%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI120_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 : n001.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 3.94s 1.34s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 29 ( 12 ~; 9 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 35 ( 0 atm; 6 fun; 17 num; 12 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 8 !; 4 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
'$inst0': $int ).
tff(pred_def_1,type,
p: $int > $o ).
tff(f1,conjecture,
( p(2)
=> ? [X1: $int,X0: $int] :
( ( $product(X1,X1) = 4 )
& p(X0)
& ( X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_X_X_4_predicate) ).
tff(f2,negated_conjecture,
~ ( p(2)
=> ? [X1: $int,X0: $int] :
( ( $product(X1,X1) = 4 )
& p(X0)
& ( X0 != X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
( ! [X1: $int,X0: $int] :
( ( X0 = X1 )
| ~ p(X0)
| ( $product(X1,X1) != 4 ) )
& p(2) ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
( ! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ~ p(X1)
| ( 4 != $product(X0,X0) ) )
& p(2) ),
inference(rectify,[],[f21]) ).
tff(f23,plain,
p(2),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
! [X0: $int,X1: $int] :
( ( 4 != $product(X0,X0) )
| ~ p(X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f22]) ).
tff(f30,plain,
! [X1: $int] :
( ( 4 != $product(-2,-2) )
| ~ p(X1)
| ( -2 = X1 ) ),
inference(instantiation,[],[f24]) ).
tff(f31,plain,
! [X1: $int] :
( ~ p(X1)
| ( -2 = X1 ) ),
inference(interpreted_simplification,[],[f30]) ).
tff(f45,plain,
2 = -2,
inference(resolution,[],[f31,f23]) ).
tff(f46,plain,
$false,
inference(evaluation,[],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI120_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:49:04 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.94/1.34 % (711602)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.94/1.34 % (711608)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1794825399:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.94/1.34 % (711608)Refutation not found, incomplete strategy
% 3.94/1.34 % (711608)------------------------------
% 3.94/1.34 % (711608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711608)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711608)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.34 % (711608)Time elapsed: 0.019 s
% 3.94/1.34 % (711608)Peak memory usage: 115 MB
% 3.94/1.34 % (711608)Instructions burned: 5 (million)
% 3.94/1.34 % (711611)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3313877559:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.94/1.34 % (711609)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3739423277:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.94/1.34 % (711607)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=232052295:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.94/1.34 % (711612)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3894794852:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.94/1.34 % (711610)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1369828583:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.94/1.34 % (711613)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2446609029:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.94/1.34 % (711611)Instruction limit reached!
% 3.94/1.34 % (711611)------------------------------
% 3.94/1.34 % (711611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711611)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711611)Termination reason: Instruction limit
% 3.94/1.34 % (711611)Termination phase: Saturation
% 3.94/1.34 % (711611)Time elapsed: 0.004 s
% 3.94/1.34 % (711611)Peak memory usage: 88 MB
% 3.94/1.34 % (711611)Instructions burned: 5 (million)
% 3.94/1.34 % (711610)Instruction limit reached!
% 3.94/1.34 % (711610)------------------------------
% 3.94/1.34 % (711610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711610)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711610)Termination reason: Instruction limit
% 3.94/1.34 % (711610)Termination phase: Saturation
% 3.94/1.34 % (711610)Time elapsed: 0.005 s
% 3.94/1.34 % (711610)Peak memory usage: 88 MB
% 3.94/1.34 % (711610)Instructions burned: 7 (million)
% 3.94/1.34 % (711612)Refutation not found, incomplete strategy
% 3.94/1.34 % (711612)------------------------------
% 3.94/1.34 % (711612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711612)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711612)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.34 % (711612)Time elapsed: 0.030 s
% 3.94/1.34 % (711612)Peak memory usage: 114 MB
% 3.94/1.34 % (711612)Instructions burned: 6 (million)
% 3.94/1.34 % (711607)Refutation not found, incomplete strategy
% 3.94/1.34 % (711607)------------------------------
% 3.94/1.34 % (711607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711607)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711607)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.34 % (711607)Time elapsed: 0.030 s
% 3.94/1.34 % (711607)Peak memory usage: 115 MB
% 3.94/1.34 % (711607)Instructions burned: 6 (million)
% 3.94/1.34 % (711609)First to succeed.
