%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI121_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 : 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 09:32:34 AM UTC 2026
% Result : Theorem 2.77s 1.24s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 36 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 8 ~; 0 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 64 ( 0 atm; 16 fun; 36 num; 12 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 : 6 ( 2 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 6 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int ).
tff(func_def_8,type,
sK1: $int ).
tff(f1,conjecture,
! [X1: $int,X0: $int] :
( ( ( $product(7,6) = X1 )
& ( $product(6,7) = X0 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_product_6_7) ).
tff(f2,negated_conjecture,
~ ! [X1: $int,X0: $int] :
( ( ( $product(7,6) = X1 )
& ( $product(6,7) = X0 ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
~ ! [X0: $int,X1: $int] :
( ( ( $product(6,7) = X1 )
& ( $product(7,6) = X0 ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
tff(f22,plain,
? [X0: $int,X1: $int] :
( ( X0 != X1 )
& ( $product(6,7) = X1 )
& ( $product(7,6) = X0 ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f23,plain,
? [X1: $int,X0: $int] :
( ( $product(6,7) = X1 )
& ( X0 != X1 )
& ( $product(7,6) = X0 ) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
? [X0: $int,X1: $int] :
( ( $product(6,7) = X0 )
& ( X0 != X1 )
& ( $product(7,6) = X1 ) ),
inference(rectify,[],[f23]) ).
tff(f25,plain,
( ( $product(6,7) = sK0 )
& ( sK1 != sK0 )
& ( $product(7,6) = sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
tff(f26,plain,
$product(7,6) = sK1,
inference(cnf_transformation,[],[f25]) ).
tff(f27,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f25]) ).
tff(f28,plain,
$product(6,7) = sK0,
inference(cnf_transformation,[],[f25]) ).
tff(f29,plain,
sK0 = 42,
inference(evaluation,[],[f28]) ).
tff(f30,plain,
sK1 = 42,
inference(evaluation,[],[f26]) ).
tff(f32,definition,
( spl2_1
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f35,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f27,f32]) ).
tff(f37,definition,
( spl2_2
<=> ( sK0 = 42 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f40,plain,
spl2_2,
inference(avatar_split_clause,[],[f29,f37]) ).
tff(f42,definition,
( spl2_3
<=> ( sK1 = 42 ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f45,plain,
spl2_3,
inference(avatar_split_clause,[],[f30,f42]) ).
tff(f46,plain,
$false,
inference(avatar_smt_refutation,[],[f45,f40,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI121_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n010.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 20:43:33 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running first-order theorem proving
% 0.08/0.25 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
% 2.77/1.24 % (2295307)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.77/1.24 % (2295320)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3924071775:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.77/1.24 % (2295320)First to succeed.
% 2.77/1.24 % (2295320)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2295307"
% 2.77/1.24 % (2295323)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3311377837:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.77/1.24 % (2295322)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=48961128:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.77/1.24 % (2295326)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3919021059:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.77/1.24 % (2295325)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2154867851:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.77/1.24 % (2295321)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3643278578:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.77/1.24 % (2295324)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=841305299:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.77/1.24 % (2295324)Also succeeded, but the first one will report.
% 2.77/1.24 % (2295323)Also succeeded, but the first one will report.
% 2.77/1.24 % (2295322)Also succeeded, but the first one will report.
% 2.77/1.24 % (2295325)Also succeeded, but the first one will report.
% 2.77/1.24 % (2295321)Also succeeded, but the first one will report.
% 2.77/1.24 % (2295326)Also succeeded, but the first one will report.
% 2.77/1.24 % (2295320)Refutation found. Thanks to Tanya!
% 2.77/1.24 % SZS status Theorem for theBenchmark
% 2.77/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.24 % (2295320)------------------------------
% 2.77/1.24 % (2295320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.24 % (2295320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.24 % (2295320)CaDiCaL version: 2.1.3
% 2.77/1.24 % (2295320)Termination reason: Refutation
% 2.77/1.24 % (2295320)Time elapsed: 0.019 s
% 2.77/1.24 % (2295320)Peak memory usage: 115 MB
% 2.77/1.24 % (2295320)Instructions burned: 8 (million)
% 2.77/1.24 % (2295320)------------------------------
% 2.77/1.24 % (2295320)------------------------------
% 2.77/1.24 % (2295307)Success in time 0.286 s
% 2.77/1.24 % Vampire exiting
%------------------------------------------------------------------------------