%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI590_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 : 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 09:33:26 AM UTC 2026
% Result : Theorem 2.53s 0.83s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 48 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 43 ( 18 ~; 22 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 91 ( 21 atm; 13 fun; 32 num; 25 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 : 4 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 22 !; 3 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK0: $int ).
tff(f1,conjecture,
! [X0: $int] :
? [X1: $int] :
( $less(0,X1)
& ( X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_pos_X_noteq_Y) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
? [X1: $int] :
( $less(0,X1)
& ( X0 != 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(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f9,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f15,plain,
? [X0: $int] :
! [X1: $int] :
( ( X0 = X1 )
| ~ $less(0,X1) ),
inference(ennf_transformation,[],[f2]) ).
tff(f16,plain,
! [X1: $int] :
( ( sK0 = X1 )
| ~ $less(0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15]) ).
tff(f17,plain,
! [X1: $int] :
( ~ $less(0,X1)
| ( sK0 = X1 ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f24,plain,
! [X0: $int] :
( $less(X0,0)
| ( $sum(X0,1) = sK0 ) ),
inference(resolution,[],[f12,f17]) ).
tff(f32,plain,
$sum(0,1) = sK0,
inference(resolution,[],[f24,f8]) ).
tff(f34,plain,
1 = sK0,
inference(evaluation,[],[f32]) ).
tff(f40,definition,
( spl1_2
<=> ( 1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f42,plain,
( ( 1 = sK0 )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f40]) ).
tff(f44,plain,
spl1_2,
inference(avatar_split_clause,[],[f34,f40]) ).
tff(f46,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ( $sum(X1,1) = sK0 )
| $less(X0,0) ),
inference(resolution,[],[f9,f24]) ).
tff(f47,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ( $sum(X1,1) = 1 )
| $less(X0,0) )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f46,f42]) ).
tff(f72,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,0)
| ( 1 = $sum($sum(X0,1),1) )
| $less(X0,X1) )
| ~ spl1_2 ),
inference(resolution,[],[f47,f12]) ).
tff(f77,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(X0,X1)
| ( 1 = $sum(1,$sum(X0,1)) ) )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f72,f3]) ).
tff(f133,plain,
( $less(0,0)
| ( 1 = $sum(1,$sum(0,1)) )
| ~ spl1_2 ),
inference(factoring,[],[f77]) ).
tff(f134,plain,
( $false
| ~ spl1_2 ),
inference(evaluation,[],[f133]) ).
tff(f135,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f134]) ).
tff(f138,plain,
$false,
inference(avatar_smt_refutation,[],[f135,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI590_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 20:52:21 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 2.53/0.83 % (1563459)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.53/0.83 % (1563470)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2693667413:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.53/0.83 % (1563470)First to succeed.
% 2.53/0.83 % (1563470)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1563459"
% 2.53/0.83 % (1563465)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3907821084:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.53/0.83 % (1563466)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=429009881:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.53/0.83 % (1563467)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4137580646:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.53/0.83 % (1563469)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2175361037:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.53/0.83 % (1563468)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=885609775:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.53/0.83 % (1563464)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=922876242:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.53/0.83 % (1563468)Instruction limit reached!
% 2.53/0.83 % (1563468)------------------------------
% 2.53/0.83 % (1563468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.83 % (1563468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.83 % (1563468)CaDiCaL version: 2.1.3
% 2.53/0.83 % (1563468)Termination reason: Instruction limit
% 2.53/0.83 % (1563468)Termination phase: Saturation
% 2.53/0.83 % (1563468)Time elapsed: 0.004 s
% 2.53/0.83 % (1563468)Peak memory usage: 88 MB
% 2.53/0.83 % (1563468)Instructions burned: 4 (million)
% 2.53/0.83 % (1563467)Instruction limit reached!
% 2.53/0.83 % (1563467)------------------------------
% 2.53/0.83 % (1563467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.83 % (1563467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.83 % (1563467)CaDiCaL version: 2.1.3
% 2.53/0.83 % (1563467)Termination reason: Instruction limit
% 2.53/0.83 % (1563467)Termination phase: Saturation
% 2.53/0.83 % (1563467)Time elapsed: 0.007 s
% 2.53/0.83 % (1563467)Peak memory usage: 88 MB
% 2.53/0.83 % (1563467)Instructions burned: 8 (million)
% 2.53/0.83 % (1563469)Refutation not found, incomplete strategy
% 2.53/0.83 % (1563469)------------------------------
% 2.53/0.83 % (1563469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.83 % (1563465)Refutation not found, incomplete strategy
% 2.53/0.83 % (1563465)------------------------------
% 2.53/0.83 % (1563465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.83 % (1563469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.83 % (1563465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.83 % (1563465)CaDiCaL version: 2.1.3
% 2.53/0.83 % (1563469)CaDiCaL version: 2.1.3
% 2.53/0.83 % (1563465)Termination reason: Refutation not found, incomplete strategy
% 2.53/0.83 % (1563465)Time elapsed: 0.028 s
% 2.53/0.83 % (1563469)Termination reason: Refutation not found, incomplete strategy
% 2.53/0.83 % (1563469)Time elapsed: 0.028 s
% 2.53/0.83 % (1563469)Peak memory usage: 111 MB
% 2.53/0.83 % (1563465)Peak memory usage: 111 MB
% 2.53/0.83 % (1563469)Instructions burned: 5 (million)
% 2.53/0.83 % (1563465)Instructions burned: 5 (million)
% 2.53/0.83 % (1563464)Refutation not found, incomplete strategy
% 2.53/0.83 % (1563464)------------------------------
% 2.53/0.83 % (1563464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.83 % (1563464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.83 % (1563464)CaDiCaL version: 2.1.3
% 2.53/0.83 % (1563464)Termination reason: Refutation not found, incomplete strategy
% 2.53/0.83 % (1563464)Time elapsed: 0.032 s
% 2.53/0.83 % (1563464)Peak memory usage: 116 MB
% 2.53/0.83 % (1563464)Instructions burned: 10 (million)
% 2.53/0.83 % (1563466)Also succeeded, but the first one will report.
% 2.53/0.83 % (1563470)Refutation found. Thanks to Tanya!
% 2.53/0.83 % SZS status Theorem for theBenchmark
% 2.53/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/0.83 % (1563470)------------------------------
% 2.53/0.83 % (1563470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.83 % (1563470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.83 % (1563470)CaDiCaL version: 2.1.3
% 2.53/0.83 % (1563470)Termination reason: Refutation
% 2.53/0.83 % (1563470)Time elapsed: 0.022 s
% 2.53/0.83 % (1563470)Peak memory usage: 116 MB
% 2.53/0.83 % (1563470)Instructions burned: 13 (million)
% 2.53/0.83 % (1563470)------------------------------
% 2.53/0.83 % (1563470)------------------------------
% 2.53/0.83 % (1563459)Success in time 0.308 s
% 2.53/0.83 % Vampire exiting
%------------------------------------------------------------------------------