%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM920_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 : n011.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 12:17:26 PM UTC 2026
% Result : Theorem 2.85s 1.40s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 28 ( 1 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 22 ( 8 ~; 5 |; 5 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 100 ( 24 atm; 34 fun; 29 num; 13 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 : 6 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 9 !; 4 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK0: $int ).
tff(f1,conjecture,
~ ? [X0: $int] :
( ! [X1: $int] :
( $less(X1,X0)
=> $less($sum(X1,1),X0) )
& $less(0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ~ ? [X0: $int] :
( ! [X1: $int] :
( $less(X1,X0)
=> $less($sum(X1,1),X0) )
& $less(0,X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f15,plain,
? [X0: $int] :
( ! [X1: $int] :
( $less(X1,X0)
=> $less($sum(X1,1),X0) )
& $less(0,X0) ),
inference(flattening,[],[f2]) ).
tff(f16,plain,
? [X0: $int] :
( $less(0,X0)
& ! [X1: $int] :
( $less($sum(X1,1),X0)
| ~ $less(X1,X0) ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
( $less(0,sK0)
& ! [X1: $int] :
( $less($sum(X1,1),sK0)
| ~ $less(X1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16]) ).
tff(f18,plain,
! [X1: $int] :
( ~ $less(X1,sK0)
| $less($sum(X1,1),sK0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f20,plain,
! [X1: $int] :
( $less(0,$sum(sK0,$uminus($sum(X1,1))))
| $less(0,$sum($sum(X1,1),$uminus(sK0))) ),
inference(evaluation,[],[f18]) ).
tff(f26,plain,
! [X0: $int] :
( ( 0 != $sum(sK0,$uminus($sum(X0,1))) )
| $less(0,$sum($sum(X0,1),$uminus(sK0))) ),
inference(constrained_resolution,[],[f8,f20]) ).
tff(f27,plain,
$less(0,$sum($sum($sum($uminus($sum(0,$uminus(sK0))),$uminus(1)),1),$uminus(sK0))),
inference(gaussian_variable_elimination,[],[f26]) ).
tff(f28,plain,
$less(0,$sum($sum($sum(sK0,-1),1),$uminus(sK0))),
inference(evaluation,[],[f27]) ).
tff(f30,definition,
( spl1_2
<=> $less(0,$sum($sum($sum(sK0,-1),1),$uminus(sK0))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f33,plain,
spl1_2,
inference(avatar_split_clause,[],[f28,f30]) ).
tff(f34,plain,
$false,
inference(avatar_smt_refutation,[],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM920_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 21:39:30 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.85/1.40 % (2781603)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.85/1.40 % (2781709)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1222318830:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.85/1.40 % (2781709)First to succeed.
% 2.85/1.40 % (2781709)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2781603"
% 2.85/1.40 % (2781714)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1485005023:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.85/1.40 % (2781712)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1874018024:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.85/1.40 % (2781711)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3808249366:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.85/1.40 % (2781715)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2678996452:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.85/1.40 % (2781710)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1733192994:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.85/1.40 % (2781713)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3885400720:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.85/1.40 % (2781713)Instruction limit reached!
% 2.85/1.40 % (2781713)------------------------------
% 2.85/1.40 % (2781713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.40 % (2781713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.40 % (2781713)CaDiCaL version: 2.1.3
% 2.85/1.40 % (2781713)Termination reason: Instruction limit
% 2.85/1.40 % (2781713)Termination phase: Saturation
% 2.85/1.40 % (2781713)Time elapsed: 0.004 s
% 2.85/1.40 % (2781713)Peak memory usage: 88 MB
% 2.85/1.40 % (2781713)Instructions burned: 4 (million)
% 2.85/1.40 % (2781712)Instruction limit reached!
% 2.85/1.40 % (2781712)------------------------------
% 2.85/1.40 % (2781712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.40 % (2781712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.40 % (2781712)CaDiCaL version: 2.1.3
% 2.85/1.40 % (2781712)Termination reason: Instruction limit
% 2.85/1.40 % (2781712)Termination phase: Saturation
% 2.85/1.40 % (2781712)Time elapsed: 0.006 s
% 2.85/1.40 % (2781712)Peak memory usage: 88 MB
% 2.85/1.40 % (2781712)Instructions burned: 7 (million)
% 2.85/1.40 % (2781714)Refutation not found, incomplete strategy
% 2.85/1.40 % (2781714)------------------------------
% 2.85/1.40 % (2781714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.40 % (2781714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.40 % (2781710)Refutation not found, incomplete strategy
% 2.85/1.40 % (2781710)------------------------------
% 2.85/1.40 % (2781710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.40 % (2781710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.40 % (2781714)CaDiCaL version: 2.1.3
% 2.85/1.40 % (2781714)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.40 % (2781714)Time elapsed: 0.029 s
% 2.85/1.40 % (2781710)CaDiCaL version: 2.1.3
% 2.85/1.40 % (2781714)Peak memory usage: 114 MB
% 2.85/1.40 % (2781710)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.40 % (2781710)Time elapsed: 0.029 s
% 2.85/1.40 % (2781714)Instructions burned: 6 (million)
% 2.85/1.40 % (2781710)Peak memory usage: 114 MB
% 2.85/1.40 % (2781710)Instructions burned: 5 (million)
% 2.85/1.40 % (2781715)Instruction limit reached!
% 2.85/1.40 % (2781715)------------------------------
% 2.85/1.40 % (2781715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.40 % (2781715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.40 % (2781715)CaDiCaL version: 2.1.3
% 2.85/1.40 % (2781715)Termination reason: Instruction limit
% 2.85/1.40 % (2781715)Termination phase: Saturation
% 2.85/1.40 % (2781715)Time elapsed: 0.047 s
% 2.85/1.40 % (2781715)Peak memory usage: 115 MB
% 2.85/1.40 % (2781715)Instructions burned: 33 (million)
% 2.85/1.40 % (2781709)Refutation found. Thanks to Tanya!
% 2.85/1.40 % SZS status Theorem for theBenchmark
% 2.85/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 2.85/1.40 % (2781709)------------------------------
% 2.85/1.40 % (2781709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.40 % (2781709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.40 % (2781709)CaDiCaL version: 2.1.3
% 2.85/1.40 % (2781709)Termination reason: Refutation
% 2.85/1.40 % (2781709)Time elapsed: 0.021 s
% 2.85/1.40 % (2781709)Peak memory usage: 116 MB
% 2.85/1.40 % (2781709)Instructions burned: 8 (million)
% 2.85/1.40 % (2781709)------------------------------
% 2.85/1.40 % (2781709)------------------------------
% 2.85/1.40 % (2781603)Success in time 0.331 s
% 2.85/1.40 % Vampire exiting
%------------------------------------------------------------------------------