%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI669_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 09:35:03 AM UTC 2026
% Result : Theorem 0.18s 0.29s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI669_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n017.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 : Mon Sep 28 20:50:51 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.22 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
% 0.18/0.29 % (4015953)Will run a generic schedule for satisfiability detection.
% 0.18/0.29 % (4015962)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2385555607:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.29 % (4015959)% WARNING: option uhcvi not known.
% 0.18/0.29 % (4015958)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1300708781_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.29 % (4015959)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=85356101:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.29 % (4015960)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1350346841:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.29 % (4015961)dis+10_1_sil=32000:sp=arity:random_seed=4146079458:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.29 % (4015958)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.29 % (4015958)Terminated due to inappropriate strategy.
% 0.18/0.29 % (4015958)------------------------------
% 0.18/0.29 % (4015958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.29 % (4015958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.29 % (4015958)CaDiCaL version: 2.1.3
% 0.18/0.29 % (4015958)Termination reason: Inappropriate
% 0.18/0.29 % (4015958)Time elapsed: 0.0000 s
% 0.18/0.29 % (4015963)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2052899471:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.29 % (4015958)Peak memory usage: 10 MB
% 0.18/0.29 % (4015964)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2525797166:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.29 % (4015958)------------------------------
% 0.18/0.29 % (4015958)------------------------------
% 0.18/0.29 % (4015961) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4015953-4015961"...
% 0.18/0.29 % (4015961)...printing done.
% 0.18/0.29 % (4015961)Refutation found. Thanks to Tanya!
% 0.18/0.29 % SZS status Theorem for theBenchmark
% 0.18/0.29 % SZS output start Proof for theBenchmark
% 0.18/0.29 tff(func_def_0, type, a: $int).
% 0.18/0.29 tff(func_def_1, type, b: $int).
% 0.18/0.29 tff(func_def_2, type, c: $int).
% 0.18/0.29 tff(f1,conjecture,(
% 0.18/0.29 $product($product($product(a,b),b),c) = 0 <=> (c = 0 | b = 0 | a = 0)),
% 0.18/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.18/0.29 tff(f2,negated_conjecture,(
% 0.18/0.29 ~($product($product($product(a,b),b),c) = 0 <=> (c = 0 | b = 0 | a = 0))),
% 0.18/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.18/0.29 tff(f15,definition,(
% 0.18/0.29 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 0.18/0.29 introduced(theory,[tha_associativity])).
% 0.18/0.29 tff(f17,definition,(
% 0.18/0.29 ( ! [X0 : $int] : (0 = $product(X0,0)) )),
% 0.18/0.29 introduced(theory,[tha_times_zero])).
% 0.18/0.29 tff(f19,definition,(
% 0.18/0.29 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : (0 = X0 | $product(X0,X2) != X1 | $product(X0,X3) != X1 | X2 = X3) )),
% 0.18/0.29 introduced(theory,[tha_divisibility])).
% 0.18/0.29 tff(f21,plain,(
% 0.18/0.29 $product($product($product(a,b),b),c) = 0 <~> (c = 0 | b = 0 | a = 0)),
% 0.18/0.29 inference(ennf_transformation,[],[f2])).
% 0.18/0.29 tff(f22,plain,(
% 0.18/0.29 ((c != 0 & b != 0 & a != 0) | $product($product($product(a,b),b),c) != 0) & ((c = 0 | b = 0 | a = 0) | $product($product($product(a,b),b),c) = 0)),
% 0.18/0.29 inference(nnf_transformation,[],[f21])).
% 0.18/0.29 tff(f23,plain,(
% 0.18/0.29 ((c != 0 & b != 0 & a != 0) | $product($product($product(a,b),b),c) != 0) & (c = 0 | b = 0 | a = 0 | $product($product($product(a,b),b),c) = 0)),
% 0.18/0.29 inference(flattening,[],[f22])).
% 0.18/0.29 tff(f24,plain,(
% 0.18/0.29 c = 0 | b = 0 | a = 0 | $product($product($product(a,b),b),c) = 0),
% 0.18/0.29 inference(cnf_transformation,[],[f23])).
% 0.18/0.29 tff(f25,plain,(
% 0.18/0.29 a != 0 | $product($product($product(a,b),b),c) != 0),
% 0.18/0.29 inference(cnf_transformation,[],[f23])).
% 0.18/0.29 tff(f26,plain,(
% 0.18/0.29 b != 0 | $product($product($product(a,b),b),c) != 0),
% 0.18/0.29 inference(cnf_transformation,[],[f23])).
