%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI614_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:34:58 AM UTC 2026
% Result : Theorem 0.27s 0.37s
% Output : Refutation 0.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI614_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 % Computer : n001.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 20:59:33 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.27 Running first-order model finding
% 0.11/0.27 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
% 0.27/0.37 % (735778)Will run a generic schedule for satisfiability detection.
% 0.27/0.37 % (735785)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2563526508:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.27/0.37 % (735783)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2542659578_3000 on theBenchmark for (3000ds/0Mi)
% 0.27/0.37 % (735783)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.27/0.37 % (735783)Terminated due to inappropriate strategy.
% 0.27/0.37 % (735783)------------------------------
% 0.27/0.37 % (735783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.37 % (735783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.37 % (735783)CaDiCaL version: 2.1.3
% 0.27/0.37 % (735783)Termination reason: Inappropriate
% 0.27/0.37 % (735783)Time elapsed: 0.0000 s
% 0.27/0.37 % (735783)Peak memory usage: 10 MB
% 0.27/0.37 % (735783)------------------------------
% 0.27/0.37 % (735783)------------------------------
% 0.27/0.37 % (735784)% WARNING: option uhcvi not known.
% 0.27/0.37 % (735788)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1649017131:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.27/0.37 % (735789)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=855575690:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.27/0.37 % (735784)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1176148756:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.27/0.37 % (735786)dis+10_1_sil=32000:sp=arity:random_seed=2687244799:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.27/0.37 % (735787)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=819863328:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.27/0.37 % (735792)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2502754645:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.27/0.37 % (735792)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.27/0.37 % (735792)Terminated due to inappropriate strategy.
% 0.27/0.37 % (735792)------------------------------
% 0.27/0.37 % (735792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.37 % (735792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.37 % (735792)CaDiCaL version: 2.1.3
% 0.27/0.37 % (735792)Termination reason: Inappropriate
% 0.27/0.37 % (735792)Time elapsed: 0.0000 s
% 0.27/0.37 % (735792)Peak memory usage: 10 MB
% 0.27/0.37 % (735792)------------------------------
% 0.27/0.37 % (735792)------------------------------
% 0.27/0.37 % (735799)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3427205049:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.27/0.37 % (735786) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-735778-735786"...
% 0.27/0.37 % (735786)...printing done.
% 0.27/0.37 % (735786)Refutation found. Thanks to Tanya!
% 0.27/0.37 % SZS status Theorem for theBenchmark
% 0.27/0.37 % SZS output start Proof for theBenchmark
% 0.27/0.37 tff(func_def_0, type, a: $int).
% 0.27/0.37 tff(pred_def_1, type, p: $int > $o).
% 0.27/0.37 tff(pred_def_2, type, q: $int > $o).
% 0.27/0.37 tff(f1,conjecture,(
% 0.27/0.37 (! [X0 : $int] : ($less(a,X0) => p(X0)) & ! [X0 : $int] : ($less(X0,0) => q(X0))) => ? [X0 : $int,X1 : $int] : (p(X0) & q(X1) & $sum(X0,X1) = 0)),
% 0.27/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',interv_a_infty_and_neginfty_1_contain_compl)).
% 0.27/0.37 tff(f2,negated_conjecture,(
% 0.27/0.37 ~((! [X0 : $int] : ($less(a,X0) => p(X0)) & ! [X0 : $int] : ($less(X0,0) => q(X0))) => ? [X0 : $int,X1 : $int] : (p(X0) & q(X1) & $sum(X0,X1) = 0))),
% 0.27/0.37 inference(negated_conjecture,[status(cth)],[f1])).
% 0.27/0.37 tff(f3,definition,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.27/0.37 introduced(theory,[tha_commutativity])).
% 0.27/0.37 tff(f4,definition,(
% 0.27/0.37 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.27/0.37 introduced(theory,[tha_associativity])).
