%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI572_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 : n017.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 09:33:23 AM UTC 2026
% Result : Theorem 2.85s 1.19s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 28 ( 17 unt; 0 typ; 10 def)
% Number of atoms : 39 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 6 ~; 0 |; 3 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 58 ( 15 atm; 35 fun; 0 num; 8 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 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 8 ( 4 !; 4 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_2,type,
sK0: $int ).
tff(func_def_3,type,
sK1: $int ).
tff(func_def_4,type,
sF2: $int ).
tff(func_def_5,type,
sF3: $int ).
tff(func_def_6,type,
sF4: $int ).
tff(func_def_7,type,
sF5: $int ).
tff(f1,conjecture,
! [X1: $int,X0: $int] :
( $less($sum(X1,$uminus(X0)),$sum(X0,$uminus(X1)))
=> $less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impl_ineq) ).
tff(f2,negated_conjecture,
~ ! [X1: $int,X0: $int] :
( $less($sum(X1,$uminus(X0)),$sum(X0,$uminus(X1)))
=> $less(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
? [X1: $int,X0: $int] :
( ~ $less(X1,X0)
& $less($sum(X1,$uminus(X0)),$sum(X0,$uminus(X1))) ),
inference(ennf_transformation,[],[f2]) ).
tff(f4,plain,
? [X0: $int,X1: $int] :
( ~ $less(X0,X1)
& $less($sum(X0,$uminus(X1)),$sum(X1,$uminus(X0))) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( ~ $less(sK0,sK1)
& $less($sum(sK0,$uminus(sK1)),$sum(sK1,$uminus(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f4]) ).
tff(f6,plain,
$less($sum(sK0,$uminus(sK1)),$sum(sK1,$uminus(sK0))),
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
~ $less(sK0,sK1),
inference(cnf_transformation,[],[f5]) ).
tff(f8,definition,
sF2 = $uminus(sK1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f9,plain,
$uminus(sK1) = sF2,
inference(reorient_equations,[],[f8]) ).
tff(f10,definition,
sF3 = $sum(sK0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f11,plain,
$sum(sK0,sF2) = sF3,
inference(reorient_equations,[],[f10]) ).
tff(f12,definition,
sF4 = $uminus(sK0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f13,plain,
$uminus(sK0) = sF4,
inference(reorient_equations,[],[f12]) ).
tff(f14,definition,
sF5 = $sum(sK1,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f15,plain,
$less(sF3,sF5),
inference(definition_folding,[],[f6,f14,f13,f11,f9]) ).
tff(f17,definition,
( spl6_1
<=> ( $uminus(sK1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f20,plain,
spl6_1,
inference(avatar_split_clause,[],[f9,f17]) ).
tff(f22,definition,
( spl6_2
<=> ( sF5 = $sum(sK1,sF4) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f25,plain,
spl6_2,
inference(avatar_split_clause,[],[f14,f22]) ).
tff(f27,definition,
( spl6_3
<=> ( $sum(sK0,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f30,plain,
spl6_3,
inference(avatar_split_clause,[],[f11,f27]) ).
tff(f32,definition,
( spl6_4
<=> $less(sF3,sF5) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
tff(f35,plain,
spl6_4,
inference(avatar_split_clause,[],[f15,f32]) ).
tff(f37,definition,
( spl6_5
<=> ( $uminus(sK0) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
tff(f40,plain,
spl6_5,
inference(avatar_split_clause,[],[f13,f37]) ).
tff(f42,definition,
( spl6_6
<=> $less(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
tff(f45,plain,
~ spl6_6,
inference(avatar_split_clause,[],[f7,f42]) ).
tff(f46,plain,
$false,
inference(avatar_smt_refutation,[],[f45,f40,f35,f30,f25,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI572_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:47:52 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.85/1.19 % (4009658)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.85/1.19 % (4009664)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1334665577:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.85/1.19 % (4009664)First to succeed.
% 2.85/1.19 % (4009664)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4009658"
% 2.85/1.19 % (4009663)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1827336600:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.85/1.19 % (4009667)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=918589957:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.85/1.19 % (4009668)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4228818383:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.85/1.19 % (4009669)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3134843336:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.85/1.19 % (4009666)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3883236291:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.85/1.19 % (4009665)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1664728648:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.85/1.19 % (4009667)Instruction limit reached!
% 2.85/1.19 % (4009667)------------------------------
% 2.85/1.19 % (4009667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.19 % (4009667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.19 % (4009667)CaDiCaL version: 2.1.3
% 2.85/1.19 % (4009667)Termination reason: Instruction limit
% 2.85/1.19 % (4009667)Termination phase: Saturation
% 2.85/1.19 % (4009667)Time elapsed: 0.004 s
% 2.85/1.19 % (4009667)Peak memory usage: 88 MB
% 2.85/1.19 % (4009667)Instructions burned: 5 (million)
% 2.85/1.19 % (4009666)Instruction limit reached!
% 2.85/1.19 % (4009666)------------------------------
% 2.85/1.19 % (4009666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.19 % (4009666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.19 % (4009666)CaDiCaL version: 2.1.3
% 2.85/1.19 % (4009666)Termination reason: Instruction limit
% 2.85/1.19 % (4009666)Termination phase: Saturation
% 2.85/1.19 % (4009666)Time elapsed: 0.006 s
% 2.85/1.19 % (4009666)Peak memory usage: 88 MB
% 2.85/1.19 % (4009666)Instructions burned: 7 (million)
% 2.85/1.19 % (4009663)Also succeeded, but the first one will report.
% 2.85/1.19 % (4009668)Also succeeded, but the first one will report.
% 2.85/1.19 % (4009669)Also succeeded, but the first one will report.
% 2.85/1.19 % (4009665)Also succeeded, but the first one will report.
% 2.85/1.19 % (4009664)Refutation found. Thanks to Tanya!
% 2.85/1.19 % SZS status Theorem for theBenchmark
% 2.85/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.85/1.19 % (4009664)------------------------------
% 2.85/1.19 % (4009664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.19 % (4009664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.19 % (4009664)CaDiCaL version: 2.1.3
% 2.85/1.19 % (4009664)Termination reason: Refutation
% 2.85/1.19 % (4009664)Time elapsed: 0.020 s
% 2.85/1.19 % (4009664)Peak memory usage: 115 MB
% 2.85/1.19 % (4009664)Instructions burned: 10 (million)
% 2.85/1.19 % (4009664)------------------------------
% 2.85/1.19 % (4009664)------------------------------
% 2.85/1.19 % (4009658)Success in time 0.308 s
% 2.85/1.19 % Vampire exiting
%------------------------------------------------------------------------------