%------------------------------------------------------------------------------
% File : Vampire---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 THM
% 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 09:33:42 AM UTC 2026
% Result : Theorem 5.43s 1.82s
% Output : Refutation 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 18 unt; 0 typ; 7 def)
% Number of atoms : 26 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 38 ( 0 atm; 29 fun; 9 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
d: $int ).
tff(func_def_8,type,
sF0: $int ).
tff(func_def_9,type,
sF1: $int ).
tff(func_def_10,type,
sF2: $int ).
tff(f1,axiom,
$product(d,d) = $product($product(2,d),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(f2,conjecture,
$product(d,d) = $product($product(d,3),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f3,negated_conjecture,
( ( ~ $product(d,d) ) = $product($product(d,3),d) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f22,plain,
$product(d,d) != $product($product(d,3),d),
inference(flattening,[],[f3]) ).
tff(f23,plain,
$product(d,d) != $product($product(d,3),d),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
$product(d,d) = $product($product(2,d),d),
inference(cnf_transformation,[],[f1]) ).
tff(f26,definition,
sF0 = $product(d,d),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f27,plain,
$product(d,d) = sF0,
inference(reorient_equations,[],[f26]) ).
tff(f28,definition,
sF1 = $product(d,3),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f29,plain,
$product(d,3) = sF1,
inference(reorient_equations,[],[f28]) ).
tff(f30,definition,
sF2 = $product(sF1,d),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f31,plain,
$product(sF1,d) = sF2,
inference(reorient_equations,[],[f30]) ).
tff(f32,plain,
sF2 != sF0,
inference(definition_folding,[],[f23,f31,f29,f27]) ).
tff(f34,definition,
( spl3_1
<=> ( $product(d,d) = $product($product(2,d),d) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f37,plain,
spl3_1,
inference(avatar_split_clause,[],[f24,f34]) ).
tff(f39,definition,
( spl3_2
<=> ( sF2 = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f42,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f32,f39]) ).
tff(f44,definition,
( spl3_3
<=> ( $product(sF1,d) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f47,plain,
spl3_3,
inference(avatar_split_clause,[],[f31,f44]) ).
tff(f54,definition,
( spl3_5
<=> ( $product(d,d) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f57,plain,
spl3_5,
inference(avatar_split_clause,[],[f27,f54]) ).
tff(f58,plain,
$false,
inference(avatar_smt_refutation,[],[f57,f47,f42,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI706_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 % Computer : n001.cluster.edu
% 0.24/0.28 % Model : x86_64 x86_64
% 0.24/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.28 % Memory : 8046.5625MB
% 0.24/0.28 % OS : Linux 6.8.0-71-generic
% 0.24/0.29 % CPULimit : 300
% 0.24/0.29 % WCLimit : 300
% 0.24/0.29 % DateTime : Mon Sep 28 21:04:04 UTC 2026
% 0.24/0.29 % CPUTime :
% 0.24/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.33 Running first-order theorem proving
% 0.24/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.43/1.82 % (743796)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.43/1.82 % (743801)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4025729071:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.43/1.82 % (743807)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3504043019:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.43/1.82 % (743801)Refutation not found, incomplete strategy
% 5.43/1.82 % (743801)------------------------------
% 5.43/1.82 % (743801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.82 % (743801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.82 % (743801)CaDiCaL version: 2.1.3
% 5.43/1.82 % (743801)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.82 % (743801)Time elapsed: 0.024 s
% 5.43/1.82 % (743801)Peak memory usage: 115 MB
% 5.43/1.82 % (743801)Instructions burned: 6 (million)
% 5.43/1.82 % (743807)First to succeed.
% 5.43/1.82 % (743807)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-743796"
% 5.43/1.82 % (743802)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1778141178:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.43/1.82 % (743805)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2533088651:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.43/1.82 % (743804)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3975349085:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.43/1.82 % (743803)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2511081928:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.43/1.82 % (743806)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2652426846:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.43/1.82 % (743805)Instruction limit reached!
