%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI702_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 09:33:41 AM UTC 2026
% Result : Theorem 3.81s 1.21s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 19 unt; 0 typ; 7 def)
% Number of atoms : 29 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 0 |; 0 &)
% ( 5 <=>; 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 : 35 ( 0 atm; 23 fun; 12 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 : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 7 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
x: $int ).
tff(func_def_1,type,
y: $int ).
tff(func_def_2,type,
a: $int ).
tff(func_def_3,type,
z: $int ).
tff(func_def_4,type,
b: $int ).
tff(func_def_8,type,
sF0: $int ).
tff(func_def_9,type,
sF1: $int ).
tff(f1,axiom,
$product($product(2,x),y) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq1) ).
tff(f3,axiom,
$product(a,z) = 2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq3) ).
tff(f4,conjecture,
$product($product(x,y),z) = 1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f5,negated_conjecture,
( ( ~ $product($product(x,y),z) ) = 1 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
$product($product(x,y),z) != 1,
inference(flattening,[],[f5]) ).
tff(f7,plain,
$product($product(2,x),y) = a,
inference(cnf_transformation,[],[f1]) ).
tff(f9,plain,
2 = $product(a,z),
inference(cnf_transformation,[],[f3]) ).
tff(f10,plain,
$product($product(x,y),z) != 1,
inference(cnf_transformation,[],[f6]) ).
tff(f11,definition,
sF0 = $product(x,y),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f12,plain,
$product(x,y) = sF0,
inference(reorient_equations,[],[f11]) ).
tff(f13,definition,
sF1 = $product(sF0,z),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f14,plain,
$product(sF0,z) = sF1,
inference(reorient_equations,[],[f13]) ).
tff(f15,plain,
1 != sF1,
inference(definition_folding,[],[f10,f14,f12]) ).
tff(f17,definition,
( spl2_1
<=> ( 1 = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f20,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f15,f17]) ).
tff(f27,definition,
( spl2_3
<=> ( $product(x,y) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f30,plain,
spl2_3,
inference(avatar_split_clause,[],[f12,f27]) ).
tff(f32,definition,
( spl2_4
<=> ( $product($product(2,x),y) = a ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f35,plain,
spl2_4,
inference(avatar_split_clause,[],[f7,f32]) ).
tff(f37,definition,
( spl2_5
<=> ( 2 = $product(a,z) ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f40,plain,
spl2_5,
inference(avatar_split_clause,[],[f9,f37]) ).
tff(f42,definition,
( spl2_6
<=> ( $product(sF0,z) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
tff(f45,plain,
spl2_6,
inference(avatar_split_clause,[],[f14,f42]) ).
tff(f46,plain,
$false,
inference(avatar_smt_refutation,[],[f45,f40,f35,f30,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI702_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n018.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 20:59:55 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running first-order theorem proving
% 0.09/0.19 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.81/1.21 % (3776776)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.81/1.21 % (3776781)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=672637111:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.81/1.21 % (3776781)Instruction limit reached!
% 3.81/1.21 % (3776781)------------------------------
% 3.81/1.21 % (3776781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (3776781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (3776781)CaDiCaL version: 2.1.3
% 3.81/1.21 % (3776781)Termination reason: Instruction limit
% 3.81/1.21 % (3776781)Termination phase: Saturation
% 3.81/1.21 % (3776781)Time elapsed: 0.021 s
% 3.81/1.21 % (3776781)Peak memory usage: 116 MB
% 3.81/1.21 % (3776781)Instructions burned: 13 (million)
% 3.81/1.21 % (3776782)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3892492237:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.81/1.21 % (3776785)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3938331806:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.81/1.21 % (3776784)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4128183497:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.81/1.21 % (3776786)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=433807080:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.81/1.21 % (3776787)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2970989569:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.81/1.21 % (3776783)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3825606388:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.81/1.21 % (3776785)Instruction limit reached!
% 3.81/1.21 % (3776785)------------------------------
% 3.81/1.21 % (3776785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (3776785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (3776785)CaDiCaL version: 2.1.3
% 3.81/1.21 % (3776785)Termination reason: Instruction limit
% 3.81/1.21 % (3776785)Termination phase: Saturation
% 3.81/1.21 % (3776785)Time elapsed: 0.004 s
% 3.81/1.21 % (3776785)Peak memory usage: 89 MB
% 3.81/1.21 % (3776785)Instructions burned: 5 (million)
% 3.81/1.21 % (3776784)Instruction limit reached!
