%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI578_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 09:33:24 AM UTC 2026
% Result : Theorem 3.69s 1.29s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 35 ( 11 ~; 12 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 116 ( 32 atm; 24 fun; 46 num; 14 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 : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 2 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 6 !; 8 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
'$inst0': $int ).
tff(func_def_9,type,
'$inst1': $int ).
tff(f1,conjecture,
? [X1: $int,X0: $int] :
( $lesseq(2,X1)
& $lesseq($sum(X0,X1),9)
& $lesseq(2,X0)
& $lesseq(12,$sum($product(2,X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq_sys_solvable_3) ).
tff(f2,negated_conjecture,
~ ? [X1: $int,X0: $int] :
( $lesseq(2,X1)
& $lesseq($sum(X0,X1),9)
& $lesseq(2,X0)
& $lesseq(12,$sum($product(2,X0),X1)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ? [X1: $int,X0: $int] :
( ~ $less(X1,2)
& ~ $less(9,$sum(X0,X1))
& ~ $less(X0,2)
& ~ $less($sum($product(2,X0),X1),12) ),
inference(theory_normalization,[],[f2]) ).
tff(f22,plain,
~ ? [X0: $int,X1: $int] :
( ~ $less(X1,2)
& ~ $less(X0,2)
& ~ $less(9,$sum(X1,X0))
& ~ $less($sum($product(2,X1),X0),12) ),
inference(rectify,[],[f3]) ).
tff(f23,plain,
! [X1: $int,X0: $int] :
( $less($sum($product(2,X1),X0),12)
| $less(X1,2)
| $less(X0,2)
| $less(9,$sum(X1,X0)) ),
inference(ennf_transformation,[],[f22]) ).
tff(f24,plain,
! [X0: $int,X1: $int] :
( $less($sum($product(2,X0),X1),12)
| $less(X0,2)
| $less(X1,2)
| $less(9,$sum(X0,X1)) ),
inference(rectify,[],[f23]) ).
tff(f25,plain,
! [X0: $int,X1: $int] :
( $less($sum($product(2,X0),X1),12)
| $less(9,$sum(X0,X1))
| $less(X1,2)
| $less(X0,2) ),
inference(cnf_transformation,[],[f24]) ).
tff(f27,plain,
( $less($sum($product(2,3),6),12)
| $less(9,$sum(3,6))
| $less(6,2)
| $less(3,2) ),
inference(instantiation,[],[f25]) ).
tff(f28,plain,
$false,
inference(interpreted_simplification,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI578_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:55:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.69/1.29 % (57678)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.69/1.29 % (57686)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1359783726:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.69/1.29 % (57686)Instruction limit reached!
% 3.69/1.29 % (57686)------------------------------
% 3.69/1.29 % (57686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57686)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57686)Termination reason: Instruction limit
% 3.69/1.29 % (57686)Termination phase: Saturation
% 3.69/1.29 % (57686)Time elapsed: 0.003 s
% 3.69/1.29 % (57686)Peak memory usage: 88 MB
% 3.69/1.29 % (57686)Instructions burned: 7 (million)
% 3.69/1.29 % (57687)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3025511724:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.69/1.29 % (57689)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=864293819:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.69/1.29 % (57684)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2949570384:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.69/1.29 % (57688)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=675363590:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.69/1.29 % (57685)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3155065536:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.69/1.29 % (57683)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2249214115:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.69/1.29 % (57687)Instruction limit reached!
% 3.69/1.29 % (57687)------------------------------
% 3.69/1.29 % (57687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57687)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57687)Termination reason: Instruction limit
% 3.69/1.29 % (57687)Termination phase: Saturation
% 3.69/1.29 % (57687)Time elapsed: 0.004 s
% 3.69/1.29 % (57687)Peak memory usage: 88 MB
% 3.69/1.29 % (57687)Instructions burned: 4 (million)
% 3.69/1.29 % (57684)Refutation not found, incomplete strategy
% 3.69/1.29 % (57684)------------------------------
% 3.69/1.29 % (57684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57688)Refutation not found, incomplete strategy
% 3.69/1.29 % (57688)------------------------------
% 3.69/1.29 % (57688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57684)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57688)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57684)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.29 % (57684)Time elapsed: 0.028 s
% 3.69/1.29 % (57688)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.29 % (57688)Time elapsed: 0.028 s
% 3.69/1.29 % (57684)Peak memory usage: 111 MB
% 3.69/1.29 % (57688)Peak memory usage: 111 MB
% 3.69/1.29 % (57684)Instructions burned: 5 (million)
% 3.69/1.29 % (57688)Instructions burned: 5 (million)
% 3.69/1.29 % (57685)First to succeed.
