%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI735_1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 09:35:09 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI735_1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:05:02 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.28 % (3016725)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (3016735)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2960754122:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (3016731)% WARNING: option uhcvi not known.
% 0.19/0.28 % (3016732)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3213093193:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (3016730)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2642401364_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (3016731)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2624325835:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (3016733)dis+10_1_sil=32000:sp=arity:random_seed=1973036142:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (3016734)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3329602177:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (3016730)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.28 % (3016730)Terminated due to inappropriate strategy.
% 0.19/0.28 % (3016730)------------------------------
% 0.19/0.28 % (3016730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3016730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3016730)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3016730)Termination reason: Inappropriate
% 0.19/0.28 % (3016730)Time elapsed: 0.0000 s
% 0.19/0.28 % (3016730)Peak memory usage: 10 MB
% 0.19/0.28 % (3016736)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=467980454:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (3016730)------------------------------
% 0.19/0.28 % (3016730)------------------------------
% 0.19/0.28 % (3016735) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3016725-3016735"...
% 0.19/0.28 % (3016735)...printing done.
% 0.19/0.28 % (3016735)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 tff(func_def_5, type, sK0: $int).
% 0.19/0.28 tff(f1,conjecture,(
% 0.19/0.28 ! [X0 : $int] : ($greatereq(X0,0) => ((X0 = 0 => $true) & (X0 != 0 => ? [X1 : $int] : (X1 = $difference(X0,1) & $greatereq(X1,0)))))),
% 0.19/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula)).
% 0.19/0.28 tff(f2,negated_conjecture,(
% 0.19/0.28 ~ ! [X0 : $int] : ($greatereq(X0,0) => ((X0 = 0 => $true) & (X0 != 0 => ? [X1 : $int] : (X1 = $difference(X0,1) & $greatereq(X1,0)))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.28 tff(f3,plain,(
% 0.19/0.28 ~ ! [X0 : $int] : (~$less(X0,0) => ((X0 = 0 => $true) & (X0 != 0 => ? [X1 : $int] : ($sum(X0,$uminus(1)) = X1 & ~$less(X1,0)))))),
% 0.19/0.28 inference(theory_normalization,[],[f2])).
% 0.19/0.28 tff(f4,definition,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.19/0.28 introduced(theory,[tha_commutativity])).
% 0.19/0.28 tff(f5,definition,(
% 0.19/0.28 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.19/0.28 introduced(theory,[tha_associativity])).
% 0.19/0.28 tff(f8,definition,(
% 0.19/0.28 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.19/0.28 introduced(theory,[tha_inverse_op_unit])).
% 0.19/0.28 tff(f11,definition,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.19/0.28 introduced(theory,[tha_order_totality])).
% 0.19/0.28 tff(f12,definition,(
% 0.19/0.28 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less($sum(X0,X2),$sum(X1,X2))) )),
% 0.19/0.28 introduced(theory,[tha_order_monotonicity])).
% 0.19/0.28 tff(f15,definition,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(X0,1))) )),
% 0.19/0.28 introduced(theory,[tha_extra_integer_ordering])).
% 0.19/0.28 tff(f16,plain,(
% 0.19/0.28 ~ ! [X0 : $int] : (~$less(X0,0) => (X0 != 0 => ? [X1 : $int] : ($sum(X0,$uminus(1)) = X1 & ~$less(X1,0))))),
% 0.19/0.28 inference(true_and_false_elimination,[],[f3])).
% 0.19/0.28 tff(f17,plain,(
% 0.19/0.28 ? [X0 : $int] : ((! [X1 : $int] : ($sum(X0,$uminus(1)) != X1 | $less(X1,0)) & X0 != 0) & ~$less(X0,0))),
% 0.19/0.28 inference(ennf_transformation,[],[f16])).
% 0.19/0.28 tff(f18,plain,(
% 0.19/0.28 ? [X0 : $int] : (! [X1 : $int] : ($sum(X0,$uminus(1)) != X1 | $less(X1,0)) & X0 != 0 & ~$less(X0,0))),
% 0.19/0.28 inference(flattening,[],[f17])).
