%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI681_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 : n013.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 3.25s 1.24s
% Output : Refutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 19 unt; 0 typ; 6 def)
% Number of atoms : 29 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 0 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 46 ( 15 atm; 16 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 : 8 ( 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,
a: $int ).
tff(func_def_1,type,
c: $int ).
tff(func_def_2,type,
d: $int ).
tff(func_def_3,type,
b: $int ).
tff(func_def_6,type,
sF0: $int ).
tff(f1,axiom,
$less(0,$product(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$less(0,$product(c,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_001) ).
tff(f3,axiom,
$less(0,$product(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002) ).
tff(f4,conjecture,
$less(0,$product(b,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_003) ).
tff(f5,negated_conjecture,
~ $less(0,$product(b,d)),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,plain,
~ $less(0,$product(b,d)),
inference(flattening,[],[f5]) ).
tff(f7,plain,
~ $less(0,$product(b,d)),
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
$less(0,$product(c,d)),
inference(cnf_transformation,[],[f2]) ).
tff(f9,plain,
$less(0,$product(a,b)),
inference(cnf_transformation,[],[f3]) ).
tff(f10,plain,
$less(0,$product(a,c)),
inference(cnf_transformation,[],[f1]) ).
tff(f11,definition,
sF0 = $product(b,d),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f12,plain,
$product(b,d) = sF0,
inference(reorient_equations,[],[f11]) ).
tff(f13,plain,
~ $less(0,sF0),
inference(definition_folding,[],[f7,f12]) ).
tff(f15,definition,
( spl1_1
<=> $less(0,sF0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f18,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f13,f15]) ).
tff(f20,definition,
( spl1_2
<=> ( $product(b,d) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f23,plain,
spl1_2,
inference(avatar_split_clause,[],[f12,f20]) ).
tff(f25,definition,
( spl1_3
<=> $less(0,$product(c,d)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f28,plain,
spl1_3,
inference(avatar_split_clause,[],[f8,f25]) ).
tff(f30,definition,
( spl1_4
<=> $less(0,$product(a,c)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
tff(f33,plain,
spl1_4,
inference(avatar_split_clause,[],[f10,f30]) ).
tff(f35,definition,
( spl1_5
<=> $less(0,$product(a,b)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
tff(f38,plain,
spl1_5,
inference(avatar_split_clause,[],[f9,f35]) ).
tff(f39,plain,
$false,
inference(avatar_smt_refutation,[],[f38,f33,f28,f23,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI681_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n013.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 20:55:21 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 3.25/1.24 % (1569794)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.25/1.24 % (1569807)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2073130053:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.25/1.24 % (1569807)First to succeed.
% 3.25/1.24 % (1569807)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1569794"
% 3.25/1.24 % (1569812)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3507786611:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.25/1.24 % (1569806)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3121469082:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.25/1.24 % (1569810)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2649033531:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.25/1.24 % (1569808)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=263975379:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.25/1.24 % (1569809)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1013100759:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.25/1.24 % (1569810)Instruction limit reached!
% 3.25/1.24 % (1569810)------------------------------
% 3.25/1.24 % (1569810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.24 % (1569810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.24 % (1569810)CaDiCaL version: 2.1.3
% 3.25/1.24 % (1569810)Termination reason: Instruction limit
% 3.25/1.24 % (1569810)Termination phase: Saturation
% 3.25/1.24 % (1569810)Time elapsed: 0.006 s
% 3.25/1.24 % (1569810)Peak memory usage: 89 MB
% 3.25/1.24 % (1569810)Instructions burned: 4 (million)
% 3.25/1.24 % (1569809)Instruction limit reached!
% 3.25/1.24 % (1569809)------------------------------
% 3.25/1.24 % (1569809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.24 % (1569809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.24 % (1569809)CaDiCaL version: 2.1.3
% 3.25/1.24 % (1569809)Termination reason: Instruction limit
% 3.25/1.24 % (1569809)Termination phase: Saturation
% 3.25/1.24 % (1569809)Time elapsed: 0.009 s
% 3.25/1.24 % (1569809)Peak memory usage: 88 MB
% 3.25/1.24 % (1569809)Instructions burned: 8 (million)
% 3.25/1.24 % (1569811)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=549408303:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.25/1.24 % (1569812)Also succeeded, but the first one will report.
% 3.25/1.24 % (1569806)Also succeeded, but the first one will report.
% 3.25/1.24 % (1569811)Also succeeded, but the first one will report.
% 3.25/1.24 % (1569807)Refutation found. Thanks to Tanya!
% 3.25/1.24 % SZS status Theorem for theBenchmark
% 3.25/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.25/1.24 % (1569807)------------------------------
% 3.25/1.24 % (1569807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.24 % (1569807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.24 % (1569807)CaDiCaL version: 2.1.3
% 3.25/1.24 % (1569807)Termination reason: Refutation
% 3.25/1.24 % (1569807)Time elapsed: 0.021 s
% 3.25/1.24 % (1569807)Peak memory usage: 116 MB
% 3.25/1.24 % (1569807)Instructions burned: 10 (million)
% 3.25/1.24 % (1569807)------------------------------
% 3.25/1.24 % (1569807)------------------------------
% 3.25/1.24 % (1569794)Success in time 0.362 s
% 3.25/1.24 % Vampire exiting
%------------------------------------------------------------------------------