% 0.27/0.37 tff(f5,definition,(
% 0.27/0.37 ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
% 0.27/0.37 introduced(theory,[tha_right_identity])).
% 0.27/0.37 tff(f7,definition,(
% 0.27/0.37 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.27/0.37 introduced(theory,[tha_inverse_op_unit])).
% 0.27/0.37 tff(f9,definition,(
% 0.27/0.37 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.27/0.37 introduced(theory,[tha_transitivity])).
% 0.27/0.37 tff(f10,definition,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 0.27/0.37 introduced(theory,[tha_order_totality])).
% 0.27/0.37 tff(f11,definition,(
% 0.27/0.37 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 0.27/0.37 introduced(theory,[tha_order_monotonicity])).
% 0.27/0.37 tff(f12,definition,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.27/0.37 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.27/0.37 tff(f13,definition,(
% 0.27/0.37 ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
% 0.27/0.37 introduced(theory,[tha_minus_minus_x])).
% 0.27/0.37 tff(f15,plain,(
% 0.27/0.37 ~((! [X0 : $int] : ($less(a,X0) => p(X0)) & ! [X1 : $int] : ($less(X1,0) => q(X1))) => ? [X2 : $int,X3 : $int] : (p(X2) & q(X3) & 0 = $sum(X2,X3)))),
% 0.27/0.37 inference(rectify,[],[f2])).
% 0.27/0.37 tff(f16,plain,(
% 0.27/0.37 ! [X2 : $int,X3 : $int] : (~p(X2) | ~q(X3) | 0 != $sum(X2,X3)) & (! [X0 : $int] : (p(X0) | ~$less(a,X0)) & ! [X1 : $int] : (q(X1) | ~$less(X1,0)))),
% 0.27/0.37 inference(ennf_transformation,[],[f15])).
% 0.27/0.37 tff(f17,plain,(
% 0.27/0.37 ! [X2 : $int,X3 : $int] : (~p(X2) | ~q(X3) | 0 != $sum(X2,X3)) & ! [X0 : $int] : (p(X0) | ~$less(a,X0)) & ! [X1 : $int] : (q(X1) | ~$less(X1,0))),
% 0.27/0.37 inference(flattening,[],[f16])).
% 0.27/0.37 tff(f18,plain,(
% 0.27/0.37 ! [X0 : $int,X1 : $int] : (~p(X0) | ~q(X1) | 0 != $sum(X0,X1)) & ! [X2 : $int] : (p(X2) | ~$less(a,X2)) & ! [X3 : $int] : (q(X3) | ~$less(X3,0))),
% 0.27/0.37 inference(rectify,[],[f17])).
% 0.27/0.37 tff(f19,plain,(
% 0.27/0.37 ( ! [X3 : $int] : (~$less(X3,0) | q(X3)) )),
% 0.27/0.37 inference(cnf_transformation,[],[f18])).
% 0.27/0.37 tff(f20,plain,(
% 0.27/0.37 ( ! [X2 : $int] : (~$less(a,X2) | p(X2)) )),
% 0.27/0.37 inference(cnf_transformation,[],[f18])).
% 0.27/0.37 tff(f21,plain,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : (0 != $sum(X0,X1) | ~q(X1) | ~p(X0)) )),
% 0.27/0.37 inference(cnf_transformation,[],[f18])).
% 0.27/0.37 tff(f32,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (0 != 0 | ~q($uminus(X0)) | ~p(X0)) )),
% 0.27/0.37 inference(superposition,[],[f21,f7])).
% 0.27/0.37 tff(f33,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (~q($uminus(X0)) | ~p(X0)) )),
% 0.27/0.37 inference(trivial_inequality_removal,[],[f32])).
% 0.27/0.37 tff(f34,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (~p($uminus(X0)) | ~q(X0)) )),
% 0.27/0.37 inference(superposition,[],[f33,f13])).
