%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP124^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:47 AM UTC 2026
% Result : Theorem 5.70s 1.19s
% Output : Refutation 5.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP124^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 20:02:05 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.70/1.19 % (832524)Will run a generic schedule for satisfiability detection.
% 5.70/1.19 % (832530)% WARNING: option uhcvi not known.
% 5.70/1.19 % (832532)dis+10_1_sil=32000:sp=arity:random_seed=1273279721:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.70/1.19 % (832529)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2779440403_2999 on theBenchmark for (2999ds/0Mi)
% 5.70/1.19 % (832533)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2036660821:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.70/1.19 % (832531)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2153411523:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.70/1.19 % (832530)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3819954259:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.70/1.19 % (832534)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3780018376:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.70/1.19 % (832535)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2666087021:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.70/1.19 % (832533)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.70/1.19 % (832530)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832530)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.70/1.19 % (832532)Instruction limit reached!
% 5.70/1.19 % (832532)------------------------------
% 5.70/1.19 % (832532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832532)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832532)Termination reason: Instruction limit
% 5.70/1.19 % (832532)Termination phase: Saturation
% 5.70/1.19 % (832532)Time elapsed: 0.046 s
% 5.70/1.19 % (832532)Peak memory usage: 12 MB
% 5.70/1.19 % (832532)Instructions burned: 105 (million)
% 5.70/1.19 % (832543)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2770306916:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.70/1.19 % (832533)Instruction limit reached!
% 5.70/1.19 % (832533)------------------------------
% 5.70/1.19 % (832533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832533)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832533)Termination reason: Instruction limit
% 5.70/1.19 % (832533)Termination phase: Saturation
% 5.70/1.19 % (832533)Time elapsed: 0.053 s
% 5.70/1.19 % (832533)Peak memory usage: 13 MB
% 5.70/1.19 % (832533)Instructions burned: 117 (million)
% 5.70/1.19 % (832534)Instruction limit reached!
% 5.70/1.19 % (832534)------------------------------
% 5.70/1.19 % (832534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832534)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832534)Termination reason: Instruction limit
% 5.70/1.19 % (832534)Termination phase: Saturation
% 5.70/1.19 % (832534)Time elapsed: 0.062 s
% 5.70/1.19 % (832534)Peak memory usage: 13 MB
% 5.70/1.19 % (832534)Instructions burned: 131 (million)
% 5.70/1.19 % (832544)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3514671429:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832546)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=1886790630:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.70/1.19 % (832549)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=48417276:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.70/1.19 % (832547)ott-21_1_sil=16000:fs=off:random_seed=1076370696:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.70/1.19 % (832546)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.70/1.19 % (832535)Instruction limit reached!
% 5.70/1.19 % (832535)------------------------------
% 5.70/1.19 % (832535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832535)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832535)Termination reason: Instruction limit
% 5.70/1.19 % (832535)Termination phase: Saturation
% 5.70/1.19 % (832535)Time elapsed: 0.114 s
% 5.70/1.19 % (832535)Peak memory usage: 13 MB
% 5.70/1.19 % (832535)Instructions burned: 159 (million)
% 5.70/1.19 % (832544)Instruction limit reached!
% 5.70/1.19 % (832544)------------------------------
% 5.70/1.19 % (832544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832544)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832544)Termination reason: Instruction limit
% 5.70/1.19 % (832544)Termination phase: Saturation
% 5.70/1.19 % (832544)Time elapsed: 0.059 s
% 5.70/1.19 % (832544)Peak memory usage: 13 MB
% 5.70/1.19 % (832544)Instructions burned: 131 (million)
% 5.70/1.19 % (832553)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3293308566:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.70/1.19 % (832546)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.70/1.19 % (832554)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2798575431:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832557)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2874988640:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832559)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=2372869568: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)
% 5.70/1.19 % (832547)Instruction limit reached!
