%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI122_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 : n008.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 3.35s 1.15s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 36 ( 8 ~; 0 |; 25 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 115 ( 0 atm; 34 fun; 57 num; 24 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 : 10 ( 4 usr; 9 con; 0-2 aty)
% Number of variables : 24 ( 12 !; 12 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
sK0: $int ).
tff(func_def_9,type,
sK1: $int ).
tff(func_def_10,type,
sK2: $int ).
tff(func_def_11,type,
sK3: $int ).
tff(f1,conjecture,
! [X3: $int,X1: $int,X2: $int,X0: $int] :
( ( ( $product(X0,6) = X1 )
& ( $product(2,3) = X0 )
& ( $product(3,6) = X2 )
& ( $product(2,X2) = X3 ) )
=> ( X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_product) ).
tff(f2,negated_conjecture,
~ ! [X3: $int,X1: $int,X2: $int,X0: $int] :
( ( ( $product(X0,6) = X1 )
& ( $product(2,3) = X0 )
& ( $product(3,6) = X2 )
& ( $product(2,X2) = X3 ) )
=> ( X1 = X3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
~ ! [X0: $int,X2: $int,X3: $int,X1: $int] :
( ( ( $product(2,X2) = X0 )
& ( $product(2,3) = X3 )
& ( $product(3,6) = X2 )
& ( $product(X3,6) = X1 ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
tff(f22,plain,
? [X0: $int,X2: $int,X3: $int,X1: $int] :
( ( X0 != X1 )
& ( $product(2,X2) = X0 )
& ( $product(2,3) = X3 )
& ( $product(3,6) = X2 )
& ( $product(X3,6) = X1 ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f23,plain,
? [X1: $int,X0: $int,X3: $int,X2: $int] :
( ( X0 != X1 )
& ( $product(X3,6) = X1 )
& ( $product(3,6) = X2 )
& ( $product(2,X2) = X0 )
& ( $product(2,3) = X3 ) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
? [X0: $int,X1: $int,X2: $int,X3: $int] :
( ( X0 != X1 )
& ( $product(X2,6) = X0 )
& ( $product(3,6) = X3 )
& ( $product(2,X3) = X1 )
& ( $product(2,3) = X2 ) ),
inference(rectify,[],[f23]) ).
tff(f25,plain,
( ( sK0 != sK1 )
& ( $product(sK2,6) = sK0 )
& ( $product(3,6) = sK3 )
& ( sK1 = $product(2,sK3) )
& ( $product(2,3) = sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f24]) ).
tff(f26,plain,
$product(2,3) = sK2,
inference(cnf_transformation,[],[f25]) ).
tff(f27,plain,
sK1 = $product(2,sK3),
inference(cnf_transformation,[],[f25]) ).
tff(f28,plain,
$product(3,6) = sK3,
inference(cnf_transformation,[],[f25]) ).
tff(f29,plain,
$product(sK2,6) = sK0,
inference(cnf_transformation,[],[f25]) ).
tff(f30,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f25]) ).
tff(f32,plain,
6 = sK2,
inference(evaluation,[],[f26]) ).
tff(f33,plain,
sK3 = 18,
inference(evaluation,[],[f28]) ).
tff(f34,plain,
$product(2,18) = sK1,
inference(forward_demodulation,[],[f27,f33]) ).
tff(f35,plain,
36 = sK1,
inference(evaluation,[],[f34]) ).
tff(f36,plain,
36 != sK0,
inference(constrained_superposition,[],[f30,f35]) ).
tff(f37,plain,
sK0 = $product(6,6),
inference(forward_demodulation,[],[f29,f32]) ).
tff(f38,plain,
36 = sK0,
inference(evaluation,[],[f37]) ).
tff(f39,plain,
$false,
inference(forward_subsumption_resolution,[],[f38,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI122_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n008.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Mon Sep 28 20:43:55 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.29 Running first-order theorem proving
% 0.10/0.29 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
% 3.35/1.15 % (2609884)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.35/1.15 % (2609895)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=345071312:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.35/1.15 % (2609892)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2691160158:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.35/1.15 % (2609890)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1635022375:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.35/1.15 % (2609893)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3719697658:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.35/1.15 % (2609891)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1301979309:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.35/1.15 % (2609889)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4276406838:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.35/1.15 % (2609893)First to succeed.
% 3.35/1.15 % (2609892)Also succeeded, but the first one will report.
% 3.35/1.15 % (2609893)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2609884"
% 3.35/1.15 % (2609895)Also succeeded, but the first one will report.
% 3.35/1.15 % (2609894)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=829626740:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.35/1.15 % (2609889)Also succeeded, but the first one will report.
% 3.35/1.15 % (2609890)Also succeeded, but the first one will report.
% 3.35/1.15 % (2609891)Also succeeded, but the first one will report.
% 3.35/1.15 % (2609894)Also succeeded, but the first one will report.
% 3.35/1.15 % (2609893)Refutation found. Thanks to Tanya!
% 3.35/1.15 % SZS status Theorem for theBenchmark
% 3.35/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.15 % (2609893)------------------------------
% 3.35/1.15 % (2609893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.15 % (2609893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.15 % (2609893)CaDiCaL version: 2.1.3
% 3.35/1.15 % (2609893)Termination reason: Refutation
% 3.35/1.15 % (2609893)Time elapsed: 0.002 s
% 3.35/1.15 % (2609893)Peak memory usage: 89 MB
% 3.35/1.15 % (2609893)Instructions burned: 1 (million)
% 3.35/1.15 % (2609893)------------------------------
% 3.35/1.15 % (2609893)------------------------------
% 3.35/1.15 % (2609884)Success in time 0.389 s
% 3.35/1.15 % Vampire exiting
%------------------------------------------------------------------------------