% 0.27/0.37 tff(f43,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (p($sum(X0,1)) | $less(X0,a)) )),
% 0.27/0.37 inference(resolution,[],[f12,f20])).
% 0.27/0.37 tff(f46,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (p($sum(1,X0)) | $less(X0,a)) )),
% 0.27/0.37 inference(superposition,[],[f43,f3])).
% 0.27/0.37 tff(f66,definition,(
% 0.27/0.37 spl0_5 <=> $less(0,a)),
% 0.27/0.37 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.27/0.37 tff(f68,plain,(
% 0.27/0.37 $less(0,a) | ~spl0_5),
% 0.27/0.37 inference(avatar_component_clause,[],[f66])).
% 0.27/0.37 tff(f77,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (q(X0) | 0 = X0 | $less(0,X0)) )),
% 0.27/0.37 inference(resolution,[],[f10,f19])).
% 0.27/0.37 tff(f85,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (~$less(X0,0) | $less(X0,a)) ) | ~spl0_5),
% 0.27/0.37 inference(resolution,[],[f68,f9])).
% 0.27/0.37 tff(f110,plain,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : ($less($sum(X0,$uminus(X1)),0) | ~$less(X0,X1)) )),
% 0.27/0.37 inference(superposition,[],[f11,f7])).
% 0.27/0.37 tff(f119,plain,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 0.27/0.37 inference(superposition,[],[f4,f7])).
% 0.27/0.37 tff(f138,plain,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 0.27/0.37 inference(evaluation,[],[f119])).
% 0.27/0.37 tff(f239,definition,(
% 0.27/0.37 spl0_11 <=> q(-1)),
% 0.27/0.37 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 0.27/0.37 tff(f240,plain,(
% 0.27/0.37 q(-1) | ~spl0_11),
% 0.27/0.37 inference(avatar_component_clause,[],[f239])).
% 0.27/0.37 tff(f241,plain,(
% 0.27/0.37 ~q(-1) | spl0_11),
% 0.27/0.37 inference(avatar_component_clause,[],[f239])).
% 0.27/0.37 tff(f264,plain,(
% 0.27/0.37 0 = -1 | $less(0,-1) | spl0_11),
% 0.27/0.37 inference(resolution,[],[f241,f77])).
% 0.27/0.37 tff(f265,plain,(
% 0.27/0.37 $false | spl0_11),
% 0.27/0.37 inference(evaluation,[],[f264])).
% 0.27/0.37 tff(f266,plain,(
% 0.27/0.37 spl0_11),
% 0.27/0.37 inference(avatar_contradiction_clause,[],[f265])).
% 0.27/0.37 tff(f286,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (p(X0) | $less($sum($uminus(1),X0),a)) )),
% 0.27/0.37 inference(superposition,[],[f46,f138])).
% 0.27/0.37 tff(f287,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (p(X0) | $less($sum(-1,X0),a)) )),
% 0.27/0.37 inference(evaluation,[],[f286])).
% 0.27/0.37 tff(f305,plain,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : (q($sum(X0,$uminus(X1))) | ~$less(X0,X1)) )),
% 0.27/0.37 inference(resolution,[],[f110,f19])).
% 0.27/0.37 tff(f382,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (~q(X0) | $less($sum(-1,$uminus(X0)),a)) )),
% 0.27/0.37 inference(resolution,[],[f287,f34])).
% 0.27/0.37 tff(f390,plain,(
% 0.27/0.37 ( ! [X0 : $int,X1 : $int] : (q($sum($uminus(X0),X1)) | ~$less(X1,X0)) )),
% 0.27/0.37 inference(superposition,[],[f305,f3])).
% 0.27/0.37 tff(f427,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (~$less(0,X0) | q($uminus(X0))) )),
% 0.27/0.37 inference(superposition,[],[f390,f5])).