% 5.70/1.19 % (832547)------------------------------
% 5.70/1.19 % (832547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832547)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832547)Termination reason: Instruction limit
% 5.70/1.19 % (832547)Termination phase: Saturation
% 5.70/1.19 % (832547)Time elapsed: 0.166 s
% 5.70/1.19 % (832547)Peak memory usage: 13 MB
% 5.70/1.19 % (832547)Instructions burned: 181 (million)
% 5.70/1.19 % (832559)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.70/1.19 % (832561)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4141882369:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 5.70/1.19 % (832561)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.70/1.19 % (832549)Instruction limit reached!
% 5.70/1.19 % (832549)------------------------------
% 5.70/1.19 % (832549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832549)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832549)Termination reason: Instruction limit
% 5.70/1.19 % (832549)Termination phase: Saturation
% 5.70/1.19 % (832549)Time elapsed: 0.240 s
% 5.70/1.19 % (832549)Peak memory usage: 14 MB
% 5.70/1.19 % (832549)Instructions burned: 478 (million)
% 5.70/1.19 % (832563)fmb+10_1_sil=64000:random_seed=2035690245:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 5.70/1.19 % (832563)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832565)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4232169444:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832567)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1510609281:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832569)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=157086667:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 5.70/1.19 % (832569)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.70/1.19 % (832546)Instruction limit reached!
% 5.70/1.19 % (832546)------------------------------
% 5.70/1.19 % (832546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832546)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832546)Termination reason: Instruction limit
% 5.70/1.19 % (832546)Termination phase: Saturation
% 5.70/1.19 % (832546)Time elapsed: 0.438 s
% 5.70/1.19 % (832546)Peak memory usage: 15 MB
% 5.70/1.19 % (832546)Instructions burned: 684 (million)
% 5.70/1.19 % (832571)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2001163170:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 5.70/1.19 % (832571)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.70/1.19 % (832571)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.70/1.19 % (832559)Instruction limit reached!
% 5.70/1.19 % (832559)------------------------------
% 5.70/1.19 % (832559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832559)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832559)Termination reason: Instruction limit
% 5.70/1.19 % (832559)Termination phase: Saturation
% 5.70/1.19 % (832559)Time elapsed: 0.394 s
% 5.70/1.19 % (832559)Peak memory usage: 19 MB
% 5.70/1.19 % (832559)Instructions burned: 693 (million)
% 5.70/1.19 % (832573)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1886332451:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832575)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=764207139:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 5.70/1.19 % (832554)Instruction limit reached!
% 5.70/1.19 % (832554)------------------------------
% 5.70/1.19 % (832554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832554)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832554)Termination reason: Instruction limit
% 5.70/1.19 % (832554)Termination phase: Saturation
% 5.70/1.19 % (832554)Time elapsed: 0.581 s
% 5.70/1.19 % (832554)Peak memory usage: 22 MB
% 5.70/1.19 % (832554)Instructions burned: 1180 (million)
% 5.70/1.19 % Exception at run slice level
% 5.70/1.19 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.70/1.19 % (832577)ott-2_1_sil=16000:newcnf=on:random_seed=1221586969:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 5.70/1.19 % (832578)ott+10_1_sil=32000:tgt=ground:random_seed=197332985:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 5.70/1.19 % (832577)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.70/1.19 % (832530) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-832524-832530"...
% 5.70/1.19 % (832530)...printing done.
% 5.70/1.19 % (832530)Refutation found. Thanks to Tanya!
% 5.70/1.19 % SZS status Theorem for theBenchmark
% 5.70/1.19 % SZS output start Proof for theBenchmark
% 5.70/1.19 thf(type_def_5, type, set: $tType > $tType).
% 5.70/1.19 thf(type_def_6, type, a: $tType).
% 5.70/1.19 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 5.70/1.19 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 5.70/1.19 thf(func_def_1, type, order: !>[X0: $tType]:($o)).