% 3.69/1.29 % (57683)Refutation not found, incomplete strategy
% 3.69/1.29 % (57683)------------------------------
% 3.69/1.29 % (57683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57683)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57683)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.29 % (57683)Time elapsed: 0.030 s
% 3.69/1.29 % (57683)Peak memory usage: 112 MB
% 3.69/1.29 % (57683)Instructions burned: 9 (million)
% 3.69/1.29 % (57685)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-57678"
% 3.69/1.29 % (57689)Instruction limit reached!
% 3.69/1.29 % (57689)------------------------------
% 3.69/1.29 % (57689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57689)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57689)Termination reason: Instruction limit
% 3.69/1.29 % (57689)Termination phase: Saturation
% 3.69/1.29 % (57689)Time elapsed: 0.046 s
% 3.69/1.29 % (57689)Peak memory usage: 115 MB
% 3.69/1.29 % (57689)Instructions burned: 33 (million)
% 3.69/1.29 % (57691)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3727124423:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.69/1.29 % (57691)Refutation not found, incomplete strategy
% 3.69/1.29 % (57691)------------------------------
% 3.69/1.29 % (57691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57691)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57691)Termination reason: Refutation not found, incomplete strategy
% 3.69/1.29 % (57691)Time elapsed: 0.001 s
% 3.69/1.29 % (57691)Peak memory usage: 88 MB
% 3.69/1.29 % (57698)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=2106667839:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.69/1.29 % (57698)Instruction limit reached!
% 3.69/1.29 % (57698)------------------------------
% 3.69/1.29 % (57698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57698)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57698)Termination reason: Instruction limit
% 3.69/1.29 % (57698)Termination phase: Saturation
% 3.69/1.29 % (57698)Time elapsed: 0.021 s
% 3.69/1.29 % (57698)Peak memory usage: 88 MB
% 3.69/1.29 % (57698)Instructions burned: 30 (million)
% 3.69/1.29 % (57700)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=666354351:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.69/1.29 % (57700)Instruction limit reached!
% 3.69/1.29 % (57700)------------------------------
% 3.69/1.29 % (57700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57700)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57700)Termination reason: Instruction limit
% 3.69/1.29 % (57700)Termination phase: Saturation
% 3.69/1.29 % (57700)Time elapsed: 0.011 s
% 3.69/1.29 % (57700)Peak memory usage: 90 MB
% 3.69/1.29 % (57700)Instructions burned: 23 (million)
% 3.69/1.29 % (57691)------------------------------
% 3.69/1.29 % (57691)------------------------------
% 3.69/1.29 % (57683)------------------------------
% 3.69/1.29 % (57683)------------------------------
% 3.69/1.29 % (57688)------------------------------
% 3.69/1.29 % (57688)------------------------------
% 3.69/1.29 % (57684)------------------------------
% 3.69/1.29 % (57684)------------------------------
% 3.69/1.29 % (57685)Refutation found. Thanks to Tanya!
% 3.69/1.29 % SZS status Theorem for theBenchmark
% 3.69/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.29 % (57685)------------------------------
% 3.69/1.29 % (57685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.29 % (57685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.29 % (57685)CaDiCaL version: 2.1.3
% 3.69/1.29 % (57685)Termination reason: Refutation
% 3.69/1.29 % (57685)Time elapsed: 0.030 s
% 3.69/1.29 % (57685)Peak memory usage: 116 MB
% 3.69/1.29 % (57685)Instructions burned: 8 (million)
% 3.69/1.29 % (57685)------------------------------
% 3.69/1.29 % (57685)------------------------------
% 3.69/1.29 % (57678)Success in time 0.435 s
% 3.69/1.29 % Vampire exiting
%------------------------------------------------------------------------------