%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI599_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:33:27 AM UTC 2026
% Result : Theorem 2.73s 1.04s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 28 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 0 |; 7 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 70 ( 14 atm; 28 fun; 28 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 : 7 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 3 usr; 4 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,
f: ( $int * $int ) > $int ).
tff(f1,conjecture,
( ( $lesseq($product(2,a),$product(2,b))
& $lesseq($product(3,b),$product(3,a)) )
=> ( f(a,b) = f(b,a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ineq_imply_f_eq_f) ).
tff(f2,negated_conjecture,
~ ( ( $lesseq($product(2,a),$product(2,b))
& $lesseq($product(3,b),$product(3,a)) )
=> ( f(a,b) = f(b,a) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ~ $less($product(3,a),$product(3,b))
& ~ $less($product(2,b),$product(2,a)) )
=> ( f(a,b) = f(b,a) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( ( f(a,b) != f(b,a) )
& ~ $less($product(3,a),$product(3,b))
& ~ $less($product(2,b),$product(2,a)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( ~ $less($product(2,b),$product(2,a))
& ~ $less($product(3,a),$product(3,b))
& ( f(a,b) != f(b,a) ) ),
inference(flattening,[],[f4]) ).
tff(f6,plain,
f(a,b) != f(b,a),
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
~ $less($product(3,a),$product(3,b)),
inference(cnf_transformation,[],[f5]) ).
tff(f8,plain,
~ $less($product(2,b),$product(2,a)),
inference(cnf_transformation,[],[f5]) ).
tff(f10,definition,
( spl0_1
<=> $less($product(3,a),$product(3,b)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f13,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f7,f10]) ).
tff(f15,definition,
( spl0_2
<=> $less($product(2,b),$product(2,a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f18,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f8,f15]) ).
tff(f20,definition,
( spl0_3
<=> ( f(a,b) = f(b,a) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f23,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f6,f20]) ).
tff(f24,plain,
$false,
inference(avatar_smt_refutation,[],[f23,f18,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI599_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:52:36 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.73/1.04 % (1564008)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.73/1.04 % (1564047)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3614424106:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.73/1.04 % (1564043)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4001375133:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.73/1.04 % (1564042)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3088319475:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.73/1.04 % (1564046)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1942698978:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.73/1.04 % (1564041)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2030450334:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.73/1.04 % (1564044)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=737182923:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.73/1.04 % (1564046)Instruction limit reached!
% 2.73/1.04 % (1564046)------------------------------
% 2.73/1.04 % (1564046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.04 % (1564046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.04 % (1564046)CaDiCaL version: 2.1.3
% 2.73/1.04 % (1564046)Termination reason: Instruction limit
% 2.73/1.04 % (1564046)Termination phase: Saturation
% 2.73/1.04 % (1564046)Time elapsed: 0.004 s
% 2.73/1.04 % (1564046)Peak memory usage: 88 MB
% 2.73/1.04 % (1564046)Instructions burned: 4 (million)
% 2.73/1.04 % (1564044)Instruction limit reached!
% 2.73/1.04 % (1564044)------------------------------
% 2.73/1.04 % (1564044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.04 % (1564044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.04 % (1564044)CaDiCaL version: 2.1.3
% 2.73/1.04 % (1564044)Termination reason: Instruction limit
% 2.73/1.04 % (1564044)Termination phase: Saturation
% 2.73/1.04 % (1564044)Time elapsed: 0.005 s
% 2.73/1.04 % (1564044)Peak memory usage: 88 MB
% 2.73/1.04 % (1564044)Instructions burned: 7 (million)
% 2.73/1.04 % (1564048)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1701955924:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.73/1.04 % (1564047)First to succeed.
% 2.73/1.04 % (1564047)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1564008"
% 2.73/1.04 % (1564041)Also succeeded, but the first one will report.
% 2.73/1.04 % (1564042)Also succeeded, but the first one will report.
% 2.73/1.04 % (1564048)Also succeeded, but the first one will report.
% 2.73/1.04 % (1564043)Instruction limit reached!
% 2.73/1.04 % (1564043)------------------------------
% 2.73/1.04 % (1564043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.04 % (1564043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.04 % (1564043)CaDiCaL version: 2.1.3
% 2.73/1.04 % (1564043)Termination reason: Instruction limit
% 2.73/1.04 % (1564043)Termination phase: Saturation
% 2.73/1.04 % (1564043)Time elapsed: 0.172 s
% 2.73/1.04 % (1564043)Peak memory usage: 116 MB
% 2.73/1.04 % (1564043)Instructions burned: 201 (million)
% 2.73/1.04 % (1564047)Refutation found. Thanks to Tanya!
% 2.73/1.04 % SZS status Theorem for theBenchmark
% 2.73/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.04 % (1564047)------------------------------
% 2.73/1.04 % (1564047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.04 % (1564047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.04 % (1564047)CaDiCaL version: 2.1.3
% 2.73/1.04 % (1564047)Termination reason: Refutation
% 2.73/1.04 % (1564047)Time elapsed: 0.020 s
% 2.73/1.04 % (1564047)Peak memory usage: 115 MB
% 2.73/1.04 % (1564047)Instructions burned: 8 (million)
% 2.73/1.04 % (1564047)------------------------------
% 2.73/1.04 % (1564047)------------------------------
% 2.73/1.04 % (1564008)Success in time 0.341 s
% 2.73/1.04 % Vampire exiting
%------------------------------------------------------------------------------