%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ARI706_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 : n010.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 09:35:06 AM UTC 2026
% Result : Theorem 1.53s 0.50s
% Output : Refutation 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI706_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 % Computer : n010.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Mon Sep 28 20:58:32 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.27 Running first-order model finding
% 0.08/0.27 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
% 1.53/0.50 % (2327631)Will run a generic schedule for satisfiability detection.
% 1.53/0.50 % (2327637)% WARNING: option uhcvi not known.
% 1.53/0.50 % (2327637)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4254077288:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.53/0.50 % (2327636)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3846429493_2999 on theBenchmark for (2999ds/0Mi)
% 1.53/0.50 % (2327636)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.53/0.50 % (2327636)Terminated due to inappropriate strategy.
% 1.53/0.50 % (2327636)------------------------------
% 1.53/0.50 % (2327636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.50 % (2327636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.50 % (2327636)CaDiCaL version: 2.1.3
% 1.53/0.50 % (2327636)Termination reason: Inappropriate
% 1.53/0.50 % (2327636)Time elapsed: 0.0000 s
% 1.53/0.50 % (2327636)Peak memory usage: 10 MB
% 1.53/0.50 % (2327636)------------------------------
% 1.53/0.50 % (2327636)------------------------------
% 1.53/0.50 % (2327640)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3989167637:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.53/0.50 % (2327642)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1407824135:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.53/0.50 % (2327641)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2457650028:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.53/0.50 % (2327639)dis+10_1_sil=32000:sp=arity:random_seed=1232511840:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.53/0.50 % (2327638)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1116718700:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.53/0.50 % (2327646)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1975851380:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.53/0.50 % (2327646)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.53/0.50 % (2327646)Terminated due to inappropriate strategy.
% 1.53/0.50 % (2327646)------------------------------
% 1.53/0.50 % (2327646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.50 % (2327646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.50 % (2327646)CaDiCaL version: 2.1.3
% 1.53/0.50 % (2327646)Termination reason: Inappropriate
% 1.53/0.50 % (2327646)Time elapsed: 0.0000 s
% 1.53/0.50 % (2327646)Peak memory usage: 10 MB
% 1.53/0.50 % (2327646)------------------------------
% 1.53/0.50 % (2327646)------------------------------
% 1.53/0.50 % (2327653)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1923262975:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.53/0.50 % (2327639)Instruction limit reached!
% 1.53/0.50 % (2327639)------------------------------
% 1.53/0.50 % (2327639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.50 % (2327639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.50 % (2327639)CaDiCaL version: 2.1.3
% 1.53/0.50 % (2327639)Termination reason: Instruction limit
% 1.53/0.50 % (2327639)Termination phase: Saturation
% 1.53/0.50 % (2327639)Time elapsed: 0.104 s
% 1.53/0.50 % (2327639)Peak memory usage: 13 MB
% 1.53/0.50 % (2327639)Instructions burned: 103 (million)
% 1.53/0.50 % (2327640)Instruction limit reached!
% 1.53/0.50 % (2327640)------------------------------
% 1.53/0.50 % (2327640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.50 % (2327640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.50 % (2327640)CaDiCaL version: 2.1.3
% 1.53/0.50 % (2327640)Termination reason: Instruction limit
% 1.53/0.50 % (2327640)Termination phase: Saturation
% 1.53/0.50 % (2327640)Time elapsed: 0.114 s
% 1.53/0.50 % (2327640)Peak memory usage: 12 MB
% 1.53/0.50 % (2327640)Instructions burned: 117 (million)
% 1.53/0.50 % (2327641)Instruction limit reached!
% 1.53/0.50 % (2327641)------------------------------
% 1.53/0.50 % (2327641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.50 % (2327641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.50 % (2327641)CaDiCaL version: 2.1.3
% 1.53/0.50 % (2327641)Termination reason: Instruction limit
% 1.53/0.50 % (2327641)Termination phase: Saturation
% 1.53/0.50 % (2327641)Time elapsed: 0.135 s
% 1.53/0.50 % (2327641)Peak memory usage: 13 MB
% 1.53/0.50 % (2327641)Instructions burned: 131 (million)
% 1.53/0.50 % (2327655)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=500317277:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.53/0.50 % (2327656)ott-21_1_sil=16000:fs=off:random_seed=1464035382:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.53/0.50 % (2327642)Instruction limit reached!
% 1.53/0.50 % (2327642)------------------------------
% 1.53/0.50 % (2327642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.50 % (2327642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.50 % (2327642)CaDiCaL version: 2.1.3
% 1.53/0.50 % (2327642)Termination reason: Instruction limit
% 1.53/0.50 % (2327642)Termination phase: Saturation
% 1.53/0.50 % (2327642)Time elapsed: 0.159 s
% 1.53/0.50 % (2327642)Peak memory usage: 12 MB
% 1.53/0.50 % (2327642)Instructions burned: 159 (million)
% 1.53/0.50 % (2327657)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2539529938:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.53/0.50 % (2327637) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2327631-2327637"...
