%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI683_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:33:39 AM UTC 2026
% Result : Theorem 3.92s 1.34s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 37 ( 30 unt; 0 typ; 7 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 0 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 193 ( 29 atm; 143 fun; 21 num; 0 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 : 10 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
b: $int ).
tff(func_def_1,type,
c: $int ).
tff(func_def_2,type,
g: $int ).
tff(func_def_3,type,
h: $int ).
tff(func_def_4,type,
a: $int ).
tff(func_def_5,type,
f: $int ).
tff(func_def_6,type,
i: $int ).
tff(func_def_7,type,
d: $int ).
tff(func_def_8,type,
e: $int ).
tff(f1,axiom,
$lesseq($sum($product(a,f),$product(-1,$product(a,h))),$sum($sum(b,$product(c,g)),$product(-1,$product(c,h)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$lesseq(g,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(f3,axiom,
$less(h,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(f4,axiom,
$less(i,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_003) ).
tff(f5,axiom,
$lesseq(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_004) ).
tff(f6,axiom,
$less(e,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_005) ).
tff(f7,conjecture,
$lesseq($sum($product(e,f),$product(-1,$product(e,i))),$sum($sum($sum($sum(b,$product(c,g)),$product(-1,$product(c,h))),$product(d,h)),$product(-1,$product(d,i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_006) ).
tff(f8,negated_conjecture,
~ $lesseq($sum($product(e,f),$product(-1,$product(e,i))),$sum($sum($sum($sum(b,$product(c,g)),$product(-1,$product(c,h))),$product(d,h)),$product(-1,$product(d,i)))),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f9,plain,
~ $less(f,g),
inference(theory_normalization,[],[f2]) ).
tff(f10,plain,
~ $less(d,a),
inference(theory_normalization,[],[f5]) ).
tff(f11,plain,
~ ~ $less($sum($sum($sum($sum(b,$product(c,g)),$product(-1,$product(c,h))),$product(d,h)),$product(-1,$product(d,i))),$sum($product(e,f),$product(-1,$product(e,i)))),
inference(theory_normalization,[],[f8]) ).
tff(f12,plain,
~ $less($sum($sum(b,$product(c,g)),$product(-1,$product(c,h))),$sum($product(a,f),$product(-1,$product(a,h)))),
inference(theory_normalization,[],[f1]) ).
tff(f13,plain,
$less($sum($sum($sum($sum(b,$product(c,g)),$product(-1,$product(c,h))),$product(d,h)),$product(-1,$product(d,i))),$sum($product(e,f),$product(-1,$product(e,i)))),
inference(flattening,[],[f11]) ).
tff(f14,plain,
~ $less(f,g),
inference(cnf_transformation,[],[f9]) ).
tff(f15,plain,
$less(i,h),
inference(cnf_transformation,[],[f4]) ).
tff(f16,plain,
~ $less($sum($sum(b,$product(c,g)),$product(-1,$product(c,h))),$sum($product(a,f),$product(-1,$product(a,h)))),
inference(cnf_transformation,[],[f12]) ).
tff(f17,plain,
$less(e,a),
inference(cnf_transformation,[],[f6]) ).
tff(f18,plain,
$less(h,g),
inference(cnf_transformation,[],[f3]) ).
tff(f19,plain,
~ $less(d,a),
inference(cnf_transformation,[],[f10]) ).
tff(f20,plain,
$less($sum($sum($sum($sum(b,$product(c,g)),$product(-1,$product(c,h))),$product(d,h)),$product(-1,$product(d,i))),$sum($product(e,f),$product(-1,$product(e,i)))),
inference(cnf_transformation,[],[f13]) ).
tff(f21,plain,
~ $less($sum($sum(b,$product(c,g)),$uminus($product(c,h))),$sum($product(a,f),$uminus($product(a,h)))),
inference(evaluation,[],[f16]) ).
tff(f22,plain,
$less($sum($sum($sum($sum(b,$product(c,g)),$uminus($product(c,h))),$product(d,h)),$uminus($product(d,i))),$sum($product(e,f),$uminus($product(e,i)))),
inference(evaluation,[],[f20]) ).
tff(f24,definition,
( spl0_1
<=> $less($sum($sum(b,$product(c,g)),$uminus($product(c,h))),$sum($product(a,f),$uminus($product(a,h)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f27,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f21,f24]) ).
tff(f29,definition,
( spl0_2
<=> $less(f,g) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f32,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f14,f29]) ).
tff(f34,definition,
( spl0_3
<=> $less($sum($sum($sum($sum(b,$product(c,g)),$uminus($product(c,h))),$product(d,h)),$uminus($product(d,i))),$sum($product(e,f),$uminus($product(e,i)))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f37,plain,
spl0_3,
inference(avatar_split_clause,[],[f22,f34]) ).