% 0.19/0.28 tff(f19,plain,(
% 0.19/0.28 ! [X1 : $int] : ($sum(sK0,$uminus(1)) != X1 | $less(X1,0)) & 0 != sK0 & ~$less(sK0,0)),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f18])).
% 0.19/0.28 tff(f20,plain,(
% 0.19/0.28 ~$less(sK0,0)),
% 0.19/0.28 inference(cnf_transformation,[],[f19])).
% 0.19/0.28 tff(f21,plain,(
% 0.19/0.28 0 != sK0),
% 0.19/0.28 inference(cnf_transformation,[],[f19])).
% 0.19/0.28 tff(f22,plain,(
% 0.19/0.28 ( ! [X1 : $int] : ($sum(sK0,$uminus(1)) != X1 | $less(X1,0)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f19])).
% 0.19/0.28 tff(f23,plain,(
% 0.19/0.28 ( ! [X1 : $int] : ($sum(sK0,-1) != X1 | $less(X1,0)) )),
% 0.19/0.28 inference(evaluation,[],[f22])).
% 0.19/0.28 tff(f24,plain,(
% 0.19/0.28 $less($sum(sK0,-1),0)),
% 0.19/0.28 inference(equality_resolution,[],[f23])).
% 0.19/0.28 tff(f25,plain,(
% 0.19/0.28 $less($sum(-1,sK0),0)),
% 0.19/0.28 inference(forward_demodulation,[],[f24,f4])).
% 0.19/0.28 tff(f58,plain,(
% 0.19/0.28 $less(0,sK0) | 0 = sK0),
% 0.19/0.28 inference(resolution,[],[f11,f20])).
% 0.19/0.28 tff(f60,plain,(
% 0.19/0.28 $less(0,sK0)),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f58,f21])).
% 0.19/0.28 tff(f73,plain,(
% 0.19/0.28 ~$less(sK0,$sum(0,1))),
% 0.19/0.28 inference(resolution,[],[f60,f15])).
% 0.19/0.28 tff(f74,plain,(
% 0.19/0.28 ~$less(sK0,1)),
% 0.19/0.28 inference(evaluation,[],[f73])).
% 0.19/0.28 tff(f98,plain,(
% 0.19/0.28 ( ! [X0 : $int] : ($less($sum($sum(-1,sK0),X0),$sum(0,X0))) )),
% 0.19/0.28 inference(resolution,[],[f12,f25])).
% 0.19/0.28 tff(f107,plain,(
% 0.19/0.28 ( ! [X0 : $int] : ($less($sum($sum(-1,sK0),X0),X0)) )),
% 0.19/0.28 inference(evaluation,[],[f98])).
% 0.19/0.28 tff(f111,plain,(
% 0.19/0.28 ( ! [X0 : $int] : ($less($sum(-1,$sum(sK0,X0)),X0)) )),
% 0.19/0.28 inference(forward_demodulation,[],[f107,f5])).
% 0.19/0.28 tff(f129,plain,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 0.19/0.28 inference(superposition,[],[f5,f8])).
% 0.19/0.28 tff(f143,plain,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 0.19/0.28 inference(evaluation,[],[f129])).
% 0.19/0.28 tff(f216,plain,(
% 0.19/0.28 ( ! [X0 : $int,X1 : $int] : ($sum(X1,$sum(X0,$uminus(X1))) = X0) )),
% 0.19/0.28 inference(superposition,[],[f143,f4])).
% 0.19/0.28 tff(f1773,plain,(
% 0.19/0.28 $less(sK0,$uminus(-1))),
% 0.19/0.28 inference(superposition,[],[f111,f216])).
% 0.19/0.28 tff(f1774,plain,(
% 0.19/0.28 $less(sK0,1)),
% 0.19/0.28 inference(evaluation,[],[f1773])).
% 0.19/0.28 tff(f1780,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f1774,f74])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (3016735)------------------------------
% 0.19/0.28 % (3016735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3016735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3016735)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3016735)Termination reason: Refutation
% 0.19/0.28 % (3016735)Time elapsed: 0.023 s
% 0.19/0.28 % (3016735)Peak memory usage: 12 MB
% 0.19/0.28 % (3016735)Instructions burned: 64 (million)
% 0.19/0.28 % (3016725)Success in time 0.046 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------