% 1.53/0.50 % (2327637)...printing done.
% 1.53/0.50 % (2327637)Refutation found. Thanks to Tanya!
% 1.53/0.50 % SZS status Theorem for theBenchmark
% 1.53/0.50 % SZS output start Proof for theBenchmark
% 1.53/0.50 tff(func_def_0, type, d: $int).
% 1.53/0.50 tff(f1,axiom,(
% 1.53/0.50 $product(d,d) = $product($product(2,d),d)),
% 1.53/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq)).
% 1.53/0.50 tff(f2,conjecture,(
% 1.53/0.50 $product(d,d) = $product($product(d,3),d)),
% 1.53/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 1.53/0.50 tff(f3,negated_conjecture,(
% 1.53/0.50 ~ $product(d,d) = $product($product(d,3),d)),
% 1.53/0.50 inference(negated_conjecture,[status(cth)],[f2])).
% 1.53/0.50 tff(f15,definition,(
% 1.53/0.50 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )),
% 1.53/0.50 introduced(theory,[tha_commutativity])).
% 1.53/0.50 tff(f16,definition,(
% 1.53/0.50 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 1.53/0.50 introduced(theory,[tha_associativity])).
% 1.53/0.50 tff(f17,definition,(
% 1.53/0.50 ( ! [X0 : $int] : ($product(X0,1) = X0) )),
% 1.53/0.50 introduced(theory,[tha_right_identity])).
% 1.53/0.50 tff(f18,definition,(
% 1.53/0.50 ( ! [X0 : $int] : (0 = $product(X0,0)) )),
% 1.53/0.50 introduced(theory,[tha_times_zero])).
% 1.53/0.50 tff(f20,definition,(
% 1.53/0.50 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : (0 = X0 | $product(X0,X2) != X1 | $product(X0,X3) != X1 | X2 = X3) )),
% 1.53/0.50 introduced(theory,[tha_divisibility])).
% 1.53/0.50 tff(f22,plain,(
% 1.53/0.50 $product(d,d) != $product($product(d,3),d)),
% 1.53/0.50 inference(flattening,[],[f3])).
% 1.53/0.50 tff(f23,plain,(
% 1.53/0.50 $product(d,d) = $product($product(2,d),d)),
% 1.53/0.50 inference(cnf_transformation,[],[f1])).
% 1.53/0.50 tff(f24,plain,(
% 1.53/0.50 $product(d,d) != $product($product(d,3),d)),
% 1.53/0.50 inference(cnf_transformation,[],[f22])).
% 1.53/0.50 tff(f25,plain,(
% 1.53/0.50 ( ! [X2 : $int,X3 : $int,X0 : $int] : ($product(X0,X2) != $product(X0,X3) | 0 = X0 | X2 = X3) )),
% 1.53/0.50 inference(equality_resolution,[],[f20])).
% 1.53/0.50 tff(f122,plain,(
% 1.53/0.50 $product(d,d) = $product(2,$product(d,d))),
% 1.53/0.50 inference(superposition,[],[f16,f23])).
% 1.53/0.50 tff(f170,plain,(
% 1.53/0.50 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) != X0 | 0 = X0 | 1 = X1) )),
% 1.53/0.50 inference(superposition,[],[f25,f17])).
% 1.53/0.50 tff(f171,plain,(
% 1.53/0.50 ( ! [X0 : $int,X1 : $int] : (0 != $product(X0,X1) | 0 = X0 | 0 = X1) )),
% 1.53/0.50 inference(superposition,[],[f25,f18])).
% 1.53/0.50 tff(f184,definition,(
% 1.53/0.50 spl0_1 <=> $product(2,d) = 0),
% 1.53/0.50 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 1.53/0.50 tff(f186,plain,(
% 1.53/0.50 $product(2,d) = 0 | ~spl0_1),
% 1.53/0.50 inference(avatar_component_clause,[],[f184])).
% 1.53/0.50 tff(f286,definition,(
% 1.53/0.50 spl0_3 <=> d = 0),
% 1.53/0.50 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 1.53/0.50 tff(f287,plain,(
% 1.53/0.50 d != 0 | spl0_3),
% 1.53/0.50 inference(avatar_component_clause,[],[f286])).
% 1.53/0.50 tff(f288,plain,(
% 1.53/0.50 d = 0 | ~spl0_3),
% 1.53/0.50 inference(avatar_component_clause,[],[f286])).
% 1.53/0.50 tff(f299,plain,(
% 1.53/0.50 $product(0,0) != $product($product(0,3),0) | ~spl0_3),
% 1.53/0.50 inference(superposition,[],[f24,f288])).
% 1.53/0.50 tff(f310,plain,(
% 1.53/0.50 $false | ~spl0_3),
% 1.53/0.50 inference(evaluation,[],[f299])).
% 1.53/0.50 tff(f311,plain,(
% 1.53/0.50 ~spl0_3),
% 1.53/0.50 inference(avatar_contradiction_clause,[],[f310])).