% 0.18/0.29 tff(f27,plain,(
% 0.18/0.29 c != 0 | $product($product($product(a,b),b),c) != 0),
% 0.18/0.29 inference(cnf_transformation,[],[f23])).
% 0.18/0.29 tff(f28,plain,(
% 0.18/0.29 ( ! [X2 : $int,X3 : $int,X0 : $int] : ($product(X0,X2) != $product(X0,X3) | 0 = X0 | X2 = X3) )),
% 0.18/0.29 inference(equality_resolution,[],[f19])).
% 0.18/0.29 tff(f30,definition,(
% 0.18/0.29 spl0_1 <=> $product($product($product(a,b),b),c) = 0),
% 0.18/0.29 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.18/0.29 tff(f31,plain,(
% 0.18/0.29 $product($product($product(a,b),b),c) != 0 | spl0_1),
% 0.18/0.29 inference(avatar_component_clause,[],[f30])).
% 0.18/0.29 tff(f32,plain,(
% 0.18/0.29 $product($product($product(a,b),b),c) = 0 | ~spl0_1),
% 0.18/0.29 inference(avatar_component_clause,[],[f30])).
% 0.18/0.29 tff(f34,definition,(
% 0.18/0.29 spl0_2 <=> a = 0),
% 0.18/0.29 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.18/0.29 tff(f35,plain,(
% 0.18/0.29 a != 0 | spl0_2),
% 0.18/0.29 inference(avatar_component_clause,[],[f34])).
% 0.18/0.29 tff(f36,plain,(
% 0.18/0.29 a = 0 | ~spl0_2),
% 0.18/0.29 inference(avatar_component_clause,[],[f34])).
% 0.18/0.29 tff(f38,definition,(
% 0.18/0.29 spl0_3 <=> b = 0),
% 0.18/0.29 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.18/0.29 tff(f39,plain,(
% 0.18/0.29 b != 0 | spl0_3),
% 0.18/0.29 inference(avatar_component_clause,[],[f38])).
% 0.18/0.29 tff(f40,plain,(
% 0.18/0.29 b = 0 | ~spl0_3),
% 0.18/0.29 inference(avatar_component_clause,[],[f38])).
% 0.18/0.29 tff(f42,definition,(
% 0.18/0.29 spl0_4 <=> c = 0),
% 0.18/0.29 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.18/0.29 tff(f43,plain,(
% 0.18/0.29 c != 0 | spl0_4),
% 0.18/0.29 inference(avatar_component_clause,[],[f42])).
% 0.18/0.29 tff(f44,plain,(
% 0.18/0.29 c = 0 | ~spl0_4),
% 0.18/0.29 inference(avatar_component_clause,[],[f42])).
% 0.18/0.29 tff(f45,plain,(
% 0.18/0.29 spl0_1 | spl0_2 | spl0_3 | spl0_4),
% 0.18/0.29 inference(avatar_split_clause,[],[f24,f42,f38,f34,f30])).
% 0.18/0.29 tff(f46,plain,(
% 0.18/0.29 ~spl0_1 | ~spl0_2),
% 0.18/0.29 inference(avatar_split_clause,[],[f25,f34,f30])).
% 0.18/0.29 tff(f47,plain,(
% 0.18/0.29 ~spl0_1 | ~spl0_3),
% 0.18/0.29 inference(avatar_split_clause,[],[f26,f38,f30])).
% 0.18/0.29 tff(f48,plain,(
% 0.18/0.29 ~spl0_1 | ~spl0_4),
% 0.18/0.29 inference(avatar_split_clause,[],[f27,f42,f30])).
% 0.18/0.29 tff(f49,plain,(
% 0.18/0.29 0 != $product($product($product(0,b),b),c) | (spl0_1 | ~spl0_2)),
% 0.18/0.29 inference(forward_demodulation,[],[f31,f36])).
% 0.18/0.29 tff(f50,plain,(
% 0.18/0.29 $false | (spl0_1 | ~spl0_2)),
% 0.18/0.29 inference(evaluation,[],[f49])).
% 0.18/0.29 tff(f51,plain,(
% 0.18/0.29 spl0_1 | ~spl0_2),
% 0.18/0.29 inference(avatar_contradiction_clause,[],[f50])).
% 0.18/0.29 tff(f52,plain,(
% 0.18/0.29 0 != $product($product($product(a,0),0),c) | (spl0_1 | ~spl0_3)),
% 0.18/0.29 inference(forward_demodulation,[],[f31,f40])).
% 0.18/0.29 tff(f53,plain,(
% 0.18/0.29 $false | (spl0_1 | ~spl0_3)),
% 0.18/0.29 inference(evaluation,[],[f52])).
