%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI164_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:32:36 AM UTC 2026
% Result : Theorem 5.60s 1.78s
% Output : Refutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 3 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 48 ( 9 atm; 11 fun; 11 num; 17 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 : 3 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 11 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
? [X1: $int,X0: $int] :
( $less(X0,X1)
& ( $sum(X0,1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exist_bigger_plus_one) ).
tff(f2,negated_conjecture,
~ ? [X1: $int,X0: $int] :
( $less(X0,X1)
& ( $sum(X0,1) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f5,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f15,plain,
~ ? [X0: $int,X1: $int] :
( ( $sum(X1,1) = X0 )
& $less(X1,X0) ),
inference(rectify,[],[f2]) ).
tff(f16,plain,
! [X1: $int,X0: $int] :
( ~ $less(X1,X0)
| ( $sum(X1,1) != X0 ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ( $sum(X0,1) != X1 ) ),
inference(rectify,[],[f16]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ( $sum(X0,1) != X1 ) ),
inference(cnf_transformation,[],[f17]) ).
tff(f19,plain,
! [X0: $int] : ~ $less(X0,$sum(X0,1)),
inference(equality_resolution,[],[f18]) ).
tff(f26,plain,
! [X0: $int] : ~ $less(X0,$sum(1,X0)),
inference(superposition,[],[f19,f3]) ).
tff(f28,plain,
~ $less(0,1),
inference(superposition,[],[f26,f5]) ).
tff(f32,plain,
$false,
inference(evaluation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI164_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.27 % Computer : n020.cluster.edu
% 0.24/0.27 % Model : x86_64 x86_64
% 0.24/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.27 % Memory : 8046.5625MB
% 0.24/0.27 % OS : Linux 6.8.0-71-generic
% 0.24/0.28 % CPULimit : 300
% 0.24/0.28 % WCLimit : 300
% 0.24/0.28 % DateTime : Mon Sep 28 20:44:34 UTC 2026
% 0.24/0.28 % CPUTime :
% 0.24/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.33 Running first-order theorem proving
% 0.24/0.33 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.60/1.78 % (519690)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.60/1.78 % (519699)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1281234024:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 5.60/1.78 % (519699)Instruction limit reached!
% 5.60/1.78 % (519699)------------------------------
% 5.60/1.78 % (519699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.78 % (519699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.78 % (519699)CaDiCaL version: 2.1.3
% 5.60/1.78 % (519699)Termination reason: Instruction limit
% 5.60/1.78 % (519699)Termination phase: Saturation
% 5.60/1.78 % (519699)Time elapsed: 0.004 s
% 5.60/1.78 % (519699)Peak memory usage: 88 MB
% 5.60/1.78 % (519699)Instructions burned: 6 (million)
% 5.60/1.78 % (519701)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3721882716:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 5.60/1.78 % (519701)First to succeed.
% 5.60/1.78 % (519701)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-519690"
% 5.60/1.78 % (519697)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3158340837:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 5.60/1.78 % (519696)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3503766095:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 5.60/1.78 % (519698)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1709226114:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 5.60/1.78 % (519695)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1974604979:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 5.60/1.78 % (519698)Also succeeded, but the first one will report.
% 5.60/1.78 % (519700)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=973753584:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 5.60/1.78 % (519696)Refutation not found, incomplete strategy
% 5.60/1.78 % (519696)------------------------------
% 5.60/1.78 % (519696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.78 % (519696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.78 % (519696)CaDiCaL version: 2.1.3
% 5.60/1.78 % (519696)Termination reason: Refutation not found, incomplete strategy
% 5.60/1.78 % (519696)Time elapsed: 0.038 s
% 5.60/1.78 % (519696)Peak memory usage: 111 MB
% 5.60/1.78 % (519696)Instructions burned: 5 (million)
% 5.60/1.78 % (519697)Also succeeded, but the first one will report.
% 5.60/1.78 % (519695)Refutation not found, incomplete strategy
% 5.60/1.78 % (519695)------------------------------
% 5.60/1.78 % (519695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.78 % (519695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.78 % (519695)CaDiCaL version: 2.1.3
% 5.60/1.78 % (519695)Termination reason: Refutation not found, incomplete strategy
% 5.60/1.78 % (519695)Time elapsed: 0.043 s
% 5.60/1.78 % (519695)Peak memory usage: 112 MB
% 5.60/1.78 % (519695)Instructions burned: 9 (million)
% 5.60/1.78 % (519700)Refutation not found, incomplete strategy
% 5.60/1.78 % (519700)------------------------------
% 5.60/1.78 % (519700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.78 % (519700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.78 % (519700)CaDiCaL version: 2.1.3
% 5.60/1.78 % (519700)Termination reason: Refutation not found, incomplete strategy
% 5.60/1.78 % (519700)Time elapsed: 0.038 s
% 5.60/1.78 % (519700)Peak memory usage: 111 MB
% 5.60/1.78 % (519700)Instructions burned: 5 (million)
% 5.60/1.78 % (519703)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=726066658:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 5.60/1.78 % (519703)Refutation not found, incomplete strategy
% 5.60/1.78 % (519703)------------------------------
% 5.60/1.78 % (519703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.78 % (519703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.78 % (519703)CaDiCaL version: 2.1.3
% 5.60/1.78 % (519703)Termination reason: Refutation not found, incomplete strategy
% 5.60/1.78 % (519703)Time elapsed: 0.001 s
% 5.60/1.78 % (519703)Peak memory usage: 88 MB
% 5.60/1.78 % (519703)------------------------------
% 5.60/1.78 % (519703)------------------------------
% 5.60/1.78 % (519701)Refutation found. Thanks to Tanya!
% 5.60/1.78 % SZS status Theorem for theBenchmark
% 5.60/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 5.60/1.78 % (519701)------------------------------
% 5.60/1.78 % (519701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.78 % (519701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.78 % (519701)CaDiCaL version: 2.1.3
% 5.60/1.78 % (519701)Termination reason: Refutation
% 5.60/1.78 % (519701)Time elapsed: 0.040 s
% 5.60/1.78 % (519701)Peak memory usage: 112 MB
% 5.60/1.78 % (519701)Instructions burned: 6 (million)
% 5.60/1.78 % (519701)------------------------------
% 5.60/1.78 % (519701)------------------------------
% 5.60/1.78 % (519690)Success in time 0.676 s
% 5.60/1.78 % Vampire exiting
%------------------------------------------------------------------------------