%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM920_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:26:03 PM UTC 2026
% Result : Theorem 1.18s 0.60s
% Output : Refutation 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM920_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.04/0.35 % CPULimit : 300
% 0.04/0.35 % WCLimit : 300
% 0.04/0.35 % DateTime : Sun Sep 27 21:45:16 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.39 Running first-order model finding
% 0.04/0.39 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
% 1.18/0.60 % (3984075)Will run a generic schedule for satisfiability detection.
% 1.18/0.60 % (3984085)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3580445958:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.18/0.60 % (3984081)% WARNING: option uhcvi not known.
% 1.18/0.60 % (3984080)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=874673078_2999 on theBenchmark for (2999ds/0Mi)
% 1.18/0.60 % (3984081)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1363484623:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.18/0.60 % (3984082)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3136763692:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.18/0.60 % (3984083)dis+10_1_sil=32000:sp=arity:random_seed=2809986715:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.18/0.60 % (3984084)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=69579227:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.18/0.60 % (3984080)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.18/0.60 % (3984080)Terminated due to inappropriate strategy.
% 1.18/0.60 % (3984080)------------------------------
% 1.18/0.60 % (3984080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984080)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984080)Termination reason: Inappropriate
% 1.18/0.60 % (3984080)Time elapsed: 0.0000 s
% 1.18/0.60 % (3984080)Peak memory usage: 10 MB
% 1.18/0.60 % (3984086)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2221750823:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.18/0.60 % (3984080)------------------------------
% 1.18/0.60 % (3984080)------------------------------
% 1.18/0.60 % (3984094)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1399444253:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.18/0.60 % (3984094)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.18/0.60 % (3984094)Terminated due to inappropriate strategy.
% 1.18/0.60 % (3984094)------------------------------
% 1.18/0.60 % (3984094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984094)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984094)Termination reason: Inappropriate
% 1.18/0.60 % (3984094)Time elapsed: 0.0000 s
% 1.18/0.60 % (3984094)Peak memory usage: 10 MB
% 1.18/0.60 % (3984094)------------------------------
% 1.18/0.60 % (3984094)------------------------------
% 1.18/0.60 % (3984085)Instruction limit reached!
% 1.18/0.60 % (3984085)------------------------------
% 1.18/0.60 % (3984085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984085)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984085)Termination reason: Instruction limit
% 1.18/0.60 % (3984085)Termination phase: Saturation
% 1.18/0.60 % (3984085)Time elapsed: 0.046 s
% 1.18/0.60 % (3984085)Peak memory usage: 13 MB
% 1.18/0.60 % (3984085)Instructions burned: 132 (million)
% 1.18/0.60 % (3984096)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4272782050:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.18/0.60 % (3984097)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=4129854524:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.18/0.60 % (3984083)Instruction limit reached!
% 1.18/0.60 % (3984083)------------------------------
% 1.18/0.60 % (3984083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984083)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984083)Termination reason: Instruction limit
% 1.18/0.60 % (3984083)Termination phase: Saturation
% 1.18/0.60 % (3984083)Time elapsed: 0.062 s
% 1.18/0.60 % (3984083)Peak memory usage: 12 MB
% 1.18/0.60 % (3984083)Instructions burned: 103 (million)
% 1.18/0.60 % (3984084)Instruction limit reached!
% 1.18/0.60 % (3984084)------------------------------
% 1.18/0.60 % (3984084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984084)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984084)Termination reason: Instruction limit
% 1.18/0.60 % (3984084)Termination phase: Saturation
% 1.18/0.60 % (3984084)Time elapsed: 0.070 s
% 1.18/0.60 % (3984084)Peak memory usage: 12 MB
% 1.18/0.60 % (3984084)Instructions burned: 116 (million)
% 1.18/0.60 % (3984100)ott-21_1_sil=16000:fs=off:random_seed=2609179078:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.18/0.60 % (3984101)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1653472987:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 1.18/0.60 % (3984086)Instruction limit reached!
% 1.18/0.60 % (3984086)------------------------------
% 1.18/0.60 % (3984086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984086)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984086)Termination reason: Instruction limit
% 1.18/0.60 % (3984086)Termination phase: Saturation
% 1.18/0.60 % (3984086)Time elapsed: 0.103 s
% 1.18/0.60 % (3984086)Peak memory usage: 13 MB
% 1.18/0.60 % (3984086)Instructions burned: 161 (million)
% 1.18/0.60 % (3984104)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=552959877:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.18/0.60 % (3984104)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.18/0.60 % (3984104)Terminated due to inappropriate strategy.