% 5.70/1.19 thf(func_def_2, type, finite_finite: !>[X0: $tType]:($o)).
% 5.70/1.19 thf(func_def_3, type, linorder: !>[X0: $tType]:($o)).
% 5.70/1.19 thf(func_def_4, type, condit2040224947_above: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 5.70/1.19 thf(func_def_5, type, condit1201339847_below: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 5.70/1.19 thf(func_def_6, type, finite_comp_fun_idem: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > $o))).
% 5.70/1.19 thf(func_def_7, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 5.70/1.19 thf(func_def_8, type, abel_semigroup: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 5.70/1.19 thf(func_def_9, type, semigroup: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 5.70/1.19 thf(func_def_10, type, semilattice: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 5.70/1.19 thf(func_def_11, type, lattic1263571978nf_fin: !>[X0: $tType]:(((X0 > X0 > X0) > set @ X0 > X0))).
% 5.70/1.19 thf(func_def_12, type, lattic35693393ce_set: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 5.70/1.19 thf(func_def_13, type, lattic1039401930up_fin: !>[X0: $tType]:(((X0 > X0 > X0) > set @ X0 > X0))).
% 5.70/1.19 thf(func_def_14, type, modula1221160330_d_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 5.70/1.19 thf(func_def_15, type, modula1593167561_e_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 5.70/1.19 thf(func_def_16, type, bot_bot: !>[X0: $tType]:(X0)).
% 5.70/1.19 thf(func_def_17, type, least: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > X0))).
% 5.70/1.19 thf(func_def_18, type, max: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > X0))).
% 5.70/1.19 thf(func_def_19, type, min: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > X0))).
% 5.70/1.19 thf(func_def_20, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.70/1.19 thf(func_def_21, type, greatest: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > X0))).
% 5.70/1.19 thf(func_def_22, type, antimono: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > $o))).
% 5.70/1.19 thf(func_def_23, type, mono: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > $o))).
% 5.70/1.19 thf(func_def_24, type, transp: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 5.70/1.19 thf(func_def_25, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 5.70/1.19 thf(func_def_26, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 5.70/1.19 thf(func_def_27, type, set_atLeast: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 5.70/1.19 thf(func_def_28, type, set_atLeastAtMost: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > set @ X0))).
% 5.70/1.19 thf(func_def_29, type, set_atMost: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 5.70/1.19 thf(func_def_30, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 5.70/1.19 thf(func_def_31, type, a2: a).
% 5.70/1.19 thf(func_def_32, type, b: a).
% 5.70/1.19 thf(func_def_33, type, c: a).
% 5.70/1.19 thf(func_def_34, type, inf: (a > a > a)).
% 5.70/1.19 thf(func_def_35, type, less_eq: (a > a > $o)).
% 5.70/1.19 thf(func_def_36, type, sup: (a > a > a)).
% 5.70/1.19 thf(func_def_40, type, db0: !>[X0: $tType]:(X0)).
% 5.70/1.19 thf(func_def_41, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.70/1.19 thf(func_def_42, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.70/1.19 thf(func_def_43, type, db1: !>[X0: $tType]:(X0)).
% 5.70/1.19 thf(func_def_44, type, vAND: ($o > $o > $o)).
% 5.70/1.19 thf(func_def_45, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.70/1.19 thf(func_def_46, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.70/1.19 thf(func_def_47, type, vIMP: ($o > $o > $o)).
% 5.70/1.19 thf(func_def_48, type, db3: !>[X0: $tType]:(X0)).
% 5.70/1.19 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 5.70/1.19 thf(func_def_50, type, vNOT: ($o > $o)).
% 5.70/1.19 thf(func_def_51, type, vOR: ($o > $o > $o)).
% 5.70/1.19 thf(func_def_52, type, sK0: a).
% 5.70/1.19 thf(func_def_53, type, sK1: a).
% 5.70/1.19 thf(func_def_54, type, sK2: a).