% 5.43/1.82 % (743805)------------------------------
% 5.43/1.82 % (743805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.82 % (743805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.82 % (743805)CaDiCaL version: 2.1.3
% 5.43/1.82 % (743805)Termination reason: Instruction limit
% 5.43/1.82 % (743805)Termination phase: Saturation
% 5.43/1.82 % (743805)Time elapsed: 0.006 s
% 5.43/1.82 % (743805)Peak memory usage: 89 MB
% 5.43/1.82 % (743805)Instructions burned: 4 (million)
% 5.43/1.82 % (743804)Instruction limit reached!
% 5.43/1.82 % (743804)------------------------------
% 5.43/1.82 % (743804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.82 % (743804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.82 % (743804)CaDiCaL version: 2.1.3
% 5.43/1.82 % (743804)Termination reason: Instruction limit
% 5.43/1.82 % (743804)Termination phase: Saturation
% 5.43/1.82 % (743804)Time elapsed: 0.009 s
% 5.43/1.82 % (743804)Peak memory usage: 88 MB
% 5.43/1.82 % (743804)Instructions burned: 7 (million)
% 5.43/1.82 % (743806)Also succeeded, but the first one will report.
% 5.43/1.82 % (743802)Also succeeded, but the first one will report.
% 5.43/1.82 % (743801)------------------------------
% 5.43/1.82 % (743801)------------------------------
% 5.43/1.82 % (743803)Instruction limit reached!
% 5.43/1.82 % (743803)------------------------------
% 5.43/1.82 % (743803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.82 % (743803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.82 % (743803)CaDiCaL version: 2.1.3
% 5.43/1.82 % (743803)Termination reason: Instruction limit
% 5.43/1.82 % (743803)Termination phase: Saturation
% 5.43/1.82 % (743803)Time elapsed: 0.222 s
% 5.43/1.82 % (743803)Peak memory usage: 113 MB
% 5.43/1.82 % (743803)Instructions burned: 201 (million)
% 5.43/1.82 % (743815)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=300531898:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.43/1.82 % (743815)Refutation not found, incomplete strategy
% 5.43/1.82 % (743815)------------------------------
% 5.43/1.82 % (743815)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.82 % (743815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.82 % (743815)CaDiCaL version: 2.1.3
% 5.43/1.82 % (743815)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.82 % (743815)Time elapsed: 0.001 s
% 5.43/1.82 % (743815)Peak memory usage: 88 MB
% 5.43/1.82 % (743816)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=3403301984:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.43/1.82 % (743816)Instruction limit reached!
% 5.43/1.82 % (743816)------------------------------
% 5.43/1.82 % (743816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.82 % (743816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.82 % (743816)CaDiCaL version: 2.1.3
% 5.43/1.82 % (743816)Termination reason: Instruction limit
% 5.43/1.82 % (743816)Termination phase: Saturation
% 5.43/1.82 % (743816)Time elapsed: 0.024 s
% 5.43/1.82 % (743816)Peak memory usage: 88 MB
% 5.43/1.82 % (743816)Instructions burned: 29 (million)
% 5.43/1.82 % (743807)Refutation found. Thanks to Tanya!
% 5.43/1.82 % SZS status Theorem for theBenchmark
% 5.43/1.82 % SZS output start Proof for theBenchmark
% See solution above
% 5.43/1.82 % (743807)------------------------------
% 5.43/1.82 % (743807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.82 % (743807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.82 % (743807)CaDiCaL version: 2.1.3
% 5.43/1.82 % (743807)Termination reason: Refutation
% 5.43/1.82 % (743807)Time elapsed: 0.040 s
% 5.43/1.82 % (743807)Peak memory usage: 116 MB
% 5.43/1.82 % (743807)Instructions burned: 11 (million)
% 5.43/1.82 % (743807)------------------------------
% 5.43/1.82 % (743807)------------------------------
% 5.43/1.82 % (743796)Success in time 0.631 s
% 5.43/1.82 % Vampire exiting
%------------------------------------------------------------------------------