%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI254_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 : n020.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 09:32:48 AM UTC 2026
% Result : Theorem 2.43s 0.83s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 49 ( 0 atm; 20 fun; 13 num; 16 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 0 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 14 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
? [X0: $rat] : ( $sum(X0,3/16) = 1/2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rat_sum_problem_9) ).
tff(f2,negated_conjecture,
~ ? [X0: $rat] : ( $sum(X0,3/16) = 1/2 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $rat,X1: $rat] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f4,plain,
! [X2: $rat,X0: $rat,X1: $rat] : ( $sum($sum(X0,X1),X2) = $sum(X0,$sum(X1,X2)) ),
introduced(definition,[],[tha_associativity]) ).
tff(f7,plain,
! [X0: $rat] : ( $sum(X0,$uminus(X0)) = 0/1 ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f14,plain,
! [X0: $rat] : ( $sum(X0,3/16) != 1/2 ),
inference(ennf_transformation,[],[f2]) ).
tff(f15,plain,
! [X0: $rat] : ( $sum(X0,3/16) != 1/2 ),
inference(cnf_transformation,[],[f14]) ).
tff(f20,plain,
! [X0: $rat] : ( 1/2 != $sum(3/16,X0) ),
inference(superposition,[],[f15,f3]) ).
tff(f83,plain,
! [X0: $rat,X1: $rat] : ( $sum(0/1,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
inference(superposition,[],[f4,f7]) ).
tff(f101,plain,
! [X0: $rat,X1: $rat] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f83]) ).
tff(f124,plain,
! [X0: $rat] : ( 1/2 != X0 ),
inference(superposition,[],[f20,f101]) ).
tff(f132,plain,
$false,
inference(equality_resolution,[],[f124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI254_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 20:46:19 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 2.43/0.83 % (524849)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.43/0.83 % (524923)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=98414769:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.43/0.83 % (524923)First to succeed.
% 2.43/0.83 % (524923)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-524849"
% 2.43/0.83 % (524920)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3744446198:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.43/0.83 % (524922)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3264325638:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.43/0.83 % (524915)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2674698114:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.43/0.83 % (524919)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1105800084:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.43/0.83 % (524917)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3471869999:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.43/0.83 % (524916)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2405185856:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.43/0.83 % (524920)Instruction limit reached!
% 2.43/0.83 % (524920)------------------------------
% 2.43/0.83 % (524920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/0.83 % (524920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.83 % (524920)CaDiCaL version: 2.1.3
% 2.43/0.83 % (524920)Termination reason: Instruction limit
% 2.43/0.83 % (524920)Termination phase: Saturation
% 2.43/0.83 % (524920)Time elapsed: 0.004 s
% 2.43/0.83 % (524920)Peak memory usage: 88 MB
% 2.43/0.83 % (524920)Instructions burned: 4 (million)
% 2.43/0.83 % (524919)Instruction limit reached!
% 2.43/0.83 % (524919)------------------------------
% 2.43/0.83 % (524919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/0.83 % (524919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.83 % (524919)CaDiCaL version: 2.1.3
% 2.43/0.83 % (524919)Termination reason: Instruction limit
% 2.43/0.83 % (524919)Termination phase: Saturation
% 2.43/0.83 % (524919)Time elapsed: 0.006 s
% 2.43/0.83 % (524919)Peak memory usage: 88 MB
% 2.43/0.83 % (524919)Instructions burned: 8 (million)
% 2.43/0.83 % (524915)Also succeeded, but the first one will report.
% 2.43/0.83 % (524922)Refutation not found, incomplete strategy
% 2.43/0.83 % (524922)------------------------------
% 2.43/0.83 % (524922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/0.83 % (524922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.83 % (524922)CaDiCaL version: 2.1.3
% 2.43/0.83 % (524922)Termination reason: Refutation not found, incomplete strategy
% 2.43/0.83 % (524922)Time elapsed: 0.028 s
% 2.43/0.83 % (524922)Peak memory usage: 111 MB
% 2.43/0.83 % (524916)Refutation not found, incomplete strategy
% 2.43/0.83 % (524916)------------------------------
% 2.43/0.83 % (524916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/0.83 % (524916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.83 % (524922)Instructions burned: 5 (million)
% 2.43/0.83 % (524916)CaDiCaL version: 2.1.3
% 2.43/0.83 % (524916)Termination reason: Refutation not found, incomplete strategy
% 2.43/0.83 % (524916)Time elapsed: 0.028 s
% 2.43/0.83 % (524916)Peak memory usage: 111 MB
% 2.43/0.83 % (524916)Instructions burned: 5 (million)
% 2.43/0.83 % (524917)Also succeeded, but the first one will report.
% 2.43/0.83 % (524923)Refutation found. Thanks to Tanya!
% 2.43/0.83 % SZS status Theorem for theBenchmark
% 2.43/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 2.43/0.83 % (524923)------------------------------
% 2.43/0.83 % (524923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/0.83 % (524923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.83 % (524923)CaDiCaL version: 2.1.3
% 2.43/0.83 % (524923)Termination reason: Refutation
% 2.43/0.83 % (524923)Time elapsed: 0.019 s
% 2.43/0.83 % (524923)Peak memory usage: 113 MB
% 2.43/0.83 % (524923)Instructions burned: 10 (million)
% 2.43/0.83 % (524923)------------------------------
% 2.43/0.83 % (524923)------------------------------
% 2.43/0.83 % (524849)Success in time 0.314 s
% 2.43/0.83 % Vampire exiting
%------------------------------------------------------------------------------