% 5.70/1.19 thf(func_def_55, type, sK3: a).
% 5.70/1.19 thf(func_def_56, type, sK4: a).
% 5.70/1.19 thf(func_def_57, type, sK5: a).
% 5.70/1.19 thf(func_def_58, type, sK6: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 5.70/1.19 thf(func_def_59, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 5.70/1.19 thf(func_def_60, type, sK8: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_61, type, sK9: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_62, type, sK10: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_63, type, sK11: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_64, type, sK12: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_65, type, sK13: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_66, type, sK14: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_67, type, sK15: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_68, type, sK16: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_69, type, sK17: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_70, type, sK18: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_71, type, sK19: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_72, type, sK20: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_73, type, sK21: ((a > a > a) > a)).
% 5.70/1.19 thf(func_def_74, type, sK22: ((a > $o) > (a > $o) > a)).
% 5.70/1.19 thf(func_def_75, type, sK23: (a > (a > $o) > a)).
% 5.70/1.19 thf(func_def_76, type, sK24: (a > (a > $o) > a)).
% 5.70/1.19 thf(func_def_77, type, sK25: (a > (a > $o) > a)).
% 5.70/1.19 thf(func_def_78, type, sK26: (a > (a > $o) > a)).
% 5.70/1.19 thf(func_def_79, type, sK27: (a > (a > $o) > a)).
% 5.70/1.19 thf(func_def_80, type, sK28: (a > (a > $o) > a)).
% 5.70/1.19 thf(func_def_81, type, sK29: ((a > $o) > (a > $o) > a)).
% 5.70/1.19 thf(func_def_82, type, sK30: (a > (a > $o) > a)).
% 5.70/1.19 thf(func_def_83, type, sK31: (a > (a > $o) > a)).
% 5.70/1.19 thf(func_def_84, type, sK32: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_85, type, sK33: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_86, type, sK34: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 5.70/1.19 thf(func_def_87, type, sK35: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 5.70/1.19 thf(func_def_88, type, sK36: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 5.70/1.19 thf(func_def_89, type, sK37: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_90, type, sK38: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_91, type, sK39: !>[X0: $tType]:(((a > X0) > a))).
% 5.70/1.19 thf(func_def_92, type, sK40: !>[X0: $tType]:(((a > X0) > a))).
% 5.70/1.19 thf(func_def_93, type, sK41: !>[X0: $tType]:(((a > X0) > a))).
% 5.70/1.19 thf(func_def_94, type, sK42: !>[X0: $tType]:(((a > X0) > a))).
% 5.70/1.19 thf(func_def_95, type, sK43: (set @ a > a)).
% 5.70/1.19 thf(func_def_96, type, sK44: (set @ a > a)).
% 5.70/1.19 thf(func_def_97, type, sK45: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_98, type, sK46: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_99, type, sK47: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 5.70/1.19 thf(func_def_100, type, sK48: !>[X0: $tType]:((set @ X0 > X0))).
% 5.70/1.19 thf(func_def_101, type, sK49: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 5.70/1.19 thf(func_def_102, type, sK50: a).
% 5.70/1.19 thf(func_def_103, type, sK51: a).
% 5.70/1.19 thf(func_def_104, type, sK52: a).
% 5.70/1.19 thf(func_def_105, type, sK53: a).
% 5.70/1.19 thf(func_def_106, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (set @ X1 > $o) > X1))).
% 5.70/1.19 thf(func_def_107, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (set @ X1 > $o) > set @ X1))).
% 5.70/1.19 thf(func_def_108, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1 > X0))).
% 5.70/1.19 thf(func_def_109, type, sK57: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1))).
% 5.70/1.19 thf(func_def_110, type, sK58: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 5.70/1.19 thf(func_def_111, type, sK59: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 5.70/1.19 thf(func_def_112, type, sK60: !>[X0: $tType]:((set @ X0 > X0))).
