%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI656_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 : n016.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 09:33:35 AM UTC 2026
% Result : Theorem 4.43s 1.74s
% Output : Refutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 27 ( 22 unt; 0 typ; 7 def)
% Number of atoms : 32 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 0 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 35 ( 15 atm; 16 fun; 4 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 : 9 ( 5 usr; 6 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,
b: $int ).
tff(func_def_1,type,
c: $int ).
tff(func_def_2,type,
a: $int ).
tff(func_def_5,type,
sF0: $int ).
tff(func_def_6,type,
sF1: $int ).
tff(f1,axiom,
$lesseq(c,b),
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,
$lesseq($product(a,c),$product(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002) ).
tff(f4,negated_conjecture,
~ $lesseq($product(a,c),$product(a,b)),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ $less(a,0),
inference(theory_normalization,[],[f2]) ).
tff(f6,plain,
~ $less(b,c),
inference(theory_normalization,[],[f1]) ).
tff(f7,plain,
~ ~ $less($product(a,b),$product(a,c)),
inference(theory_normalization,[],[f4]) ).
tff(f8,plain,
$less($product(a,b),$product(a,c)),
inference(flattening,[],[f7]) ).
tff(f9,plain,
~ $less(a,0),
inference(cnf_transformation,[],[f5]) ).
tff(f10,plain,
$less($product(a,b),$product(a,c)),
inference(cnf_transformation,[],[f8]) ).
tff(f11,plain,
~ $less(b,c),
inference(cnf_transformation,[],[f6]) ).
tff(f12,definition,
sF0 = $product(a,b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f13,plain,
$product(a,b) = sF0,
inference(reorient_equations,[],[f12]) ).
tff(f14,definition,
sF1 = $product(a,c),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f15,plain,
$product(a,c) = sF1,
inference(reorient_equations,[],[f14]) ).
tff(f16,plain,
$less(sF0,sF1),
inference(definition_folding,[],[f10,f15,f13]) ).
tff(f18,definition,
( spl2_1
<=> ( $product(a,b) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f21,plain,
spl2_1,
inference(avatar_split_clause,[],[f13,f18]) ).
tff(f23,definition,
( spl2_2
<=> $less(b,c) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f26,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f11,f23]) ).
tff(f28,definition,
( spl2_3
<=> $less(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f31,plain,
spl2_3,
inference(avatar_split_clause,[],[f16,f28]) ).
tff(f33,definition,
( spl2_4
<=> ( $product(a,c) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f36,plain,
spl2_4,
inference(avatar_split_clause,[],[f15,f33]) ).
tff(f38,definition,
( spl2_5
<=> $less(a,0) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f41,plain,
~ spl2_5,
inference(avatar_split_clause,[],[f9,f38]) ).
tff(f42,plain,
$false,
inference(avatar_smt_refutation,[],[f41,f36,f31,f26,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI656_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n016.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Mon Sep 28 21:00:03 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running first-order theorem proving
% 0.24/0.31 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
% 4.43/1.74 % (4000457)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.43/1.74 % (4000463)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1338118624:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.43/1.74 % (4000467)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2103535497:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.43/1.74 % (4000463)First to succeed.
% 4.43/1.74 % (4000463)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4000457"
% 4.43/1.74 % (4000462)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=556920595:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.43/1.74 % (4000465)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1559946915:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.43/1.74 % (4000468)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=403343758:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.43/1.74 % (4000466)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2241556964:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.43/1.74 % (4000464)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2867099293:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.43/1.74 % (4000466)Instruction limit reached!
% 4.43/1.74 % (4000466)------------------------------
% 4.43/1.74 % (4000466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.74 % (4000466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.74 % (4000466)CaDiCaL version: 2.1.3
% 4.43/1.74 % (4000466)Termination reason: Instruction limit
% 4.43/1.74 % (4000466)Termination phase: Saturation
% 4.43/1.74 % (4000466)Time elapsed: 0.006 s
% 4.43/1.74 % (4000466)Peak memory usage: 89 MB
% 4.43/1.74 % (4000466)Instructions burned: 4 (million)
% 4.43/1.74 % (4000465)Instruction limit reached!
% 4.43/1.74 % (4000465)------------------------------
% 4.43/1.74 % (4000465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.74 % (4000465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.74 % (4000465)CaDiCaL version: 2.1.3
% 4.43/1.74 % (4000465)Termination reason: Instruction limit
% 4.43/1.74 % (4000465)Termination phase: Saturation
% 4.43/1.74 % (4000465)Time elapsed: 0.009 s
% 4.43/1.74 % (4000465)Peak memory usage: 88 MB
% 4.43/1.74 % (4000465)Instructions burned: 7 (million)
% 4.43/1.74 % (4000467)Also succeeded, but the first one will report.
% 4.43/1.74 % (4000462)Also succeeded, but the first one will report.
% 4.43/1.74 % (4000468)Also succeeded, but the first one will report.
% 4.43/1.74 % (4000482)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2389109923:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 4.43/1.74 % (4000482)Refutation not found, incomplete strategy
% 4.43/1.74 % (4000482)------------------------------
% 4.43/1.74 % (4000482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.74 % (4000482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.74 % (4000482)CaDiCaL version: 2.1.3
% 4.43/1.74 % (4000482)Termination reason: Refutation not found, incomplete strategy
% 4.43/1.74 % (4000482)Time elapsed: 0.001 s
% 4.43/1.74 % (4000482)Peak memory usage: 88 MB
% 4.43/1.74 % (4000464)Instruction limit reached!
% 4.43/1.74 % (4000464)------------------------------
% 4.43/1.74 % (4000464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.74 % (4000464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.74 % (4000464)CaDiCaL version: 2.1.3
% 4.43/1.74 % (4000464)Termination reason: Instruction limit
% 4.43/1.74 % (4000464)Termination phase: Saturation
% 4.43/1.74 % (4000464)Time elapsed: 0.224 s
% 4.43/1.74 % (4000464)Peak memory usage: 117 MB
% 4.43/1.74 % (4000464)Instructions burned: 201 (million)
% 4.43/1.74 % (4000463)Refutation found. Thanks to Tanya!
% 4.43/1.74 % SZS status Theorem for theBenchmark
% 4.43/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 4.43/1.74 % (4000463)------------------------------
% 4.43/1.74 % (4000463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.74 % (4000463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.74 % (4000463)CaDiCaL version: 2.1.3
% 4.43/1.74 % (4000463)Termination reason: Refutation
% 4.43/1.74 % (4000463)Time elapsed: 0.029 s
% 4.43/1.74 % (4000463)Peak memory usage: 117 MB
% 4.43/1.74 % (4000463)Instructions burned: 10 (million)
% 4.43/1.74 % (4000463)------------------------------
% 4.43/1.74 % (4000463)------------------------------
% 4.43/1.74 % (4000457)Success in time 0.485 s
% 4.43/1.74 % Vampire exiting
%------------------------------------------------------------------------------