%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI645_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 : n020.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 09:33:34 AM UTC 2026
% Result : Theorem 4.21s 1.57s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 16 unt; 0 typ; 8 def)
% Number of atoms : 48 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 13 ~; 0 |; 12 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 61 ( 29 atm; 18 fun; 14 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 : 12 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
d: $int ).
tff(func_def_5,type,
sF0: $int ).
tff(func_def_6,type,
sF1: $int ).
tff(f1,conjecture,
( ( $greatereq(b,a)
& $greatereq(d,0)
& $greater(a,0) )
=> $lesseq($quotient_e(d,b),$quotient_e(d,a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( ( $greatereq(b,a)
& $greatereq(d,0)
& $greater(a,0) )
=> $lesseq($quotient_e(d,b),$quotient_e(d,a)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( $less(0,a)
& ~ $less(b,a)
& ~ $less(d,0) )
=> ~ $less($quotient_e(d,a),$quotient_e(d,b)) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( $less($quotient_e(d,a),$quotient_e(d,b))
& $less(0,a)
& ~ $less(b,a)
& ~ $less(d,0) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( ~ $less(b,a)
& $less(0,a)
& $less($quotient_e(d,a),$quotient_e(d,b))
& ~ $less(d,0) ),
inference(flattening,[],[f4]) ).
tff(f6,plain,
~ $less(d,0),
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
$less($quotient_e(d,a),$quotient_e(d,b)),
inference(cnf_transformation,[],[f5]) ).
tff(f8,plain,
$less(0,a),
inference(cnf_transformation,[],[f5]) ).
tff(f9,plain,
~ $less(b,a),
inference(cnf_transformation,[],[f5]) ).
tff(f10,definition,
sF0 = $quotient_e(d,a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f11,plain,
$quotient_e(d,a) = sF0,
inference(reorient_equations,[],[f10]) ).
tff(f12,definition,
sF1 = $quotient_e(d,b),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f13,plain,
$quotient_e(d,b) = sF1,
inference(reorient_equations,[],[f12]) ).
tff(f14,plain,
$less(sF0,sF1),
inference(definition_folding,[],[f7,f13,f11]) ).
tff(f16,definition,
( spl2_1
<=> ( $quotient_e(d,a) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f19,plain,
spl2_1,
inference(avatar_split_clause,[],[f11,f16]) ).
tff(f21,definition,
( spl2_2
<=> ( $quotient_e(d,b) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f24,plain,
spl2_2,
inference(avatar_split_clause,[],[f13,f21]) ).
tff(f26,definition,
( spl2_3
<=> $less(0,a) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f29,plain,
spl2_3,
inference(avatar_split_clause,[],[f8,f26]) ).
tff(f31,definition,
( spl2_4
<=> $less(b,a) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f34,plain,
~ spl2_4,
inference(avatar_split_clause,[],[f9,f31]) ).
tff(f36,definition,
( spl2_5
<=> $less(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f39,plain,
spl2_5,
inference(avatar_split_clause,[],[f14,f36]) ).
tff(f41,definition,
( spl2_6
<=> $less(d,0) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
tff(f44,plain,
~ spl2_6,
inference(avatar_split_clause,[],[f6,f41]) ).
tff(f45,plain,
$false,
inference(avatar_smt_refutation,[],[f44,f39,f34,f29,f24,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI645_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n020.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 20:55:34 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.28 Running first-order theorem proving
% 0.26/0.28 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
% 4.21/1.57 % (546070)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.21/1.57 % (546076)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=243465411:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.21/1.57 % (546081)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=383967054:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.21/1.57 % (546076)First to succeed.
% 4.21/1.57 % (546076)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-546070"
% 4.21/1.57 % (546079)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=850009074:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.21/1.57 % (546078)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3611224557:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.21/1.57 % (546077)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2049528189:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.21/1.57 % (546075)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2135598587:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.21/1.57 % (546079)Instruction limit reached!
% 4.21/1.57 % (546079)------------------------------
% 4.21/1.57 % (546079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.57 % (546079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.57 % (546079)CaDiCaL version: 2.1.3
% 4.21/1.57 % (546079)Termination reason: Instruction limit
% 4.21/1.57 % (546079)Termination phase: Saturation
% 4.21/1.57 % (546079)Time elapsed: 0.007 s
% 4.21/1.57 % (546079)Peak memory usage: 88 MB
% 4.21/1.57 % (546079)Instructions burned: 5 (million)
% 4.21/1.57 % (546078)Instruction limit reached!
% 4.21/1.57 % (546078)------------------------------
% 4.21/1.57 % (546078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.57 % (546078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.57 % (546078)CaDiCaL version: 2.1.3
% 4.21/1.57 % (546078)Termination reason: Instruction limit
% 4.21/1.57 % (546078)Termination phase: Saturation
% 4.21/1.57 % (546078)Time elapsed: 0.009 s
% 4.21/1.57 % (546078)Peak memory usage: 88 MB
% 4.21/1.57 % (546078)Instructions burned: 7 (million)
% 4.21/1.57 % (546080)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4028307984:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.21/1.57 % (546081)Also succeeded, but the first one will report.
% 4.21/1.57 % (546075)Instruction limit reached!
% 4.21/1.57 % (546075)------------------------------
% 4.21/1.57 % (546075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.57 % (546075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.57 % (546075)CaDiCaL version: 2.1.3
% 4.21/1.57 % (546075)Termination reason: Instruction limit
% 4.21/1.57 % (546075)Termination phase: Saturation
% 4.21/1.57 % (546075)Time elapsed: 0.045 s
% 4.21/1.57 % (546075)Peak memory usage: 116 MB
% 4.21/1.57 % (546075)Instructions burned: 12 (million)
% 4.21/1.57 % (546080)Also succeeded, but the first one will report.
% 4.21/1.57 % (546076)Refutation found. Thanks to Tanya!
% 4.21/1.57 % SZS status Theorem for theBenchmark
% 4.21/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 4.21/1.57 % (546076)------------------------------
% 4.21/1.57 % (546076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.57 % (546076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.57 % (546076)CaDiCaL version: 2.1.3
% 4.21/1.57 % (546076)Termination reason: Refutation
% 4.21/1.57 % (546076)Time elapsed: 0.039 s
% 4.21/1.57 % (546076)Peak memory usage: 118 MB
% 4.21/1.57 % (546076)Instructions burned: 27 (million)
% 4.21/1.57 % (546076)------------------------------
% 4.21/1.57 % (546076)------------------------------
% 4.21/1.57 % (546070)Success in time 0.477 s
% 4.21/1.57 % Vampire exiting
%------------------------------------------------------------------------------