% 5.70/1.19 thf(func_def_113, type, sK61: !>[X0: $tType]:((set @ X0 > X0))).
% 5.70/1.19 thf(func_def_114, type, sK62: !>[X0: $tType]:(((X0 > $o) > X0))).
% 5.70/1.19 thf(func_def_115, type, sK63: !>[X0: $tType]:(((X0 > $o) > X0))).
% 5.70/1.19 thf(func_def_116, type, sK64: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_117, type, sK65: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_118, type, sK66: !>[X0: $tType]:(((a > X0) > a))).
% 5.70/1.19 thf(func_def_119, type, sK67: !>[X0: $tType]:(((a > X0) > a))).
% 5.70/1.19 thf(func_def_120, type, sK68: !>[X0: $tType]:(((a > X0) > a))).
% 5.70/1.19 thf(func_def_121, type, sK69: !>[X0: $tType]:(((a > X0) > a))).
% 5.70/1.19 thf(func_def_122, type, sK70: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 5.70/1.19 thf(func_def_123, type, sK71: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 5.70/1.19 thf(func_def_124, type, sK72: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 5.70/1.19 thf(func_def_125, type, sK73: (set @ a > a)).
% 5.70/1.19 thf(func_def_126, type, sK74: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_127, type, sK75: (set @ a > a)).
% 5.70/1.19 thf(func_def_128, type, sK76: (a > set @ a > a)).
% 5.70/1.19 thf(func_def_130, type, db4: !>[X0: $tType]:(X0)).
% 5.70/1.19 thf(func_def_131, type, db5: !>[X0: $tType]:(X0)).
% 5.70/1.19 thf(f1,axiom,(
% 5.70/1.19 ! [X2 : a,X3 : a,X4 : a] : (((inf @ (inf @ X2 @ X3) @ X4)) = ((inf @ X2 @ (inf @ X3 @ X4))))),
% 5.70/1.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_local_Oinf_Oassoc)).
% 5.70/1.19 thf(f2,axiom,(
% 5.70/1.19 ! [X0 : a,X1 : a] : (((inf @ X0 @ X1)) = ((inf @ X1 @ X0)))),
% 5.70/1.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_local_Oinf_Ocommute)).
% 5.70/1.19 thf(f8,axiom,(
% 5.70/1.19 ! [X0 : a,X1 : a] : (((sup @ X0 @ X1)) = ((sup @ X1 @ X0)))),
% 5.70/1.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_local_Osup_Ocommute)).
% 5.70/1.19 thf(f15,axiom,(
% 5.70/1.19 ! [X0 : a,X1 : a,X2 : a] : (((modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) = ((inf @ (inf @ (sup @ X0 @ X1) @ (sup @ X1 @ X2)) @ (sup @ X2 @ X0))))),
% 5.70/1.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_e__aux__def)).
% 5.70/1.19 thf(f264,conjecture,(
% 5.70/1.19 (((modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) = ((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 5.70/1.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 5.70/1.19 thf(f265,negated_conjecture,(
% 5.70/1.19 ~ (((modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) = ((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 5.70/1.19 inference(negated_conjecture,[status(cth)],[f264])).
% 5.70/1.19 thf(f674,plain,(
% 5.70/1.19 ! [X0 : a,X1 : a,X2 : a] : (((inf @ X0 @ (inf @ X1 @ X2))) = ((inf @ (inf @ X0 @ X1) @ X2)))),
% 5.70/1.19 inference(rectify,[],[f1])).
% 5.70/1.19 thf(f689,plain,(
% 5.70/1.19 (((modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != ((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 5.70/1.19 inference(flattening,[],[f265])).
% 5.70/1.19 thf(f929,plain,(
% 5.70/1.19 ( ! [X2 : a,X0 : a,X1 : a] : ((((inf @ X0 @ (inf @ X1 @ X2))) = ((inf @ (inf @ X0 @ X1) @ X2)))) )),
% 5.70/1.19 inference(cnf_transformation,[],[f674])).
