%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI672_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 : 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 09:33:37 AM UTC 2026
% Result : Theorem 0.20s 1.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 59 ( 43 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 62 ( 21 ~; 25 |; 9 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 44 ( 0 atm; 12 fun; 32 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 : 5 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(f1,conjecture,
( ( ( a = b )
& ( ( a = -1 )
| ( a = 1 ) ) )
<=> ( $product(a,b) = 1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( ( ( a = b )
& ( ( a = -1 )
| ( a = 1 ) ) )
<=> ( $product(a,b) = 1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
( ( ( a = b )
& ( ( a = -1 )
| ( a = 1 ) ) )
<~> ( $product(a,b) = 1 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
( ( ( $product(a,b) != 1 )
| ( a != b )
| ( ( a != -1 )
& ( a != 1 ) ) )
& ( ( $product(a,b) = 1 )
| ( ( a = b )
& ( ( a = -1 )
| ( a = 1 ) ) ) ) ),
inference(nnf_transformation,[],[f21]) ).
tff(f23,plain,
( ( ( $product(a,b) != 1 )
| ( a != b )
| ( ( a != -1 )
& ( a != 1 ) ) )
& ( ( $product(a,b) = 1 )
| ( ( a = b )
& ( ( a = -1 )
| ( a = 1 ) ) ) ) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
( ( a = -1 )
| ( a = 1 )
| ( $product(a,b) = 1 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f25,plain,
( ( $product(a,b) = 1 )
| ( a = b ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f26,plain,
( ( a != b )
| ( a != 1 )
| ( $product(a,b) != 1 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f27,plain,
( ( a != b )
| ( $product(a,b) != 1 )
| ( a != -1 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f29,definition,
( spl0_1
<=> ( a = b ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f33,definition,
( spl0_2
<=> ( $product(a,b) = 1 ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f37,definition,
( spl0_3
<=> ( a = 1 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f40,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f26,f37,f33,f29]) ).
tff(f41,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f25,f33,f29]) ).
tff(f43,definition,
( spl0_4
<=> ( a = -1 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f46,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f27,f43,f33,f29]) ).
tff(f47,plain,
( spl0_4
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f24,f37,f33,f43]) ).
tff(f48,plain,
$false,
inference(avatar_smt_refutation,[],[f47,f46,f41,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI672_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:56:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.20/1.30 % (2324600)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.20/1.30 % (2324672)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1566874820:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.20/1.30 % (2324668)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1153544937:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.20/1.30 % (2324669)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=339793470:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/1.30 % (2324667)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=958306319:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.20/1.30 % (2324670)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3101667094:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.20/1.30 % (2324666)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=874341886:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/1.30 % (2324671)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3361198405:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.20/1.30 % (2324670)Instruction limit reached!
% 0.20/1.30 % (2324670)------------------------------
% 0.20/1.30 % (2324670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (2324670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (2324670)CaDiCaL version: 2.1.3
% 0.20/1.30 % (2324670)Termination reason: Instruction limit
% 0.20/1.30 % (2324670)Termination phase: Saturation
% 0.20/1.30 % (2324670)Time elapsed: 0.004 s
% 0.20/1.30 % (2324670)Peak memory usage: 89 MB
% 0.20/1.30 % (2324670)Instructions burned: 5 (million)
% 0.20/1.30 % (2324669)Instruction limit reached!
% 0.20/1.30 % (2324669)------------------------------
% 0.20/1.30 % (2324669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (2324669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (2324669)CaDiCaL version: 2.1.3
% 0.20/1.30 % (2324669)Termination reason: Instruction limit
% 0.20/1.30 % (2324669)Termination phase: Saturation
% 0.20/1.30 % (2324669)Time elapsed: 0.006 s
% 0.20/1.30 % (2324669)Peak memory usage: 88 MB
% 0.20/1.30 % (2324669)Instructions burned: 8 (million)
% 0.20/1.30 % (2324666)First to succeed.
% 0.20/1.30 % (2324671)Also succeeded, but the first one will report.
% 0.20/1.30 % (2324667)Also succeeded, but the first one will report.
% 0.20/1.30 % (2324666)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2324600"
% 0.20/1.30 % (2324672)Also succeeded, but the first one will report.
% 0.20/1.30 % (2324680)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2881125997:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.20/1.30 % (2324680)Refutation not found, incomplete strategy
% 0.20/1.30 % (2324680)------------------------------
% 0.20/1.30 % (2324680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (2324680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (2324680)CaDiCaL version: 2.1.3
% 0.20/1.30 % (2324680)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.30 % (2324680)Time elapsed: 0.001 s
% 0.20/1.30 % (2324680)Peak memory usage: 89 MB
% 0.20/1.30 % (2324681)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=1771862851:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.20/1.30 % (2324668)Instruction limit reached!
% 0.20/1.30 % (2324668)------------------------------
% 0.20/1.30 % (2324668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (2324668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (2324668)CaDiCaL version: 2.1.3
% 0.20/1.30 % (2324668)Termination reason: Instruction limit
% 0.20/1.30 % (2324668)Termination phase: Saturation
% 0.20/1.30 % (2324668)Time elapsed: 0.169 s
% 0.20/1.30 % (2324668)Peak memory usage: 117 MB
% 0.20/1.30 % (2324668)Instructions burned: 201 (million)
% 0.20/1.30 % (2324681)Instruction limit reached!
% 0.20/1.30 % (2324681)------------------------------
% 0.20/1.30 % (2324681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (2324681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (2324681)CaDiCaL version: 2.1.3
% 0.20/1.30 % (2324681)Termination reason: Instruction limit
% 0.20/1.30 % (2324681)Termination phase: Saturation
% 0.20/1.30 % (2324681)Time elapsed: 0.015 s
% 0.20/1.30 % (2324681)Peak memory usage: 88 MB
% 0.20/1.30 % (2324681)Instructions burned: 31 (million)
% 0.20/1.30 % (2324666)Refutation found. Thanks to Tanya!
% 0.20/1.30 % SZS status Theorem for theBenchmark
% 0.20/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.30 % (2324666)------------------------------
% 0.20/1.30 % (2324666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.30 % (2324666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.30 % (2324666)CaDiCaL version: 2.1.3
% 0.20/1.30 % (2324666)Termination reason: Refutation
% 0.20/1.30 % (2324666)Time elapsed: 0.036 s
% 0.20/1.30 % (2324666)Peak memory usage: 118 MB
% 0.20/1.30 % (2324666)Instructions burned: 13 (million)
% 0.20/1.30 % (2324666)------------------------------
% 0.20/1.30 % (2324666)------------------------------
% 0.20/1.30 % (2324600)Success in time 0.439 s
% 0.20/1.30 % Vampire exiting
%------------------------------------------------------------------------------