
% 65.20/9.40 thf(f14993,plain,(
% 65.20/9.40 $false | ~spl7_12),
% 65.20/9.40 inference(forward_subsumption_resolution,[],[f14947,f20])).
% 65.20/9.40 thf(f14994,plain,(
% 65.20/9.40 ~spl7_12),
% 65.20/9.40 inference(avatar_contradiction_clause,[],[f14993])).
% 65.20/9.40 thf(f15123,plain,(
% 65.20/9.40 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK3 @ X0))) | ($false = ((in @ X0 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1)))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))) ) | ~spl7_13),
% 65.20/9.40 inference(constrained_superposition,[],[f46,f14434])).
% 65.20/9.40 thf(f15189,plain,(
% 65.20/9.40 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK3 @ X0))) | ($false = ((in @ X0 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))) ) | ~spl7_13),
% 65.20/9.40 inference(duplicate_literal_removal,[],[f15123])).
% 65.20/9.40 thf(f15190,plain,(
% 65.20/9.40 ( ! [X0 : $i] : (($true = ((sK3 @ X0))) | ($false = ((in @ X0 @ sK2))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))) ) | ~spl7_13),
% 65.20/9.40 inference(trivial_inequality_removal,[],[f15189])).
% 65.20/9.40 thf(f15220,plain,(
% 65.20/9.40 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK3 @ X0))) | ($false = ((in @ X0 @ sK2)))) ) | ~spl7_13),
% 65.20/9.40 inference(forward_demodulation,[],[f15190,f25])).
% 65.20/9.40 thf(f15221,plain,(
% 65.20/9.40 ( ! [X0 : $i] : (($true = ((sK3 @ X0))) | ($false = ((in @ X0 @ sK2)))) ) | ~spl7_13),
% 65.20/9.40 inference(trivial_inequality_removal,[],[f15220])).
% 65.20/9.40 thf(f15226,plain,(
% 65.20/9.40 spl7_12 | ~spl7_13),
% 65.20/9.40 inference(avatar_split_clause,[],[f15221,f14433,f14430])).
% 65.20/9.40 cnf(s8, plain, spl7_12 | spl7_13, inference(sat_conversion,[],[f14435])).
% 65.20/9.40 cnf(s10, plain, ~spl7_12, inference(sat_conversion,[],[f14994])).
% 65.20/9.40 cnf(s11, plain, spl7_12 | ~spl7_13, inference(sat_conversion,[],[f15226])).
% 65.20/9.40 cnf(s13, plain, ~spl7_13, inference(rat,[],[s11,s10])).
% 65.20/9.40 cnf(s14, plain, $false, inference(rat,[],[s8,s13,s10])).
% 65.20/9.40 thf(f15227,plain,(
% 65.20/9.40 $false),
% 65.20/9.40 inference(avatar_sat_refutation,[],[s14])).
% 65.20/9.40 % SZS output end Proof for theBenchmark
% 65.20/9.40 % (2718306)------------------------------
% 65.20/9.40 % (2718306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.20/9.40 % (2718306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.20/9.40 % (2718306)CaDiCaL version: 2.1.3
% 65.20/9.40 % (2718306)Termination reason: Refutation
% 65.20/9.40 % (2718306)Time elapsed: 2.251 s
% 65.20/9.40 % (2718306)Peak memory usage: 21 MB
% 65.20/9.40 % (2718306)Instructions burned: 5229 (million)
% 65.20/9.40 % (2717676)Success in time 9.181 s
% 65.20/9.40 % Vampire exiting
%------------------------------------------------------------------------------