%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI123_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:32:34 AM UTC 2026
% Result : Theorem 3.54s 1.23s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 30 ( 6 ~; 0 |; 21 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 68 ( 0 atm; 24 fun; 0 num; 44 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 0 usr; 0 con; 2-2 aty)
% Number of variables : 44 ( 23 !; 21 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
? [X0: $int,X1: $int,X5: $int,X2: $int,X3: $int,X6: $int,X4: $int] :
( ( ( $product(X3,X2) = X4 )
& ( $product(X0,X1) = X3 )
& ( $product(X0,X5) = X6 )
& ( $product(X1,X2) = X5 ) )
=> ( X4 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_product_exists) ).
tff(f2,negated_conjecture,
~ ? [X0: $int,X1: $int,X5: $int,X2: $int,X3: $int,X6: $int,X4: $int] :
( ( ( $product(X3,X2) = X4 )
& ( $product(X0,X1) = X3 )
& ( $product(X0,X5) = X6 )
& ( $product(X1,X2) = X5 ) )
=> ( X4 = X6 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
~ ? [X1: $int,X2: $int,X6: $int,X0: $int,X3: $int,X4: $int,X5: $int] :
( ( ( $product(X4,X3) = X6 )
& ( $product(X1,X3) = X2 )
& ( $product(X0,X1) = X4 )
& ( $product(X0,X2) = X5 ) )
=> ( X5 = X6 ) ),
inference(rectify,[],[f2]) ).
tff(f22,plain,
! [X1: $int,X2: $int,X6: $int,X0: $int,X3: $int,X4: $int,X5: $int] :
( ( X5 != X6 )
& ( $product(X4,X3) = X6 )
& ( $product(X1,X3) = X2 )
& ( $product(X0,X1) = X4 )
& ( $product(X0,X2) = X5 ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f23,plain,
! [X2: $int,X1: $int,X3: $int,X0: $int,X5: $int,X6: $int,X4: $int] :
( ( $product(X0,X2) = X5 )
& ( X5 != X6 )
& ( $product(X0,X1) = X4 )
& ( $product(X4,X3) = X6 )
& ( $product(X1,X3) = X2 ) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
! [X0: $int,X1: $int,X2: $int,X3: $int,X4: $int,X5: $int,X6: $int] :
( ( $product(X3,X0) = X4 )
& ( X4 != X5 )
& ( $product(X3,X1) = X6 )
& ( $product(X6,X2) = X5 )
& ( $product(X1,X2) = X0 ) ),
inference(rectify,[],[f23]) ).
tff(f28,plain,
! [X4: $int,X5: $int] : ( X4 != X5 ),
inference(cnf_transformation,[],[f24]) ).
tff(f30,plain,
$false,
inference(equality_resolution,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI123_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n015.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Mon Sep 28 20:46:32 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.26 Running first-order theorem proving
% 0.08/0.26 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
% 3.54/1.23 % (2985252)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.54/1.23 % (2985275)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3886889969:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.54/1.23 % (2985281)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3941678062:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.54/1.23 % (2985280)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2358219290:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.54/1.23 % (2985278)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2934551895:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.54/1.23 % (2985276)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=356306061:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.54/1.23 % (2985279)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2378314242:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.54/1.23 % (2985274)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2194401665:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.54/1.23 % (2985278)Also succeeded, but the first one will report.
% 3.54/1.23 % (2985279)First to succeed.
% 3.54/1.23 % (2985279)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2985252"
% 3.54/1.23 % (2985275)Also succeeded, but the first one will report.
% 3.54/1.23 % (2985280)Also succeeded, but the first one will report.
% 3.54/1.23 % (2985274)Also succeeded, but the first one will report.
% 3.54/1.23 % (2985281)Also succeeded, but the first one will report.
% 3.54/1.23 % (2985276)Also succeeded, but the first one will report.
% 3.54/1.23 % (2985279)Refutation found. Thanks to Tanya!
% 3.54/1.23 % SZS status Theorem for theBenchmark
% 3.54/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.23 % (2985279)------------------------------
% 3.54/1.23 % (2985279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.23 % (2985279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.23 % (2985279)CaDiCaL version: 2.1.3
% 3.54/1.23 % (2985279)Termination reason: Refutation
% 3.54/1.23 % (2985279)Time elapsed: 0.002 s
% 3.54/1.23 % (2985279)Peak memory usage: 88 MB
% 3.54/1.23 % (2985279)Instructions burned: 1 (million)
% 3.54/1.23 % (2985279)------------------------------
% 3.54/1.23 % (2985279)------------------------------
% 3.54/1.23 % (2985252)Success in time 0.409 s
% 3.54/1.23 % Vampire exiting
%------------------------------------------------------------------------------