%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI278_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 : n008.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 09:32:51 AM UTC 2026
% Result : Theorem 0.20s 1.20s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 30 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 0 |; 2 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 43 ( 0 atm; 14 fun; 25 num; 4 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 3 usr; 7 con; 0-2 aty)
% Number of variables : 4 ( 3 !; 1 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
sK0: $rat ).
tff(func_def_9,type,
sF1: $rat ).
tff(func_def_10,type,
sF2: $rat ).
tff(f1,conjecture,
! [X0: $rat] :
( ( $difference(5/12,1/12) = X0 )
=> ( X0 = 1/3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rat_difference_problem_6) ).
tff(f2,negated_conjecture,
~ ! [X0: $rat] :
( ( $difference(5/12,1/12) = X0 )
=> ( X0 = 1/3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $rat] :
( ( $sum(5/12,$uminus(1/12)) = X0 )
=> ( X0 = 1/3 ) ),
inference(theory_normalization,[],[f2]) ).
tff(f15,plain,
? [X0: $rat] :
( ( $sum(5/12,$uminus(1/12)) = X0 )
& ( 1/3 != X0 ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f16,plain,
( ( $sum(5/12,$uminus(1/12)) = sK0 )
& ( 1/3 != sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15]) ).
tff(f17,plain,
1/3 != sK0,
inference(cnf_transformation,[],[f16]) ).
tff(f18,plain,
$sum(5/12,$uminus(1/12)) = sK0,
inference(cnf_transformation,[],[f16]) ).
tff(f19,definition,
sF1 = $uminus(1/12),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f20,plain,
$uminus(1/12) = sF1,
inference(reorient_equations,[],[f19]) ).
tff(f21,definition,
sF2 = $sum(5/12,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f22,plain,
sF2 = sK0,
inference(definition_folding,[],[f18,f21,f20]) ).
tff(f23,plain,
-1/12 = sF1,
inference(evaluation,[],[f20]) ).
tff(f25,definition,
( spl3_1
<=> ( sF2 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f28,plain,
spl3_1,
inference(avatar_split_clause,[],[f22,f25]) ).
tff(f30,definition,
( spl3_2
<=> ( -1/12 = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f33,plain,
spl3_2,
inference(avatar_split_clause,[],[f23,f30]) ).
tff(f35,definition,
( spl3_3
<=> ( 1/3 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f38,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f17,f35]) ).
tff(f40,definition,
( spl3_4
<=> ( sF2 = $sum(5/12,sF1) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f43,plain,
spl3_4,
inference(avatar_split_clause,[],[f21,f40]) ).
tff(f44,plain,
$false,
inference(avatar_smt_refutation,[],[f43,f38,f33,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI278_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:46:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.20/1.20 % (2616670)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.20/1.20 % (2616799)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2638755672:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.20/1.20 % (2616799)First to succeed.
% 0.20/1.20 % (2616799)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2616670"
% 0.20/1.20 % (2616790)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2830360473:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/1.20 % (2616793)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1199873916:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.20/1.20 % (2616796)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3648207284:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.20/1.20 % (2616791)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2134476930:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.20/1.20 % (2616796)Also succeeded, but the first one will report.
% 0.20/1.20 % (2616798)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2117266976:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.20/1.20 % (2616795)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4092235386:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/1.20 % (2616795)Also succeeded, but the first one will report.
% 0.20/1.20 % (2616793)Also succeeded, but the first one will report.
% 0.20/1.20 % (2616790)Also succeeded, but the first one will report.
% 0.20/1.20 % (2616791)Also succeeded, but the first one will report.
% 0.20/1.20 % (2616798)Also succeeded, but the first one will report.
% 0.20/1.20 % (2616799)Refutation found. Thanks to Tanya!
% 0.20/1.20 % SZS status Theorem for theBenchmark
% 0.20/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.20 % (2616799)------------------------------
% 0.20/1.20 % (2616799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (2616799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (2616799)CaDiCaL version: 2.1.3
% 0.20/1.20 % (2616799)Termination reason: Refutation
% 0.20/1.20 % (2616799)Time elapsed: 0.019 s
% 0.20/1.20 % (2616799)Peak memory usage: 115 MB
% 0.20/1.20 % (2616799)Instructions burned: 9 (million)
% 0.20/1.20 % (2616799)------------------------------
% 0.20/1.20 % (2616799)------------------------------
% 0.20/1.20 % (2616670)Success in time 0.323 s
% 0.20/1.20 % Vampire exiting
%------------------------------------------------------------------------------