%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI701_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 : n013.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 09:33:41 AM UTC 2026
% Result : Theorem 3.38s 1.34s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 37 ( 0 atm; 23 fun; 9 num; 5 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 : 7 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 5 ( 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
x: $int ).
tff(func_def_1,type,
y: $int ).
tff(func_def_2,type,
a: $int ).
tff(func_def_3,type,
z: $int ).
tff(func_def_4,type,
b: $int ).
tff(f1,axiom,
$product(x,y) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq1) ).
tff(f3,axiom,
$product(a,z) = 1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq3) ).
tff(f4,conjecture,
$product($product(z,y),x) = 1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f5,negated_conjecture,
( ( ~ $product($product(z,y),x) ) = 1 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $product(X1,X0) = $product(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f18,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product($product(X0,X1),X2) = $product(X0,$product(X1,X2)) ),
introduced(definition,[],[tha_associativity]) ).
tff(f24,plain,
1 != $product($product(z,y),x),
inference(flattening,[],[f5]) ).
tff(f25,plain,
$product(a,z) = 1,
inference(cnf_transformation,[],[f3]) ).
tff(f27,plain,
1 != $product($product(z,y),x),
inference(cnf_transformation,[],[f24]) ).
tff(f28,plain,
$product(x,y) = a,
inference(cnf_transformation,[],[f1]) ).
tff(f30,plain,
1 != $product(z,$product(y,x)),
inference(forward_demodulation,[],[f27,f18]) ).
tff(f31,plain,
1 = $product(z,a),
inference(forward_demodulation,[],[f25,f17]) ).
tff(f32,plain,
a = $product(y,x),
inference(forward_demodulation,[],[f28,f17]) ).
tff(f57,plain,
1 != $product(z,a),
inference(superposition,[],[f30,f32]) ).
tff(f58,plain,
$false,
inference(forward_subsumption_resolution,[],[f57,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI701_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n013.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 20:57:06 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running first-order theorem proving
% 0.26/0.32 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
% 3.38/1.34 % (1571152)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.38/1.34 % (1571160)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2307998980:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.38/1.34 % (1571160)First to succeed.
% 3.38/1.34 % (1571160)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1571152"
% 3.38/1.34 % (1571159)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=808809297:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.38/1.34 % (1571162)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=87925921:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.38/1.34 % (1571161)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1456738267:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.38/1.34 % (1571163)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1426470204:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.38/1.34 % (1571158)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=872512814:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.38/1.34 % (1571157)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4287530544:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.38/1.34 % (1571161)Instruction limit reached!
% 3.38/1.34 % (1571161)------------------------------
% 3.38/1.34 % (1571161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.34 % (1571161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.34 % (1571161)CaDiCaL version: 2.1.3
% 3.38/1.34 % (1571161)Termination reason: Instruction limit
% 3.38/1.34 % (1571161)Termination phase: Saturation
% 3.38/1.34 % (1571161)Time elapsed: 0.006 s
% 3.38/1.34 % (1571161)Peak memory usage: 89 MB
% 3.38/1.34 % (1571161)Instructions burned: 4 (million)
% 3.38/1.34 % (1571159)Also succeeded, but the first one will report.
% 3.38/1.34 % (1571157)Instruction limit reached!
% 3.38/1.34 % (1571157)------------------------------
% 3.38/1.34 % (1571157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.34 % (1571157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.34 % (1571157)CaDiCaL version: 2.1.3
% 3.38/1.34 % (1571157)Termination reason: Instruction limit
% 3.38/1.34 % (1571157)Termination phase: Saturation
% 3.38/1.34 % (1571157)Time elapsed: 0.044 s
% 3.38/1.34 % (1571157)Peak memory usage: 116 MB
% 3.38/1.34 % (1571157)Instructions burned: 12 (million)
% 3.38/1.34 % (1571163)Instruction limit reached!
% 3.38/1.34 % (1571163)------------------------------
% 3.38/1.34 % (1571163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.34 % (1571163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.34 % (1571163)CaDiCaL version: 2.1.3
% 3.38/1.34 % (1571163)Termination reason: Instruction limit
% 3.38/1.34 % (1571163)Termination phase: Saturation
% 3.38/1.34 % (1571163)Time elapsed: 0.068 s
% 3.38/1.34 % (1571163)Peak memory usage: 117 MB
% 3.38/1.34 % (1571163)Instructions burned: 33 (million)
% 3.38/1.34 % (1571162)Also succeeded, but the first one will report.
% 3.38/1.34 % (1571158)Also succeeded, but the first one will report.
% 3.38/1.34 % (1571160)Refutation found. Thanks to Tanya!
% 3.38/1.34 % SZS status Theorem for theBenchmark
% 3.38/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.34 % (1571160)------------------------------
% 3.38/1.34 % (1571160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.34 % (1571160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.34 % (1571160)CaDiCaL version: 2.1.3
% 3.38/1.34 % (1571160)Termination reason: Refutation
% 3.38/1.34 % (1571160)Time elapsed: 0.002 s
% 3.38/1.34 % (1571160)Peak memory usage: 89 MB
% 3.38/1.34 % (1571160)Instructions burned: 2 (million)
% 3.38/1.34 % (1571160)------------------------------
% 3.38/1.34 % (1571160)------------------------------
% 3.38/1.34 % (1571152)Success in time 0.364 s
% 3.38/1.34 % Vampire exiting
%------------------------------------------------------------------------------