%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM901_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:17:24 PM UTC 2026
% Result : Theorem 2.42s 1.08s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 10 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 6 ~; 0 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 23 ( 0 atm; 12 fun; 7 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 : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 3 !; 1 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK0: $rat ).
tff(f1,conjecture,
! [X0: $rat] : ( $difference(X0,X0) = 0/1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rat_difference_problem_12) ).
tff(f2,negated_conjecture,
~ ! [X0: $rat] : ( $difference(X0,X0) = 0/1 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $rat] : ( 0/1 = $sum(X0,$uminus(X0)) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
? [X0: $rat] : ( 0/1 != $sum(X0,$uminus(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
0/1 != $sum(sK0,$uminus(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f4]) ).
tff(f6,plain,
0/1 != $sum(sK0,$uminus(sK0)),
inference(cnf_transformation,[],[f5]) ).
tff(f8,definition,
( spl1_1
<=> ( 0/1 = $sum(sK0,$uminus(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f11,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f6,f8]) ).
tff(f12,plain,
$false,
inference(avatar_smt_refutation,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM901_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 21:41:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.42/1.08 % (3911925)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.42/1.08 % (3911935)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2495502105:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.42/1.08 % (3911935)First to succeed.
% 2.42/1.08 % (3911935)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3911925"
% 2.42/1.08 % (3911936)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=446536621:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.42/1.08 % (3911934)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=79371779:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.42/1.08 % (3911933)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2128887482:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.42/1.08 % (3911931)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1972034130:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.42/1.08 % (3911930)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1777003636:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.42/1.08 % (3911932)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=553302404:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.42/1.08 % (3911933)Also succeeded, but the first one will report.
% 2.42/1.08 % (3911934)Instruction limit reached!
% 2.42/1.08 % (3911934)------------------------------
% 2.42/1.08 % (3911934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.08 % (3911934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.08 % (3911934)CaDiCaL version: 2.1.3
% 2.42/1.08 % (3911934)Termination reason: Instruction limit
% 2.42/1.08 % (3911934)Termination phase: Saturation
% 2.42/1.08 % (3911934)Time elapsed: 0.004 s
% 2.42/1.08 % (3911934)Peak memory usage: 88 MB
% 2.42/1.08 % (3911934)Instructions burned: 6 (million)
% 2.42/1.08 % (3911932)Also succeeded, but the first one will report.
% 2.42/1.08 % (3911930)Also succeeded, but the first one will report.
% 2.42/1.08 % (3911936)Also succeeded, but the first one will report.
% 2.42/1.08 % (3911931)Also succeeded, but the first one will report.
% 2.42/1.08 % (3911944)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=693159687:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.42/1.08 % (3911944)Refutation not found, incomplete strategy
% 2.42/1.08 % (3911944)------------------------------
% 2.42/1.08 % (3911944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.08 % (3911944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.08 % (3911944)CaDiCaL version: 2.1.3
% 2.42/1.08 % (3911944)Termination reason: Refutation not found, incomplete strategy
% 2.42/1.08 % (3911944)Time elapsed: 0.001 s
% 2.42/1.08 % (3911944)Peak memory usage: 89 MB
% 2.42/1.08 % (3911935)Refutation found. Thanks to Tanya!
% 2.42/1.08 % SZS status Theorem for theBenchmark
% 2.42/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 2.42/1.08 % (3911935)------------------------------
% 2.42/1.08 % (3911935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.08 % (3911935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.08 % (3911935)CaDiCaL version: 2.1.3
% 2.42/1.08 % (3911935)Termination reason: Refutation
% 2.42/1.08 % (3911935)Time elapsed: 0.018 s
% 2.42/1.08 % (3911935)Peak memory usage: 115 MB
% 2.42/1.08 % (3911935)Instructions burned: 7 (million)
% 2.42/1.08 % (3911935)------------------------------
% 2.42/1.08 % (3911935)------------------------------
% 2.42/1.08 % (3911925)Success in time 0.293 s
% 2.42/1.08 % Vampire exiting
%------------------------------------------------------------------------------