%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI678_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:33:38 AM UTC 2026
% Result : Theorem 3.75s 1.33s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 30 ( 24 unt; 0 typ; 9 def)
% Number of atoms : 36 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 0 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 61 ( 15 atm; 31 fun; 15 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 : 11 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 4 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_5,type,
sF0: $int ).
tff(func_def_6,type,
sF1: $int ).
tff(func_def_7,type,
sF2: $int ).
tff(f1,axiom,
$greatereq(7,$product($product(a,a),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$lesseq(0,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_001) ).
tff(f3,conjecture,
$greatereq(1,$product($product($product(a,a),a),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002) ).
tff(f4,negated_conjecture,
~ $greatereq(1,$product($product($product(a,a),a),a)),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ $less(7,$product($product(a,a),a)),
inference(theory_normalization,[],[f1]) ).
tff(f6,plain,
~ $less(a,0),
inference(theory_normalization,[],[f2]) ).
tff(f7,plain,
~ ~ $less(1,$product($product($product(a,a),a),a)),
inference(theory_normalization,[],[f4]) ).
tff(f8,plain,
$less(1,$product($product($product(a,a),a),a)),
inference(flattening,[],[f7]) ).
tff(f9,plain,
$less(1,$product($product($product(a,a),a),a)),
inference(cnf_transformation,[],[f8]) ).
tff(f10,plain,
~ $less(a,0),
inference(cnf_transformation,[],[f6]) ).
tff(f11,plain,
~ $less(7,$product($product(a,a),a)),
inference(cnf_transformation,[],[f5]) ).
tff(f12,definition,
sF0 = $product(a,a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f13,plain,
$product(a,a) = sF0,
inference(reorient_equations,[],[f12]) ).
tff(f14,definition,
sF1 = $product(sF0,a),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f15,plain,
$product(sF0,a) = sF1,
inference(reorient_equations,[],[f14]) ).
tff(f16,definition,
sF2 = $product(sF1,a),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f17,plain,
$less(1,sF2),
inference(definition_folding,[],[f9,f16,f15,f13]) ).
tff(f19,definition,
( spl3_1
<=> $less(a,0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f22,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f10,f19]) ).
tff(f24,definition,
( spl3_2
<=> ( $product(sF0,a) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f27,plain,
spl3_2,
inference(avatar_split_clause,[],[f15,f24]) ).
tff(f29,definition,
( spl3_3
<=> ( sF2 = $product(sF1,a) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f32,plain,
spl3_3,
inference(avatar_split_clause,[],[f16,f29]) ).
tff(f34,definition,
( spl3_4
<=> $less(7,$product($product(a,a),a)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f37,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f11,f34]) ).
tff(f39,definition,
( spl3_5
<=> ( $product(a,a) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f42,plain,
spl3_5,
inference(avatar_split_clause,[],[f13,f39]) ).
tff(f44,definition,
( spl3_6
<=> $less(1,sF2) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f47,plain,
spl3_6,
inference(avatar_split_clause,[],[f17,f44]) ).
tff(f48,plain,
$false,
inference(avatar_smt_refutation,[],[f47,f42,f37,f32,f27,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI678_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n001.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 21:01:49 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.28 Running first-order theorem proving
% 0.09/0.28 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
% 3.75/1.33 % (741620)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.75/1.33 % (741703)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2220976632:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.75/1.33 % (741700)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1944723857:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.75/1.33 % (741701)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=511799366:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.75/1.33 % (741707)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4170036548:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.75/1.33 % (741708)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2379101507:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.75/1.33 % (741706)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=580901800:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.75/1.33 % (741704)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3811948262:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.75/1.33 % (741706)Instruction limit reached!
% 3.75/1.33 % (741706)------------------------------
% 3.75/1.33 % (741706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741706)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741706)Termination reason: Instruction limit
% 3.75/1.33 % (741706)Termination phase: Saturation
% 3.75/1.33 % (741706)Time elapsed: 0.004 s
% 3.75/1.33 % (741706)Peak memory usage: 89 MB
% 3.75/1.33 % (741706)Instructions burned: 5 (million)
% 3.75/1.33 % (741704)Instruction limit reached!
% 3.75/1.33 % (741704)------------------------------
% 3.75/1.33 % (741704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741704)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741704)Termination reason: Instruction limit
% 3.75/1.33 % (741704)Termination phase: Saturation
% 3.75/1.33 % (741704)Time elapsed: 0.005 s
% 3.75/1.33 % (741704)Peak memory usage: 88 MB
% 3.75/1.33 % (741704)Instructions burned: 7 (million)
% 3.75/1.33 % (741700)Instruction limit reached!
