%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI673_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 : n011.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 4.44s 1.69s
% Output : Refutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 1 unt; 0 typ; 3 def)
% Number of atoms : 42 ( 31 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 42 ( 15 ~; 17 |; 4 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 42 ( 0 atm; 11 fun; 31 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(f1,conjecture,
( ( ( a = -1 )
| ( a = 1 ) )
<=> ( $product(a,a) = 1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( ( ( a = -1 )
| ( a = 1 ) )
<=> ( $product(a,a) = 1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
( ( ( a = -1 )
| ( a = 1 ) )
<~> ( $product(a,a) = 1 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
( ( ( $product(a,a) != 1 )
| ( ( a != -1 )
& ( a != 1 ) ) )
& ( ( $product(a,a) = 1 )
| ( a = -1 )
| ( a = 1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
tff(f23,plain,
( ( ( $product(a,a) != 1 )
| ( ( a != -1 )
& ( a != 1 ) ) )
& ( ( $product(a,a) = 1 )
| ( a = -1 )
| ( a = 1 ) ) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
( ( a = 1 )
| ( $product(a,a) = 1 )
| ( a = -1 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f25,plain,
( ( $product(a,a) != 1 )
| ( a != 1 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f26,plain,
( ( $product(a,a) != 1 )
| ( a != -1 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f28,definition,
( spl0_1
<=> ( $product(a,a) = 1 ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f32,definition,
( spl0_2
<=> ( a = -1 ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f35,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f26,f32,f28]) ).
tff(f37,definition,
( spl0_3
<=> ( a = 1 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f40,plain,
( spl0_2
| spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f24,f28,f37,f32]) ).
tff(f41,plain,
( ~ spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f25,f28,f37]) ).
tff(f42,plain,
$false,
inference(avatar_smt_refutation,[],[f41,f40,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI673_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n011.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Mon Sep 28 20:55:45 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running first-order theorem proving
% 0.25/0.29 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
% 4.44/1.69 % (3777901)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.44/1.69 % (3777906)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1839404198:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.44/1.69 % (3777912)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4148396308:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.44/1.69 % (3777906)First to succeed.
% 4.44/1.69 % (3777906)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3777901"
% 4.44/1.69 % (3777912)Also succeeded, but the first one will report.
% 4.44/1.69 % (3777911)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=751453726:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.44/1.69 % (3777908)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2871942064:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.44/1.69 % (3777909)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=905373213:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.44/1.69 % (3777910)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3218495170:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.44/1.69 % (3777907)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2925406163:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.44/1.69 % (3777910)Instruction limit reached!
% 4.44/1.69 % (3777910)------------------------------
% 4.44/1.69 % (3777910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.69 % (3777910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.69 % (3777910)CaDiCaL version: 2.1.3
% 4.44/1.69 % (3777910)Termination reason: Instruction limit
% 4.44/1.69 % (3777910)Termination phase: Saturation
% 4.44/1.69 % (3777910)Time elapsed: 0.006 s
% 4.44/1.69 % (3777910)Peak memory usage: 89 MB
% 4.44/1.69 % (3777910)Instructions burned: 4 (million)
% 4.44/1.69 % (3777909)Instruction limit reached!
% 4.44/1.69 % (3777909)------------------------------
% 4.44/1.69 % (3777909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.69 % (3777909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.69 % (3777909)CaDiCaL version: 2.1.3
% 4.44/1.69 % (3777909)Termination reason: Instruction limit
% 4.44/1.69 % (3777909)Termination phase: Saturation
% 4.44/1.69 % (3777909)Time elapsed: 0.010 s
% 4.44/1.69 % (3777909)Peak memory usage: 88 MB
% 4.44/1.69 % (3777909)Instructions burned: 7 (million)
% 4.44/1.69 % (3777911)Also succeeded, but the first one will report.
% 4.44/1.69 % (3777907)Also succeeded, but the first one will report.
% 4.44/1.69 % (3777906)Refutation found. Thanks to Tanya!
% 4.44/1.69 % SZS status Theorem for theBenchmark
% 4.44/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 4.44/1.69 % (3777906)------------------------------
% 4.44/1.69 % (3777906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.69 % (3777906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.69 % (3777906)CaDiCaL version: 2.1.3
% 4.44/1.69 % (3777906)Termination reason: Refutation
% 4.44/1.69 % (3777906)Time elapsed: 0.027 s
% 4.44/1.69 % (3777906)Peak memory usage: 116 MB
% 4.44/1.69 % (3777906)Instructions burned: 10 (million)
% 4.44/1.69 % (3777906)------------------------------
% 4.44/1.69 % (3777906)------------------------------
% 4.44/1.69 % (3777901)Success in time 0.502 s
% 4.44/1.69 % Vampire exiting
%------------------------------------------------------------------------------