% 5.70/1.19 thf(f930,plain,(
% 5.70/1.19 ( ! [X0 : a,X1 : a] : ((((inf @ X0 @ X1)) = ((inf @ X1 @ X0)))) )),
% 5.70/1.19 inference(cnf_transformation,[],[f2])).
% 5.70/1.19 thf(f936,plain,(
% 5.70/1.19 ( ! [X0 : a,X1 : a] : ((((sup @ X0 @ X1)) = ((sup @ X1 @ X0)))) )),
% 5.70/1.19 inference(cnf_transformation,[],[f8])).
% 5.70/1.19 thf(f943,plain,(
% 5.70/1.19 ( ! [X2 : a,X0 : a,X1 : a] : ((((modula1593167561_e_aux @ a @ inf @ sup @ X0 @ X1 @ X2)) = ((inf @ (inf @ (sup @ X0 @ X1) @ (sup @ X1 @ X2)) @ (sup @ X2 @ X0))))) )),
% 5.70/1.19 inference(cnf_transformation,[],[f15])).
% 5.70/1.19 thf(f1245,plain,(
% 5.70/1.19 (((modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2)) != ((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)))),
% 5.70/1.19 inference(cnf_transformation,[],[f689])).
% 5.70/1.19 thf(f19860,plain,(
% 5.70/1.19 (((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) != ((inf @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)) @ (sup @ a2 @ b))))),
% 5.70/1.19 inference(constrained_superposition,[],[f1245,f943])).
% 5.70/1.19 thf(f19901,plain,(
% 5.70/1.19 (((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) != ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ c @ a2)))))),
% 5.70/1.19 inference(forward_demodulation,[],[f19860,f930])).
% 5.70/1.19 thf(f19922,plain,(
% 5.70/1.19 (((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) != ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))))),
% 5.70/1.19 inference(forward_demodulation,[],[f19901,f936])).
% 5.70/1.19 thf(f19927,plain,(
% 5.70/1.19 (((modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c)) != ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))))),
% 5.70/1.19 inference(forward_demodulation,[],[f19922,f930])).
% 5.70/1.19 thf(f20032,plain,(
% 5.70/1.19 (((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) != ((inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ c @ a2))))),
% 5.70/1.19 inference(constrained_superposition,[],[f19927,f943])).
% 5.70/1.19 thf(f20033,plain,(
% 5.70/1.19 (((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) != ((inf @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (sup @ a2 @ c))))),
% 5.70/1.19 inference(forward_demodulation,[],[f20032,f936])).
% 5.70/1.19 thf(f20036,plain,(
% 5.70/1.19 (((inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ c)))) != ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))))),
% 5.70/1.19 inference(constrained_superposition,[],[f20033,f929])).
% 5.70/1.19 thf(f20037,plain,(
% 5.70/1.19 (((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))) != ((inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))))),
% 5.70/1.19 inference(forward_demodulation,[],[f20036,f930])).
% 5.70/1.19 thf(f20038,plain,(
% 5.70/1.19 $false),
% 5.70/1.19 inference(trivial_inequality_removal,[],[f20037])).
% 5.70/1.19 % SZS output end Proof for theBenchmark
% 5.70/1.19 % (832530)------------------------------
% 5.70/1.19 % (832530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.70/1.19 % (832530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.19 % (832530)CaDiCaL version: 2.1.3
% 5.70/1.19 % (832530)Termination reason: Refutation
% 5.70/1.19 % (832530)Time elapsed: 0.895 s
% 5.70/1.19 % (832530)Peak memory usage: 25 MB
% 5.70/1.19 % (832530)Instructions burned: 1811 (million)
% 5.70/1.19 % (832524)Success in time 0.948 s
% 5.70/1.19 % Vampire exiting
%------------------------------------------------------------------------------