tff(f39,definition,
( spl0_4
<=> $less(e,a) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f42,plain,
spl0_4,
inference(avatar_split_clause,[],[f17,f39]) ).
tff(f44,definition,
( spl0_5
<=> $less(d,a) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
tff(f47,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f19,f44]) ).
tff(f49,definition,
( spl0_6
<=> $less(h,g) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
tff(f52,plain,
spl0_6,
inference(avatar_split_clause,[],[f18,f49]) ).
tff(f54,definition,
( spl0_7
<=> $less(i,h) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
tff(f57,plain,
spl0_7,
inference(avatar_split_clause,[],[f15,f54]) ).
tff(f58,plain,
$false,
inference(avatar_smt_refutation,[],[f57,f52,f47,f42,f37,f32,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI683_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 20:58:19 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 2.79/1.15 % (2641034)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.79/1.15 % (2641041)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1754501807:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.79/1.15 % (2641045)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3460693853:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.79/1.15 % (2641043)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=535481886:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.79/1.15 % (2641040)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4085502775:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.79/1.15 % (2641044)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2684835234:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.79/1.15 % (2641039)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2386784105:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.79/1.15 % (2641042)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4215282696:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.79/1.15 % (2641043)Instruction limit reached!
% 2.79/1.15 % (2641043)------------------------------
% 2.79/1.15 % (2641043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.15 % (2641043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.15 % (2641043)CaDiCaL version: 2.1.3
% 2.79/1.15 % (2641043)Termination reason: Instruction limit
% 2.79/1.15 % (2641043)Termination phase: Saturation
% 2.79/1.15 % (2641043)Time elapsed: 0.003 s
% 2.79/1.15 % (2641043)Peak memory usage: 88 MB
% 2.79/1.15 % (2641043)Instructions burned: 4 (million)
% 2.79/1.15 % (2641042)Instruction limit reached!
% 2.79/1.15 % (2641042)------------------------------
% 2.79/1.15 % (2641042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.15 % (2641042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.15 % (2641042)CaDiCaL version: 2.1.3
% 2.79/1.15 % (2641042)Termination reason: Instruction limit
% 2.79/1.15 % (2641042)Termination phase: Saturation
% 2.79/1.15 % (2641042)Time elapsed: 0.005 s
% 2.79/1.15 % (2641042)Peak memory usage: 88 MB
% 2.79/1.15 % (2641042)Instructions burned: 9 (million)
% 2.79/1.15 % (2641039)Instruction limit reached!
% 2.79/1.15 % (2641039)------------------------------
% 2.79/1.15 % (2641039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.15 % (2641039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.15 % (2641039)CaDiCaL version: 2.1.3
% 2.79/1.15 % (2641039)Termination reason: Instruction limit
% 2.79/1.15 % (2641039)Termination phase: Saturation
% 2.79/1.15 % (2641039)Time elapsed: 0.031 s
% 2.79/1.15 % (2641039)Peak memory usage: 116 MB
% 2.79/1.15 % (2641039)Instructions burned: 12 (million)
% 2.79/1.15 % (2641044)First to succeed.
% 2.79/1.15 % (2641044)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2641034"
% 2.79/1.15 % (2641045)Instruction limit reached!
% 2.79/1.15 % (2641045)------------------------------
% 2.79/1.15 % (2641045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.15 % (2641045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.15 % (2641045)CaDiCaL version: 2.1.3
% 2.79/1.15 % (2641045)Termination reason: Instruction limit
% 2.79/1.15 % (2641045)Termination phase: Saturation
% 2.79/1.15 % (2641045)Time elapsed: 0.043 s
% 2.79/1.15 % (2641045)Peak memory usage: 117 MB
% 2.79/1.15 % (2641045)Instructions burned: 33 (million)
% 2.79/1.15 % (2641041)Instruction limit reached!
% 2.79/1.15 % (2641041)------------------------------
% 2.79/1.15 % (2641041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.15 % (2641041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.15 % (2641041)CaDiCaL version: 2.1.3
% 2.79/1.15 % (2641041)Termination reason: Instruction limit
% 2.79/1.15 % (2641041)Termination phase: Saturation
% 2.79/1.15 % (2641041)Time elapsed: 0.085 s
% 2.79/1.15 % (2641041)Peak memory usage: 117 MB
% 2.79/1.15 % (2641041)Instructions burned: 202 (million)
% 2.79/1.15 % (2641054)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=4190747371:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.92/1.34 % (2641053)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=283598589:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.92/1.34 % (2641053)Refutation not found, incomplete strategy
% 3.92/1.34 % (2641053)------------------------------
% 3.92/1.34 % (2641053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.34 % (2641053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.34 % (2641053)CaDiCaL version: 2.1.3
% 3.92/1.34 % (2641053)Termination reason: Refutation not found, incomplete strategy
% 3.92/1.34 % (2641053)Time elapsed: 0.001 s
% 3.92/1.34 % (2641053)Peak memory usage: 88 MB
% 3.92/1.34 % (2641057)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=1918098716:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.92/1.34 % (2641057)Instruction limit reached!