% 3.81/1.21 % (3776784)------------------------------
% 3.81/1.21 % (3776784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (3776784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (3776784)CaDiCaL version: 2.1.3
% 3.81/1.21 % (3776784)Termination reason: Instruction limit
% 3.81/1.21 % (3776784)Termination phase: Saturation
% 3.81/1.21 % (3776784)Time elapsed: 0.006 s
% 3.81/1.21 % (3776784)Peak memory usage: 88 MB
% 3.81/1.21 % (3776784)Instructions burned: 8 (million)
% 3.81/1.21 % (3776782)First to succeed.
% 3.81/1.21 % (3776782)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3776776"
% 3.81/1.21 % (3776787)Also succeeded, but the first one will report.
% 3.81/1.21 % (3776786)Also succeeded, but the first one will report.
% 3.81/1.21 % (3776789)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3656818797:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.81/1.21 % (3776789)Refutation not found, incomplete strategy
% 3.81/1.21 % (3776789)------------------------------
% 3.81/1.21 % (3776789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (3776789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (3776789)CaDiCaL version: 2.1.3
% 3.81/1.21 % (3776789)Termination reason: Refutation not found, incomplete strategy
% 3.81/1.21 % (3776789)Time elapsed: 0.001 s
% 3.81/1.21 % (3776789)Peak memory usage: 88 MB
% 3.81/1.21 % (3776783)Instruction limit reached!
% 3.81/1.21 % (3776783)------------------------------
% 3.81/1.21 % (3776783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (3776783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (3776783)CaDiCaL version: 2.1.3
% 3.81/1.21 % (3776783)Termination reason: Instruction limit
% 3.81/1.21 % (3776783)Termination phase: Saturation
% 3.81/1.21 % (3776783)Time elapsed: 0.153 s
% 3.81/1.21 % (3776783)Peak memory usage: 114 MB
% 3.81/1.21 % (3776783)Instructions burned: 202 (million)
% 3.81/1.21 % (3776796)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=280075561:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.81/1.21 % (3776797)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=4290497796:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.81/1.21 % (3776797)Instruction limit reached!
% 3.81/1.21 % (3776797)------------------------------
% 3.81/1.21 % (3776797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (3776797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (3776797)CaDiCaL version: 2.1.3
% 3.81/1.21 % (3776797)Termination reason: Instruction limit
% 3.81/1.21 % (3776797)Termination phase: Saturation
% 3.81/1.21 % (3776797)Time elapsed: 0.010 s
% 3.81/1.21 % (3776797)Peak memory usage: 90 MB
% 3.81/1.21 % (3776797)Instructions burned: 17 (million)
% 3.81/1.21 % (3776796)Instruction limit reached!
% 3.81/1.21 % (3776796)------------------------------
% 3.81/1.21 % (3776796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (3776796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (3776796)CaDiCaL version: 2.1.3
% 3.81/1.21 % (3776796)Termination reason: Instruction limit
% 3.81/1.21 % (3776796)Termination phase: Saturation
% 3.81/1.21 % (3776796)Time elapsed: 0.015 s
% 3.81/1.21 % (3776796)Peak memory usage: 88 MB
% 3.81/1.21 % (3776796)Instructions burned: 31 (million)
% 3.81/1.21 % (3776789)------------------------------
% 3.81/1.21 % (3776789)------------------------------
% 3.81/1.21 % (3776782)Refutation found. Thanks to Tanya!
% 3.81/1.21 % SZS status Theorem for theBenchmark
% 3.81/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.21 % (3776782)------------------------------
% 3.81/1.21 % (3776782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.21 % (3776782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.21 % (3776782)CaDiCaL version: 2.1.3
% 3.81/1.21 % (3776782)Termination reason: Refutation
% 3.81/1.21 % (3776782)Time elapsed: 0.039 s
% 3.81/1.21 % (3776782)Peak memory usage: 117 MB
% 3.81/1.21 % (3776782)Instructions burned: 17 (million)
% 3.81/1.21 % (3776782)------------------------------
% 3.81/1.21 % (3776782)------------------------------
% 3.81/1.21 % (3776776)Success in time 0.459 s
% 3.81/1.21 % Vampire exiting
%------------------------------------------------------------------------------