% 1.18/0.60 % (3984104)------------------------------
% 1.18/0.60 % (3984104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984104)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984104)Termination reason: Inappropriate
% 1.18/0.60 % (3984104)Time elapsed: 0.0000 s
% 1.18/0.60 % (3984104)Peak memory usage: 10 MB
% 1.18/0.60 % (3984104)------------------------------
% 1.18/0.60 % (3984104)------------------------------
% 1.18/0.60 % (3984096)Instruction limit reached!
% 1.18/0.60 % (3984096)------------------------------
% 1.18/0.60 % (3984096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984096)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984096)Termination reason: Instruction limit
% 1.18/0.60 % (3984096)Termination phase: Saturation
% 1.18/0.60 % (3984096)Time elapsed: 0.086 s
% 1.18/0.60 % (3984096)Peak memory usage: 13 MB
% 1.18/0.60 % (3984096)Instructions burned: 132 (million)
% 1.18/0.60 % (3984106)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3066215880:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.18/0.60 % (3984107)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2538049942:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.18/0.60 % (3984107)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.18/0.60 % (3984107)Terminated due to inappropriate strategy.
% 1.18/0.60 % (3984107)------------------------------
% 1.18/0.60 % (3984107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984107)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984107)Termination reason: Inappropriate
% 1.18/0.60 % (3984107)Time elapsed: 0.0000 s
% 1.18/0.60 % (3984107)Peak memory usage: 10 MB
% 1.18/0.60 % (3984107)------------------------------
% 1.18/0.60 % (3984107)------------------------------
% 1.18/0.60 % (3984100)Instruction limit reached!
% 1.18/0.60 % (3984100)------------------------------
% 1.18/0.60 % (3984100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984100)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984100)Termination reason: Instruction limit
% 1.18/0.60 % (3984100)Termination phase: Saturation
% 1.18/0.60 % (3984100)Time elapsed: 0.078 s
% 1.18/0.60 % (3984100)Peak memory usage: 12 MB
% 1.18/0.60 % (3984100)Instructions burned: 181 (million)
% 1.18/0.60 % (3984110)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=3952907076: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)
% 1.18/0.60 % (3984106) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3984075-3984106"...
% 1.18/0.60 % (3984106)...printing done.
% 1.18/0.60 % (3984106)Refutation found. Thanks to Tanya!
% 1.18/0.60 % SZS status Theorem for theBenchmark
% 1.18/0.60 % SZS output start Proof for theBenchmark
% 1.18/0.60 tff(func_def_4, type, sK0: $int).
% 1.18/0.60 tff(func_def_5, type, sF1: $int > $int).
% 1.18/0.60 tff(f1,conjecture,(
% 1.18/0.60 ~ ? [X0 : $int] : ($less(0,X0) & ! [X1 : $int] : ($less(X1,X0) => $less($sum(X1,1),X0)))),
% 1.18/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 1.18/0.60 tff(f2,negated_conjecture,(
% 1.18/0.60 ~ ~ ? [X0 : $int] : ($less(0,X0) & ! [X1 : $int] : ($less(X1,X0) => $less($sum(X1,1),X0)))),
% 1.18/0.60 inference(negated_conjecture,[status(cth)],[f1])).
% 1.18/0.60 tff(f3,definition,(
% 1.18/0.60 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 1.18/0.60 introduced(theory,[tha_commutativity])).
% 1.18/0.60 tff(f4,definition,(
% 1.18/0.60 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 1.18/0.60 introduced(theory,[tha_associativity])).
% 1.18/0.60 tff(f7,definition,(
% 1.18/0.60 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 1.18/0.60 introduced(theory,[tha_inverse_op_unit])).
% 1.18/0.60 tff(f8,definition,(
% 1.18/0.60 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 1.18/0.60 introduced(theory,[tha_non-reflexivity])).
% 1.18/0.60 tff(f12,definition,(
% 1.18/0.60 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,$sum(X0,1))) )),
% 1.18/0.60 introduced(theory,[tha_order_plus_one_dichotomy])).
% 1.18/0.60 tff(f15,plain,(
% 1.18/0.60 ? [X0 : $int] : ($less(0,X0) & ! [X1 : $int] : ($less(X1,X0) => $less($sum(X1,1),X0)))),
% 1.18/0.60 inference(flattening,[],[f2])).
% 1.18/0.60 tff(f16,plain,(
% 1.18/0.60 ? [X0 : $int] : ($less(0,X0) & ! [X1 : $int] : ($less($sum(X1,1),X0) | ~$less(X1,X0)))),
% 1.18/0.60 inference(ennf_transformation,[],[f15])).