% 0.18/0.29 tff(f54,plain,(
% 0.18/0.29 spl0_1 | ~spl0_3),
% 0.18/0.29 inference(avatar_contradiction_clause,[],[f53])).
% 0.18/0.29 tff(f55,plain,(
% 0.18/0.29 0 != $product($product($product(a,b),b),0) | (spl0_1 | ~spl0_4)),
% 0.18/0.29 inference(forward_demodulation,[],[f31,f44])).
% 0.18/0.29 tff(f56,plain,(
% 0.18/0.29 $false | (spl0_1 | ~spl0_4)),
% 0.18/0.29 inference(evaluation,[],[f55])).
% 0.18/0.29 tff(f57,plain,(
% 0.18/0.29 spl0_1 | ~spl0_4),
% 0.18/0.29 inference(avatar_contradiction_clause,[],[f56])).
% 0.18/0.29 tff(f252,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 != $product($product($product(a,b),b),X0) | $product($product(a,b),b) = 0 | c = X0) ) | ~spl0_1),
% 0.18/0.29 inference(superposition,[],[f28,f32])).
% 0.18/0.29 tff(f268,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 != $product($product(a,b),$product(b,X0)) | $product($product(a,b),b) = 0 | c = X0) ) | ~spl0_1),
% 0.18/0.29 inference(forward_demodulation,[],[f252,f15])).
% 0.18/0.29 tff(f272,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 != $product(a,$product(b,$product(b,X0))) | $product($product(a,b),b) = 0 | c = X0) ) | ~spl0_1),
% 0.18/0.29 inference(forward_demodulation,[],[f268,f15])).
% 0.18/0.29 tff(f274,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 = $product(a,$product(b,b)) | 0 != $product(a,$product(b,$product(b,X0))) | c = X0) ) | ~spl0_1),
% 0.18/0.29 inference(forward_demodulation,[],[f272,f15])).
% 0.18/0.29 tff(f276,definition,(
% 0.18/0.29 spl0_5 <=> ! [X0 : $int] : (0 != $product(a,$product(b,$product(b,X0))) | c = X0)),
% 0.18/0.29 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.18/0.29 tff(f277,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 != $product(a,$product(b,$product(b,X0))) | c = X0) ) | ~spl0_5),
% 0.18/0.29 inference(avatar_component_clause,[],[f276])).
% 0.18/0.29 tff(f279,definition,(
% 0.18/0.29 spl0_6 <=> 0 = $product(a,$product(b,b))),
% 0.18/0.29 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.18/0.29 tff(f281,plain,(
% 0.18/0.29 0 = $product(a,$product(b,b)) | ~spl0_6),
% 0.18/0.29 inference(avatar_component_clause,[],[f279])).
% 0.18/0.29 tff(f283,plain,(
% 0.18/0.29 spl0_5 | spl0_6 | ~spl0_1),
% 0.18/0.29 inference(avatar_split_clause,[],[f274,f30,f279,f276])).
% 0.18/0.29 tff(f288,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 != $product(a,X0) | a = 0 | $product(b,b) = X0) ) | ~spl0_6),
% 0.18/0.29 inference(superposition,[],[f28,f281])).
% 0.18/0.29 tff(f292,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 != $product(a,X0) | $product(b,b) = X0) ) | (spl0_2 | ~spl0_6)),
% 0.18/0.29 inference(forward_subsumption_resolution,[],[f288,f35])).
% 0.18/0.29 tff(f332,plain,(
% 0.18/0.29 0 != 0 | 0 = $product(b,b) | (spl0_2 | ~spl0_6)),
% 0.18/0.29 inference(superposition,[],[f292,f17])).
% 0.18/0.29 tff(f335,plain,(
% 0.18/0.29 0 = $product(b,b) | (spl0_2 | ~spl0_6)),
% 0.18/0.29 inference(trivial_inequality_removal,[],[f332])).
% 0.18/0.29 tff(f354,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 != $product(b,X0) | b = 0 | b = X0) ) | (spl0_2 | ~spl0_6)),
% 0.18/0.29 inference(superposition,[],[f28,f335])).
% 0.18/0.29 tff(f358,plain,(
% 0.18/0.29 ( ! [X0 : $int] : (0 != $product(b,X0) | b = X0) ) | (spl0_2 | spl0_3 | ~spl0_6)),
% 0.18/0.29 inference(forward_subsumption_resolution,[],[f354,f39])).
% 0.18/0.29 tff(f433,plain,(
% 0.18/0.29 0 != 0 | b = 0 | (spl0_2 | spl0_3 | ~spl0_6)),
% 0.18/0.29 inference(superposition,[],[f358,f17])).