% 0.27/0.37 tff(f435,plain,(
% 0.27/0.37 q($uminus(a)) | ~spl0_5),
% 0.27/0.37 inference(resolution,[],[f427,f68])).
% 0.27/0.37 tff(f438,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (q($uminus($sum(X0,1))) | $less(X0,0)) )),
% 0.27/0.37 inference(resolution,[],[f427,f12])).
% 0.27/0.37 tff(f467,plain,(
% 0.27/0.37 ~p(a) | ~spl0_5),
% 0.27/0.37 inference(resolution,[],[f435,f33])).
% 0.27/0.37 tff(f911,plain,(
% 0.27/0.37 $less($sum(-1,$uminus(-1)),a) | ~spl0_11),
% 0.27/0.37 inference(resolution,[],[f382,f240])).
% 0.27/0.37 tff(f912,plain,(
% 0.27/0.37 $less(0,a) | ~spl0_11),
% 0.27/0.37 inference(evaluation,[],[f911])).
% 0.27/0.37 tff(f1030,plain,(
% 0.27/0.37 ( ! [X0 : $int] : (~p($sum(X0,1)) | $less(X0,0)) )),
% 0.27/0.37 inference(resolution,[],[f438,f33])).
% 0.27/0.37 tff(f1088,plain,(
% 0.27/0.37 ( ! [X0 : $int] : ($less(X0,0) | $less(X0,a)) )),
% 0.27/0.37 inference(resolution,[],[f1030,f43])).
% 0.27/0.37 tff(f1098,plain,(
% 0.27/0.37 ( ! [X0 : $int] : ($less(X0,a)) ) | ~spl0_5),
% 0.27/0.37 inference(forward_subsumption_resolution,[],[f1088,f85])).
% 0.27/0.37 tff(f1287,plain,(
% 0.27/0.37 p(a) | ~spl0_5),
% 0.27/0.37 inference(resolution,[],[f1098,f20])).
% 0.27/0.37 tff(f1292,plain,(
% 0.27/0.37 $false | ~spl0_5),
% 0.27/0.37 inference(forward_subsumption_resolution,[],[f1287,f467])).
% 0.27/0.37 tff(f1293,plain,(
% 0.27/0.37 ~spl0_5),
% 0.27/0.37 inference(avatar_contradiction_clause,[],[f1292])).
% 0.27/0.37 tff(f1300,plain,(
% 0.27/0.37 spl0_5 | ~spl0_11),
% 0.27/0.37 inference(avatar_split_clause,[],[f912,f239,f66])).
% 0.27/0.37 cnf(s8, plain, spl0_11, inference(sat_conversion,[],[f266])).
% 0.27/0.37 cnf(s14, plain, ~spl0_5, inference(sat_conversion,[],[f1293])).
% 0.27/0.37 cnf(s17, plain, spl0_5 | ~spl0_11, inference(sat_conversion,[],[f1300])).
% 0.27/0.37 cnf(s18, plain, ~spl0_11, inference(rat,[],[s17,s14])).
% 0.27/0.37 cnf(s21, plain, $false, inference(rat,[],[s8,s18])).
% 0.27/0.37 tff(f1301,plain,(
% 0.27/0.37 $false),
% 0.27/0.37 inference(avatar_sat_refutation,[],[s21])).
% 0.27/0.37 % SZS output end Proof for theBenchmark
% 0.27/0.37 % (735786)------------------------------
% 0.27/0.37 % (735786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.37 % (735786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.37 % (735786)CaDiCaL version: 2.1.3
% 0.27/0.37 % (735786)Termination reason: Refutation
% 0.27/0.37 % (735786)Time elapsed: 0.053 s
% 0.27/0.37 % (735786)Peak memory usage: 13 MB
% 0.27/0.37 % (735786)Instructions burned: 52 (million)
% 0.27/0.37 % (735778)Success in time 0.091 s
% 0.27/0.37 % Vampire exiting
%------------------------------------------------------------------------------