% 3.94/1.34 % (711609)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-711602"
% 3.94/1.34 % (711613)Instruction limit reached!
% 3.94/1.34 % (711613)------------------------------
% 3.94/1.34 % (711613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711613)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711613)Termination reason: Instruction limit
% 3.94/1.34 % (711613)Termination phase: Saturation
% 3.94/1.34 % (711613)Time elapsed: 0.045 s
% 3.94/1.34 % (711613)Peak memory usage: 114 MB
% 3.94/1.34 % (711613)Instructions burned: 34 (million)
% 3.94/1.34 % (711608)------------------------------
% 3.94/1.34 % (711608)------------------------------
% 3.94/1.34 % (711622)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=1344060965:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.94/1.34 % (711621)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3831852034:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.94/1.34 % (711621)Refutation not found, incomplete strategy
% 3.94/1.34 % (711621)------------------------------
% 3.94/1.34 % (711621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711621)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711621)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.34 % (711621)Time elapsed: 0.001 s
% 3.94/1.34 % (711621)Peak memory usage: 88 MB
% 3.94/1.34 % (711622)Instruction limit reached!
% 3.94/1.34 % (711622)------------------------------
% 3.94/1.34 % (711622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711622)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711622)Termination reason: Instruction limit
% 3.94/1.34 % (711622)Termination phase: Saturation
% 3.94/1.34 % (711622)Time elapsed: 0.015 s
% 3.94/1.34 % (711622)Peak memory usage: 88 MB
% 3.94/1.34 % (711622)Instructions burned: 30 (million)
% 3.94/1.34 % (711623)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=709240694:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.94/1.34 % (711623)Instruction limit reached!
% 3.94/1.34 % (711623)------------------------------
% 3.94/1.34 % (711623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711623)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711623)Termination reason: Instruction limit
% 3.94/1.34 % (711623)Termination phase: Saturation
% 3.94/1.34 % (711623)Time elapsed: 0.010 s
% 3.94/1.34 % (711623)Peak memory usage: 90 MB
% 3.94/1.34 % (711623)Instructions burned: 16 (million)
% 3.94/1.34 % (711624)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=4070648958:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 3.94/1.34 % (711624)Instruction limit reached!
% 3.94/1.34 % (711624)------------------------------
% 3.94/1.34 % (711624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711624)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711624)Termination reason: Instruction limit
% 3.94/1.34 % (711624)Termination phase: Saturation
% 3.94/1.34 % (711624)Time elapsed: 0.009 s
% 3.94/1.34 % (711624)Peak memory usage: 89 MB
% 3.94/1.34 % (711624)Instructions burned: 26 (million)
% 3.94/1.34 % (711607)------------------------------
% 3.94/1.34 % (711607)------------------------------
% 3.94/1.34 % (711612)------------------------------
% 3.94/1.34 % (711612)------------------------------
% 3.94/1.34 % (711609)Refutation found. Thanks to Tanya!
% 3.94/1.34 % SZS status Theorem for theBenchmark
% 3.94/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.34 % (711609)------------------------------
% 3.94/1.34 % (711609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.34 % (711609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.34 % (711609)CaDiCaL version: 2.1.3
% 3.94/1.34 % (711609)Termination reason: Refutation
% 3.94/1.34 % (711609)Time elapsed: 0.032 s
% 3.94/1.34 % (711609)Peak memory usage: 117 MB
% 3.94/1.34 % (711609)Instructions burned: 9 (million)
% 3.94/1.34 % (711609)------------------------------
% 3.94/1.34 % (711609)------------------------------
% 3.94/1.34 % (711602)Success in time 0.468 s
% 3.94/1.34 % Vampire exiting
%------------------------------------------------------------------------------