% 3.92/1.34 % (2641057)------------------------------
% 3.92/1.34 % (2641057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.34 % (2641057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.34 % (2641057)CaDiCaL version: 2.1.3
% 3.92/1.34 % (2641057)Termination reason: Instruction limit
% 3.92/1.34 % (2641057)Termination phase: Saturation
% 3.92/1.34 % (2641057)Time elapsed: 0.009 s
% 3.92/1.34 % (2641057)Peak memory usage: 89 MB
% 3.92/1.34 % (2641057)Instructions burned: 27 (million)
% 3.92/1.34 % (2641054)Instruction limit reached!
% 3.92/1.34 % (2641054)------------------------------
% 3.92/1.34 % (2641054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.34 % (2641054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.34 % (2641054)CaDiCaL version: 2.1.3
% 3.92/1.34 % (2641054)Termination reason: Instruction limit
% 3.92/1.34 % (2641054)Termination phase: Saturation
% 3.92/1.34 % (2641054)Time elapsed: 0.021 s
% 3.92/1.34 % (2641054)Peak memory usage: 88 MB
% 3.92/1.34 % (2641054)Instructions burned: 29 (million)
% 3.92/1.34 % (2641040)Instruction limit reached!
% 3.92/1.34 % (2641040)------------------------------
% 3.92/1.34 % (2641040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.34 % (2641040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.34 % (2641040)CaDiCaL version: 2.1.3
% 3.92/1.34 % (2641040)Termination reason: Instruction limit
% 3.92/1.34 % (2641040)Termination phase: Saturation
% 3.92/1.34 % (2641040)Time elapsed: 0.178 s
% 3.92/1.34 % (2641040)Peak memory usage: 117 MB
% 3.92/1.34 % (2641040)Instructions burned: 309 (million)
% 3.92/1.34 % (2641055)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=441801967:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.92/1.34 % (2641056)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=275494365:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.92/1.34 % (2641055)Instruction limit reached!
% 3.92/1.34 % (2641055)------------------------------
% 3.92/1.34 % (2641055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.34 % (2641055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.34 % (2641055)CaDiCaL version: 2.1.3
% 3.92/1.34 % (2641055)Termination reason: Instruction limit
% 3.92/1.34 % (2641055)Termination phase: Saturation
% 3.92/1.34 % (2641055)Time elapsed: 0.009 s
% 3.92/1.34 % (2641055)Peak memory usage: 90 MB
% 3.92/1.34 % (2641055)Instructions burned: 16 (million)
% 3.92/1.34 % (2641056)Instruction limit reached!
% 3.92/1.34 % (2641056)------------------------------
% 3.92/1.34 % (2641056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.34 % (2641056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.34 % (2641056)CaDiCaL version: 2.1.3
% 3.92/1.34 % (2641056)Termination reason: Instruction limit
% 3.92/1.34 % (2641056)Termination phase: Saturation
% 3.92/1.34 % (2641056)Time elapsed: 0.008 s
% 3.92/1.34 % (2641056)Peak memory usage: 89 MB
% 3.92/1.34 % (2641056)Instructions burned: 25 (million)
% 3.92/1.34 % (2641044)Refutation found. Thanks to Tanya!
% 3.92/1.34 % SZS status Theorem for theBenchmark
% 3.92/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.34 % (2641044)------------------------------
% 3.92/1.34 % (2641044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.34 % (2641044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.34 % (2641044)CaDiCaL version: 2.1.3
% 3.92/1.34 % (2641044)Termination reason: Refutation
% 3.92/1.34 % (2641044)Time elapsed: 0.035 s
% 3.92/1.34 % (2641044)Peak memory usage: 117 MB
% 3.92/1.34 % (2641044)Instructions burned: 14 (million)
% 3.92/1.34 % (2641044)------------------------------
% 3.92/1.34 % (2641044)------------------------------
% 3.92/1.34 % (2641034)Success in time 0.466 s
% 3.92/1.34 % Vampire exiting
%------------------------------------------------------------------------------