%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI594_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:33:26 AM UTC 2026
% Result : Theorem 2.73s 1.17s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 26 ( 7 ~; 8 |; 5 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 67 ( 16 atm; 10 fun; 28 num; 13 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 : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 1 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 10 !; 3 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
'$inst0': $int ).
tff(pred_def_1,type,
p: $int > $o ).
tff(f1,conjecture,
( ! [X0: $int] :
( ( $lesseq(5,X0)
& $lesseq(X0,7) )
=> p(X0) )
=> ? [X1: $int] : p($product(3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_X_in_5_to_7_div_3) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] :
( ( $lesseq(5,X0)
& $lesseq(X0,7) )
=> p(X0) )
=> ? [X1: $int] : p($product(3,X1)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] :
( ( ~ $less(7,X0)
& ~ $less(X0,5) )
=> p(X0) )
=> ? [X1: $int] : p($product(3,X1)) ),
inference(theory_normalization,[],[f2]) ).
tff(f22,plain,
( ! [X1: $int] : ~ p($product(3,X1))
& ! [X0: $int] :
( p(X0)
| $less(7,X0)
| $less(X0,5) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f23,plain,
( ! [X0: $int] :
( $less(X0,5)
| p(X0)
| $less(7,X0) )
& ! [X1: $int] : ~ p($product(3,X1)) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
! [X1: $int] : ~ p($product(3,X1)),
inference(cnf_transformation,[],[f23]) ).
tff(f25,plain,
! [X0: $int] :
( p(X0)
| $less(7,X0)
| $less(X0,5) ),
inference(cnf_transformation,[],[f23]) ).
tff(f33,plain,
! [X0: $int] :
( $less($product(3,X0),5)
| $less(7,$product(3,X0)) ),
inference(resolution,[],[f25,f24]) ).
tff(f165,plain,
( $less($product(3,2),5)
| $less(7,$product(3,2)) ),
inference(instantiation,[],[f33]) ).
tff(f166,plain,
$false,
inference(interpreted_simplification,[],[f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI594_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:55:57 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.73/1.17 % (59198)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.73/1.17 % (59244)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2511558154:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.73/1.17 % (59244)First to succeed.
% 2.73/1.17 % (59244)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-59198"
% 2.73/1.17 % (59247)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=609747350:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.73/1.17 % (59246)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1578079687:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.73/1.17 % (59243)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1294091728:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.73/1.17 % (59248)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3963208199:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.73/1.17 % (59242)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1088673677:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.73/1.17 % (59245)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=757098280:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.73/1.17 % (59246)Instruction limit reached!
% 2.73/1.17 % (59246)------------------------------
% 2.73/1.17 % (59246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (59246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (59246)CaDiCaL version: 2.1.3
% 2.73/1.17 % (59246)Termination reason: Instruction limit
% 2.73/1.17 % (59246)Termination phase: Saturation
% 2.73/1.17 % (59246)Time elapsed: 0.004 s
% 2.73/1.17 % (59246)Peak memory usage: 88 MB
% 2.73/1.17 % (59246)Instructions burned: 4 (million)
% 2.73/1.17 % (59245)Instruction limit reached!
% 2.73/1.17 % (59245)------------------------------
% 2.73/1.17 % (59245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (59245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (59245)CaDiCaL version: 2.1.3
% 2.73/1.17 % (59245)Termination reason: Instruction limit
% 2.73/1.17 % (59245)Termination phase: Saturation
% 2.73/1.17 % (59245)Time elapsed: 0.006 s
% 2.73/1.17 % (59245)Peak memory usage: 88 MB
% 2.73/1.17 % (59245)Instructions burned: 8 (million)
% 2.73/1.17 % (59243)Refutation not found, incomplete strategy
% 2.73/1.17 % (59243)------------------------------
% 2.73/1.17 % (59243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (59243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (59243)CaDiCaL version: 2.1.3
% 2.73/1.17 % (59243)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.17 % (59243)Time elapsed: 0.027 s
% 2.73/1.17 % (59243)Peak memory usage: 111 MB
% 2.73/1.17 % (59243)Instructions burned: 5 (million)
% 2.73/1.17 % (59247)Refutation not found, incomplete strategy
% 2.73/1.17 % (59247)------------------------------
% 2.73/1.17 % (59247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (59247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (59247)CaDiCaL version: 2.1.3
% 2.73/1.17 % (59247)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.17 % (59247)Time elapsed: 0.027 s
% 2.73/1.17 % (59247)Peak memory usage: 112 MB
% 2.73/1.17 % (59247)Instructions burned: 5 (million)
% 2.73/1.17 % (59242)Refutation not found, incomplete strategy
% 2.73/1.17 % (59242)------------------------------
% 2.73/1.17 % (59242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (59242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (59242)CaDiCaL version: 2.1.3
% 2.73/1.17 % (59242)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.17 % (59242)Time elapsed: 0.031 s
% 2.73/1.17 % (59242)Peak memory usage: 115 MB
% 2.73/1.17 % (59242)Instructions burned: 9 (million)
% 2.73/1.17 % (59248)Instruction limit reached!
% 2.73/1.17 % (59248)------------------------------
% 2.73/1.17 % (59248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (59248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (59248)CaDiCaL version: 2.1.3
% 2.73/1.17 % (59248)Termination reason: Instruction limit
% 2.73/1.17 % (59248)Termination phase: Saturation
% 2.73/1.17 % (59248)Time elapsed: 0.046 s
% 2.73/1.17 % (59248)Peak memory usage: 115 MB
% 2.73/1.17 % (59248)Instructions burned: 33 (million)
% 2.73/1.17 % (59244)Refutation found. Thanks to Tanya!
% 2.73/1.17 % SZS status Theorem for theBenchmark
% 2.73/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.17 % (59244)------------------------------
% 2.73/1.17 % (59244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.17 % (59244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.17 % (59244)CaDiCaL version: 2.1.3
% 2.73/1.17 % (59244)Termination reason: Refutation
% 2.73/1.17 % (59244)Time elapsed: 0.021 s
% 2.73/1.17 % (59244)Peak memory usage: 116 MB
% 2.73/1.17 % (59244)Instructions burned: 13 (million)
% 2.73/1.17 % (59244)------------------------------
% 2.73/1.17 % (59244)------------------------------
% 2.73/1.17 % (59198)Success in time 0.291 s
% 2.73/1.17 % Vampire exiting
%------------------------------------------------------------------------------