% 1.18/0.60 tff(f17,plain,(
% 1.18/0.60 $less(0,sK0) & ! [X1 : $int] : ($less($sum(X1,1),sK0) | ~$less(X1,sK0))),
% 1.18/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16])).
% 1.18/0.60 tff(f18,plain,(
% 1.18/0.60 ( ! [X1 : $int] : ($less($sum(X1,1),sK0) | ~$less(X1,sK0)) )),
% 1.18/0.60 inference(cnf_transformation,[],[f17])).
% 1.18/0.60 tff(f20,definition,(
% 1.18/0.60 ( ! [X1 : $int] : (sF1(X1) = $sum(X1,1)) )),
% 1.18/0.60 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 1.18/0.60 tff(f21,plain,(
% 1.18/0.60 ( ! [X1 : $int] : ($sum(X1,1) = sF1(X1)) )),
% 1.18/0.60 inference(reorient_equations,[],[f20])).
% 1.18/0.60 tff(f22,plain,(
% 1.18/0.60 ( ! [X1 : $int] : ($less(sF1(X1),sK0) | ~$less(X1,sK0)) )),
% 1.18/0.60 inference(definition_folding,[],[f18,f21])).
% 1.18/0.60 tff(f25,plain,(
% 1.18/0.60 ( ! [X0 : $int] : ($less($sum(X0,1),sK0) | ~$less(X0,sK0)) )),
% 1.18/0.60 inference(superposition,[],[f22,f21])).
% 1.18/0.60 tff(f31,plain,(
% 1.18/0.60 ( ! [X0 : $int] : ($less($sum(1,X0),sK0) | ~$less(X0,sK0)) )),
% 1.18/0.60 inference(superposition,[],[f25,f3])).
% 1.18/0.60 tff(f95,plain,(
% 1.18/0.60 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 1.18/0.60 inference(superposition,[],[f4,f7])).
% 1.18/0.60 tff(f110,plain,(
% 1.18/0.60 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less(X2,$sum(X0,$sum(X1,1))) | $less($sum(X0,X1),X2)) )),
% 1.18/0.60 inference(superposition,[],[f12,f4])).
% 1.18/0.60 tff(f113,plain,(
% 1.18/0.60 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 1.18/0.60 inference(evaluation,[],[f95])).
% 1.18/0.60 tff(f185,plain,(
% 1.18/0.60 ( ! [X0 : $int] : ($less(X0,sK0) | ~$less($sum($uminus(1),X0),sK0)) )),
% 1.18/0.60 inference(superposition,[],[f31,f113])).
% 1.18/0.60 tff(f187,plain,(
% 1.18/0.60 ( ! [X0 : $int] : (~$less($sum(-1,X0),sK0) | $less(X0,sK0)) )),
% 1.18/0.60 inference(evaluation,[],[f185])).
% 1.18/0.60 tff(f315,plain,(
% 1.18/0.60 ( ! [X0 : $int] : (~$less($sum(X0,-1),sK0) | $less(X0,sK0)) )),
% 1.18/0.60 inference(superposition,[],[f187,f3])).
% 1.18/0.60 tff(f936,plain,(
% 1.18/0.60 ( ! [X0 : $int] : ($less(sK0,$sum(X0,$sum(-1,1))) | $less(X0,sK0)) )),
% 1.18/0.60 inference(resolution,[],[f110,f315])).
% 1.18/0.60 tff(f969,plain,(
% 1.18/0.60 ( ! [X0 : $int] : ($less(sK0,X0) | $less(X0,sK0)) )),
% 1.18/0.60 inference(evaluation,[],[f936])).
% 1.18/0.60 tff(f1017,plain,(
% 1.18/0.60 $less(sK0,sK0)),
% 1.18/0.60 inference(factoring,[],[f969])).
% 1.18/0.60 tff(f1018,plain,(
% 1.18/0.60 $false),
% 1.18/0.60 inference(forward_subsumption_resolution,[],[f1017,f8])).
% 1.18/0.60 % SZS output end Proof for theBenchmark
% 1.18/0.60 % (3984106)------------------------------
% 1.18/0.60 % (3984106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.60 % (3984106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.60 % (3984106)CaDiCaL version: 2.1.3
% 1.18/0.60 % (3984106)Termination reason: Refutation
% 1.18/0.60 % (3984106)Time elapsed: 0.026 s
% 1.18/0.60 % (3984106)Peak memory usage: 12 MB
% 1.18/0.60 % (3984106)Instructions burned: 41 (million)
% 1.18/0.60 % (3984075)Success in time 0.203 s
% 1.18/0.60 % Vampire exiting
%------------------------------------------------------------------------------