% 1.53/0.50 tff(f1094,plain,(
% 1.53/0.50 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) != X1 | 0 = X1 | 1 = X0) )),
% 1.53/0.50 inference(superposition,[],[f170,f15])).
% 1.53/0.50 tff(f1139,plain,(
% 1.53/0.50 $product(d,d) != 0 | $product(2,d) = 0 | d = 0),
% 1.53/0.50 inference(superposition,[],[f171,f23])).
% 1.53/0.50 tff(f1143,plain,(
% 1.53/0.50 $product(d,d) != 0 | $product(2,d) = 0 | spl0_3),
% 1.53/0.50 inference(forward_subsumption_resolution,[],[f1139,f287])).
% 1.53/0.50 tff(f1146,definition,(
% 1.53/0.50 spl0_11 <=> $product(d,d) = 0),
% 1.53/0.50 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 1.53/0.50 tff(f1148,plain,(
% 1.53/0.50 $product(d,d) != 0 | spl0_11),
% 1.53/0.50 inference(avatar_component_clause,[],[f1146])).
% 1.53/0.50 tff(f1149,plain,(
% 1.53/0.50 spl0_1 | ~spl0_11 | spl0_3),
% 1.53/0.50 inference(avatar_split_clause,[],[f1143,f286,f1146,f184])).
% 1.53/0.50 tff(f1461,plain,(
% 1.53/0.50 0 != 0 | 2 = 0 | d = 0 | ~spl0_1),
% 1.53/0.50 inference(superposition,[],[f171,f186])).
% 1.53/0.50 tff(f1462,plain,(
% 1.53/0.50 2 = 0 | d = 0 | ~spl0_1),
% 1.53/0.50 inference(trivial_inequality_removal,[],[f1461])).
% 1.53/0.50 tff(f1463,plain,(
% 1.53/0.50 d = 0 | ~spl0_1),
% 1.53/0.50 inference(evaluation,[],[f1462])).
% 1.53/0.50 tff(f1478,plain,(
% 1.53/0.50 $false | (~spl0_1 | spl0_3)),
% 1.53/0.50 inference(forward_subsumption_resolution,[],[f1463,f287])).
% 1.53/0.50 tff(f1479,plain,(
% 1.53/0.50 ~spl0_1 | spl0_3),
% 1.53/0.50 inference(avatar_contradiction_clause,[],[f1478])).
% 1.53/0.50 tff(f8903,plain,(
% 1.53/0.50 $product(d,d) != $product(d,d) | $product(d,d) = 0 | 2 = 1),
% 1.53/0.50 inference(superposition,[],[f1094,f122])).
% 1.53/0.50 tff(f8904,plain,(
% 1.53/0.50 $product(d,d) = 0 | 2 = 1),
% 1.53/0.50 inference(trivial_inequality_removal,[],[f8903])).
% 1.53/0.50 tff(f8905,plain,(
% 1.53/0.50 $product(d,d) = 0),
% 1.53/0.50 inference(evaluation,[],[f8904])).
% 1.53/0.50 tff(f8906,plain,(
% 1.53/0.50 $false | spl0_11),
% 1.53/0.50 inference(forward_subsumption_resolution,[],[f8905,f1148])).
% 1.53/0.50 tff(f8907,plain,(
% 1.53/0.50 spl0_11),
% 1.53/0.50 inference(avatar_contradiction_clause,[],[f8906])).
% 1.53/0.50 cnf(s8, plain, ~spl0_3, inference(sat_conversion,[],[f311])).
% 1.53/0.50 cnf(s12, plain, spl0_1 | spl0_3 | ~spl0_11, inference(sat_conversion,[],[f1149])).
% 1.53/0.50 cnf(s19, plain, ~spl0_1 | spl0_3, inference(sat_conversion,[],[f1479])).
% 1.53/0.50 cnf(s23, plain, spl0_11, inference(sat_conversion,[],[f8907])).
% 1.53/0.50 cnf(s26, plain, spl0_1 | spl0_3, inference(rat,[],[s12,s23])).
% 1.53/0.50 cnf(s28, plain, ~spl0_1, inference(rat,[],[s19,s8])).
% 1.53/0.50 cnf(s29, plain, $false, inference(rat,[],[s26,s8,s28])).
% 1.53/0.50 tff(f8912,plain,(
% 1.53/0.50 $false),
% 1.53/0.50 inference(avatar_sat_refutation,[],[s29])).
% 1.53/0.50 % SZS output end Proof for theBenchmark
% 1.53/0.50 % (2327637)------------------------------
% 1.53/0.50 % (2327637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.50 % (2327637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.50 % (2327637)CaDiCaL version: 2.1.3
% 1.53/0.50 % (2327637)Termination reason: Refutation
% 1.53/0.50 % (2327637)Time elapsed: 0.186 s
% 1.53/0.50 % (2327637)Peak memory usage: 15 MB
% 1.53/0.50 % (2327637)Instructions burned: 357 (million)
% 1.53/0.50 % (2327631)Success in time 0.209 s
% 1.53/0.50 % Vampire exiting
%------------------------------------------------------------------------------