%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI081_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:32:29 AM UTC 2026
% Result : Theorem 2.58s 0.93s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 17 unt; 0 typ; 7 def)
% Number of atoms : 45 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 7 ~; 0 |; 9 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 68 ( 0 atm; 18 fun; 40 num; 10 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 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 4 usr; 7 con; 0-2 aty)
% Number of variables : 10 ( 6 !; 4 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK0: $int ).
tff(func_def_7,type,
sK1: $int ).
tff(func_def_8,type,
sF2: $int ).
tff(func_def_9,type,
sF3: $int ).
tff(f1,conjecture,
! [X1: $int,X0: $int] :
( ( ( $sum(6,7) = X0 )
& ( $sum(7,6) = X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',communative_sum_6_7) ).
tff(f2,negated_conjecture,
~ ! [X1: $int,X0: $int] :
( ( ( $sum(6,7) = X0 )
& ( $sum(7,6) = X1 ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f15,plain,
~ ! [X0: $int,X1: $int] :
( ( ( $sum(7,6) = X0 )
& ( $sum(6,7) = X1 ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
tff(f16,plain,
? [X0: $int,X1: $int] :
( ( X0 != X1 )
& ( $sum(7,6) = X0 )
& ( $sum(6,7) = X1 ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
? [X0: $int,X1: $int] :
( ( X0 != X1 )
& ( $sum(7,6) = X0 )
& ( $sum(6,7) = X1 ) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
( ( sK1 != sK0 )
& ( $sum(7,6) = sK0 )
& ( $sum(6,7) = sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f17]) ).
tff(f19,plain,
$sum(6,7) = sK1,
inference(cnf_transformation,[],[f18]) ).
tff(f20,plain,
$sum(7,6) = sK0,
inference(cnf_transformation,[],[f18]) ).
tff(f21,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f18]) ).
tff(f22,definition,
sF2 = $sum(7,6),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f23,plain,
$sum(7,6) = sF2,
inference(reorient_equations,[],[f22]) ).
tff(f24,plain,
sK0 = sF2,
inference(definition_folding,[],[f20,f23]) ).
tff(f25,definition,
sF3 = $sum(6,7),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f26,plain,
$sum(6,7) = sF3,
inference(reorient_equations,[],[f25]) ).
tff(f27,plain,
sK1 = sF3,
inference(definition_folding,[],[f19,f26]) ).
tff(f28,plain,
13 = sF2,
inference(evaluation,[],[f23]) ).
tff(f29,plain,
sF3 = 13,
inference(evaluation,[],[f26]) ).
tff(f31,definition,
( spl4_1
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f34,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f21,f31]) ).
tff(f36,definition,
( spl4_2
<=> ( sK1 = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f39,plain,
spl4_2,
inference(avatar_split_clause,[],[f27,f36]) ).
tff(f41,definition,
( spl4_3
<=> ( 13 = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f44,plain,
spl4_3,
inference(avatar_split_clause,[],[f28,f41]) ).
tff(f46,definition,
( spl4_4
<=> ( sK0 = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f49,plain,
spl4_4,
inference(avatar_split_clause,[],[f24,f46]) ).
tff(f51,definition,
( spl4_5
<=> ( sF3 = 13 ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f54,plain,
spl4_5,
inference(avatar_split_clause,[],[f29,f51]) ).
tff(f55,plain,
$false,
inference(avatar_smt_refutation,[],[f54,f49,f44,f39,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI081_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:48:19 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.58/0.93 % (709030)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.58/0.93 % (709130)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=774843548:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.58/0.93 % (709130)First to succeed.
% 2.58/0.93 % (709130)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-709030"
% 2.58/0.93 % (709122)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2733085573:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.58/0.93 % (709127)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1923002413:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.58/0.93 % (709123)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3052549808:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.58/0.93 % (709126)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4138680487:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.58/0.93 % (709129)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=234059404:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.58/0.93 % (709124)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=924689567:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.58/0.93 % (709127)Also succeeded, but the first one will report.
% 2.58/0.93 % (709126)Also succeeded, but the first one will report.
% 2.58/0.93 % (709124)Also succeeded, but the first one will report.
% 2.58/0.93 % (709122)Also succeeded, but the first one will report.
% 2.58/0.93 % (709129)Also succeeded, but the first one will report.
% 2.58/0.93 % (709123)Also succeeded, but the first one will report.
% 2.58/0.93 % (709130)Refutation found. Thanks to Tanya!
% 2.58/0.93 % SZS status Theorem for theBenchmark
% 2.58/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/0.93 % (709130)------------------------------
% 2.58/0.93 % (709130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/0.93 % (709130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.93 % (709130)CaDiCaL version: 2.1.3
% 2.58/0.93 % (709130)Termination reason: Refutation
% 2.58/0.93 % (709130)Time elapsed: 0.019 s
% 2.58/0.93 % (709130)Peak memory usage: 115 MB
% 2.58/0.93 % (709130)Instructions burned: 9 (million)
% 2.58/0.93 % (709130)------------------------------
% 2.58/0.93 % (709130)------------------------------
% 2.58/0.93 % (709030)Success in time 0.314 s
% 2.58/0.93 % Vampire exiting
%------------------------------------------------------------------------------