%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM892_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 : n006.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 12:17:23 PM UTC 2026
% Result : Theorem 4.18s 1.75s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 1 unt; 0 typ; 5 def)
% Number of atoms : 62 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 18 ~; 25 |; 6 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 81 ( 34 atm; 22 fun; 13 num; 12 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 : 9 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 6 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK0: $int ).
tff(func_def_5,type,
sK1: $int ).
tff(f1,conjecture,
! [X0: $int,X1: $int] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<=> $lesseq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_lesseq) ).
tff(f2,negated_conjecture,
~ ! [X0: $int,X1: $int] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<=> $lesseq(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X1: $int,X0: $int] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<=> ~ $less(X1,X0) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
? [X0: $int,X1: $int] :
( ( ( X0 = X1 )
| $less(X0,X1) )
<~> ~ $less(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
tff(f17,plain,
? [X0: $int,X1: $int] :
( ( $less(X1,X0)
| ( ( X0 != X1 )
& ~ $less(X0,X1) ) )
& ( ~ $less(X1,X0)
| ( X0 = X1 )
| $less(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
tff(f18,plain,
? [X0: $int,X1: $int] :
( ( $less(X1,X0)
| ( ( X0 != X1 )
& ~ $less(X0,X1) ) )
& ( ~ $less(X1,X0)
| ( X0 = X1 )
| $less(X0,X1) ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( ( $less(sK1,sK0)
| ( ( sK1 != sK0 )
& ~ $less(sK0,sK1) ) )
& ( ~ $less(sK1,sK0)
| ( sK1 = sK0 )
| $less(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18]) ).
tff(f20,plain,
( ( sK1 = sK0 )
| $less(sK0,sK1)
| ~ $less(sK1,sK0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f21,plain,
( ~ $less(sK0,sK1)
| $less(sK1,sK0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f22,plain,
( $less(sK1,sK0)
| ( sK1 != sK0 ) ),
inference(cnf_transformation,[],[f19]) ).
tff(f23,plain,
( $less(0,$sum(sK1,$uminus(sK0)))
| ( sK1 = sK0 )
| $less(0,$sum($sum(sK1,1),$uminus(sK0))) ),
inference(evaluation,[],[f20]) ).
tff(f24,plain,
( $less(0,$sum(sK0,$uminus(sK1)))
| ( sK1 != sK0 ) ),
inference(evaluation,[],[f22]) ).
tff(f25,plain,
( $less(0,$sum(sK0,$uminus(sK1)))
| $less(0,$sum($sum(sK0,1),$uminus(sK1))) ),
inference(evaluation,[],[f21]) ).
tff(f27,definition,
( spl2_1
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f31,definition,
( spl2_2
<=> $less(0,$sum(sK1,$uminus(sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f35,definition,
( spl2_3
<=> $less(0,$sum($sum(sK1,1),$uminus(sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f38,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f23,f35,f31,f27]) ).
tff(f40,definition,
( spl2_4
<=> $less(0,$sum(sK0,$uminus(sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f43,plain,
( spl2_4
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f24,f27,f40]) ).
tff(f45,definition,
( spl2_5
<=> $less(0,$sum($sum(sK0,1),$uminus(sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f48,plain,
( spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f25,f45,f40]) ).
tff(f49,plain,
$false,
inference(avatar_smt_refutation,[],[f48,f43,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM892_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n006.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 21:38:25 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.47 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
% 4.18/1.75 % (3339224)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.18/1.75 % (3339234)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=350402389:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 4.18/1.75 % (3339234)First to succeed.
% 4.18/1.75 % (3339234)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3339224"
% 4.18/1.75 % (3339239)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2316700166:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 4.18/1.75 % (3339237)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4294499454:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 4.18/1.75 % (3339240)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=883567853:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 4.18/1.75 % (3339236)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3950867661:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 4.18/1.75 % (3339235)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=768499549:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 4.18/1.75 % (3339238)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1586383156:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 4.18/1.75 % (3339238)Instruction limit reached!
% 4.18/1.75 % (3339238)------------------------------
% 4.18/1.75 % (3339238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.75 % (3339238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.75 % (3339238)CaDiCaL version: 2.1.3
% 4.18/1.75 % (3339238)Termination reason: Instruction limit
% 4.18/1.75 % (3339238)Termination phase: Saturation
% 4.18/1.75 % (3339238)Time elapsed: 0.006 s
% 4.18/1.75 % (3339238)Peak memory usage: 89 MB
% 4.18/1.75 % (3339238)Instructions burned: 4 (million)
% 4.18/1.75 % (3339237)Instruction limit reached!
% 4.18/1.75 % (3339237)------------------------------
% 4.18/1.75 % (3339237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.75 % (3339237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.75 % (3339237)CaDiCaL version: 2.1.3
% 4.18/1.75 % (3339237)Termination reason: Instruction limit
% 4.18/1.75 % (3339237)Termination phase: Saturation
% 4.18/1.75 % (3339237)Time elapsed: 0.009 s
% 4.18/1.75 % (3339237)Peak memory usage: 88 MB
% 4.18/1.75 % (3339237)Instructions burned: 7 (million)
% 4.18/1.75 % (3339239)Also succeeded, but the first one will report.
% 4.18/1.75 % (3339240)Also succeeded, but the first one will report.
% 4.18/1.75 % (3339235)Also succeeded, but the first one will report.
% 4.18/1.75 % (3339236)Also succeeded, but the first one will report.
% 4.18/1.75 % (3339234)Refutation found. Thanks to Tanya!
% 4.18/1.75 % SZS status Theorem for theBenchmark
% 4.18/1.75 % SZS output start Proof for theBenchmark
% See solution above
% 4.18/1.75 % (3339234)------------------------------
% 4.18/1.75 % (3339234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.75 % (3339234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.75 % (3339234)CaDiCaL version: 2.1.3
% 4.18/1.75 % (3339234)Termination reason: Refutation
% 4.18/1.75 % (3339234)Time elapsed: 0.024 s
% 4.18/1.75 % (3339234)Peak memory usage: 116 MB
% 4.18/1.75 % (3339234)Instructions burned: 9 (million)
% 4.18/1.75 % (3339234)------------------------------
% 4.18/1.75 % (3339234)------------------------------
% 4.18/1.75 % (3339224)Success in time 0.472 s
% 4.18/1.75 % Vampire exiting
%------------------------------------------------------------------------------