% 0.18/0.29 tff(f436,plain,(
% 0.18/0.29 b = 0 | (spl0_2 | spl0_3 | ~spl0_6)),
% 0.18/0.29 inference(trivial_inequality_removal,[],[f433])).
% 0.18/0.29 tff(f439,plain,(
% 0.18/0.29 $false | (spl0_2 | spl0_3 | ~spl0_6)),
% 0.18/0.29 inference(forward_subsumption_resolution,[],[f436,f39])).
% 0.18/0.29 tff(f440,plain,(
% 0.18/0.29 spl0_2 | spl0_3 | ~spl0_6),
% 0.18/0.29 inference(avatar_contradiction_clause,[],[f439])).
% 0.18/0.29 tff(f460,plain,(
% 0.18/0.29 0 != $product(a,$product(b,0)) | c = 0 | ~spl0_5),
% 0.18/0.29 inference(superposition,[],[f277,f17])).
% 0.18/0.29 tff(f465,plain,(
% 0.18/0.29 c = 0 | ~spl0_5),
% 0.18/0.29 inference(evaluation,[],[f460])).
% 0.18/0.29 tff(f466,plain,(
% 0.18/0.29 $false | (spl0_4 | ~spl0_5)),
% 0.18/0.29 inference(forward_subsumption_resolution,[],[f465,f43])).
% 0.18/0.29 tff(f467,plain,(
% 0.18/0.29 spl0_4 | ~spl0_5),
% 0.18/0.29 inference(avatar_contradiction_clause,[],[f466])).
% 0.18/0.29 cnf(s1, plain, spl0_1 | spl0_2 | spl0_3 | spl0_4, inference(sat_conversion,[],[f45])).
% 0.18/0.29 cnf(s2, plain, ~spl0_1 | ~spl0_2, inference(sat_conversion,[],[f46])).
% 0.18/0.29 cnf(s3, plain, ~spl0_1 | ~spl0_3, inference(sat_conversion,[],[f47])).
% 0.18/0.29 cnf(s4, plain, ~spl0_1 | ~spl0_4, inference(sat_conversion,[],[f48])).
% 0.18/0.29 cnf(s5, plain, spl0_1 | ~spl0_2, inference(sat_conversion,[],[f51])).
% 0.18/0.29 cnf(s6, plain, spl0_1 | ~spl0_3, inference(sat_conversion,[],[f54])).
% 0.18/0.29 cnf(s7, plain, spl0_1 | ~spl0_4, inference(sat_conversion,[],[f57])).
% 0.18/0.29 cnf(s9, plain, ~spl0_1 | spl0_5 | spl0_6, inference(sat_conversion,[],[f283])).
% 0.18/0.29 cnf(s10, plain, spl0_2 | spl0_3 | ~spl0_6, inference(sat_conversion,[],[f440])).
% 0.18/0.29 cnf(s11, plain, spl0_4 | ~spl0_5, inference(sat_conversion,[],[f467])).
% 0.18/0.29 cnf(s12, plain, spl0_1, inference(rat,[],[s1,s5,s6,s7])).
% 0.18/0.29 cnf(s13, plain, ~spl0_4, inference(rat,[],[s4,s12])).
% 0.18/0.29 cnf(s14, plain, ~spl0_3, inference(rat,[],[s3,s12])).
% 0.18/0.29 cnf(s15, plain, ~spl0_2, inference(rat,[],[s2,s12])).
% 0.18/0.29 cnf(s16, plain, ~spl0_5, inference(rat,[],[s11,s13])).
% 0.18/0.29 cnf(s17, plain, ~spl0_6, inference(rat,[],[s10,s14,s15])).
% 0.18/0.29 cnf(s18, plain, $false, inference(rat,[],[s9,s12,s16,s17])).
% 0.18/0.29 tff(f468,plain,(
% 0.18/0.29 $false),
% 0.18/0.29 inference(avatar_sat_refutation,[],[s18])).
% 0.18/0.29 % SZS output end Proof for theBenchmark
% 0.18/0.29 % (4015961)------------------------------
% 0.18/0.29 % (4015961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.29 % (4015961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.29 % (4015961)CaDiCaL version: 2.1.3
% 0.18/0.29 % (4015961)Termination reason: Refutation
% 0.18/0.29 % (4015961)Time elapsed: 0.014 s
% 0.18/0.29 % (4015961)Peak memory usage: 12 MB
% 0.18/0.29 % (4015961)Instructions burned: 20 (million)
% 0.18/0.29 % (4015953)Success in time 0.062 s
% 0.18/0.29 % Vampire exiting
%------------------------------------------------------------------------------