% 3.75/1.33 % (741700)------------------------------
% 3.75/1.33 % (741700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741700)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741700)Termination reason: Instruction limit
% 3.75/1.33 % (741700)Termination phase: Saturation
% 3.75/1.33 % (741700)Time elapsed: 0.031 s
% 3.75/1.33 % (741700)Peak memory usage: 116 MB
% 3.75/1.33 % (741700)Instructions burned: 12 (million)
% 3.75/1.33 % (741701)First to succeed.
% 3.75/1.33 % (741701)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-741620"
% 3.75/1.33 % (741707)Also succeeded, but the first one will report.
% 3.75/1.33 % (741708)Also succeeded, but the first one will report.
% 3.75/1.33 % (741703)Instruction limit reached!
% 3.75/1.33 % (741703)------------------------------
% 3.75/1.33 % (741703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741703)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741703)Termination reason: Instruction limit
% 3.75/1.33 % (741703)Termination phase: Saturation
% 3.75/1.33 % (741703)Time elapsed: 0.098 s
% 3.75/1.33 % (741703)Peak memory usage: 117 MB
% 3.75/1.33 % (741703)Instructions burned: 202 (million)
% 3.75/1.33 % (741748)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=737700597:i=24:canc=force:rtra=on_2998 on theBenchmark for (2998ds/24Mi)
% 3.75/1.33 % (741742)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=3919385250:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.75/1.33 % (741740)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2747752190:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.75/1.33 % (741740)Refutation not found, incomplete strategy
% 3.75/1.33 % (741740)------------------------------
% 3.75/1.33 % (741740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741740)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741740)Termination reason: Refutation not found, incomplete strategy
% 3.75/1.33 % (741740)Time elapsed: 0.001 s
% 3.75/1.33 % (741740)Peak memory usage: 88 MB
% 3.75/1.33 % (741748)Instruction limit reached!
% 3.75/1.33 % (741748)------------------------------
% 3.75/1.33 % (741748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741748)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741748)Termination reason: Instruction limit
% 3.75/1.33 % (741748)Termination phase: Saturation
% 3.75/1.33 % (741748)Time elapsed: 0.010 s
% 3.75/1.33 % (741748)Peak memory usage: 89 MB
% 3.75/1.33 % (741748)Instructions burned: 24 (million)
% 3.75/1.33 % (741742)Instruction limit reached!
% 3.75/1.33 % (741742)------------------------------
% 3.75/1.33 % (741742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741747)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=153232965:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.75/1.33 % (741742)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741742)Termination reason: Instruction limit
% 3.75/1.33 % (741742)Termination phase: Saturation
% 3.75/1.33 % (741742)Time elapsed: 0.020 s
% 3.75/1.33 % (741742)Peak memory usage: 88 MB
% 3.75/1.33 % (741742)Instructions burned: 30 (million)
% 3.75/1.33 % (741747)Instruction limit reached!
% 3.75/1.33 % (741747)------------------------------
% 3.75/1.33 % (741747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741747)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741747)Termination reason: Instruction limit
% 3.75/1.33 % (741747)Termination phase: Saturation
% 3.75/1.33 % (741747)Time elapsed: 0.010 s
% 3.75/1.33 % (741747)Peak memory usage: 90 MB
% 3.75/1.33 % (741747)Instructions burned: 18 (million)
% 3.75/1.33 % (741757)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=2538205396:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.75/1.33 % (741757)Instruction limit reached!
% 3.75/1.33 % (741757)------------------------------
% 3.75/1.33 % (741757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741757)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741757)Termination reason: Instruction limit
% 3.75/1.33 % (741757)Termination phase: Saturation
% 3.75/1.33 % (741757)Time elapsed: 0.011 s
% 3.75/1.33 % (741757)Peak memory usage: 89 MB
% 3.75/1.33 % (741757)Instructions burned: 29 (million)
% 3.75/1.33 % (741701)Refutation found. Thanks to Tanya!
% 3.75/1.33 % SZS status Theorem for theBenchmark
% 3.75/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.33 % (741701)------------------------------
% 3.75/1.33 % (741701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (741701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (741701)CaDiCaL version: 2.1.3
% 3.75/1.33 % (741701)Termination reason: Refutation
% 3.75/1.33 % (741701)Time elapsed: 0.038 s
% 3.75/1.33 % (741701)Peak memory usage: 117 MB
% 3.75/1.33 % (741701)Instructions burned: 18 (million)
% 3.75/1.33 % (741701)------------------------------
% 3.75/1.33 % (741701)------------------------------
% 3.75/1.33 % (741620)Success in time 0.428 s
% 3.75/1.33 % Vampire exiting
%------------------------------------------------------------------------------