%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI201_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 09:32:41 AM UTC 2026
% Result : Theorem 2.73s 1.08s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 64 ( 11 atm; 21 fun; 11 num; 21 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 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 0 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 19 !; 2 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
? [X0: $rat] : $less(X0,-13/4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rat_less_problem_12) ).
tff(f2,negated_conjecture,
~ ? [X0: $rat] : $less(X0,-13/4),
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] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f7,plain,
! [X0: $rat] : ( $sum(X0,$uminus(X0)) = 0/1 ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f8,plain,
! [X0: $rat] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f12,plain,
! [X0: $rat,X1: $rat] :
( $less(X1,$sum(X0,1/1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f14,plain,
! [X0: $rat] : ~ $less(X0,-13/4),
inference(ennf_transformation,[],[f2]) ).
tff(f15,plain,
! [X0: $rat] : ~ $less(X0,-13/4),
inference(cnf_transformation,[],[f14]) ).
tff(f22,plain,
! [X0: $rat] : $less(X0,$sum(X0,1/1)),
inference(resolution,[],[f12,f8]) ).
tff(f28,plain,
! [X0: $rat] : $less(X0,$sum(1/1,X0)),
inference(superposition,[],[f22,f3]) ).
tff(f76,plain,
! [X0: $rat,X1: $rat] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0/1,X1) ),
inference(superposition,[],[f4,f7]) ).
tff(f93,plain,
! [X0: $rat,X1: $rat] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f76]) ).
tff(f111,plain,
! [X0: $rat] : $less($sum($uminus(1/1),X0),X0),
inference(superposition,[],[f28,f93]) ).
tff(f113,plain,
! [X0: $rat] : $less($sum(-1/1,X0),X0),
inference(evaluation,[],[f111]) ).
tff(f117,plain,
$false,
inference(resolution,[],[f113,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI201_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % 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 20:45:19 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 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
% 2.73/1.08 % (521500)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.73/1.08 % (521596)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1998458199:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.73/1.08 % (521596)First to succeed.
% 2.73/1.08 % (521596)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-521500"
% 2.73/1.08 % (521589)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2253005426:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.73/1.08 % (521588)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3782133184:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.73/1.08 % (521592)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4040737863:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.73/1.08 % (521590)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1931204272:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.73/1.08 % (521592)Instruction limit reached!
% 2.73/1.08 % (521592)------------------------------
% 2.73/1.08 % (521592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.08 % (521592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.08 % (521592)CaDiCaL version: 2.1.3
% 2.73/1.08 % (521592)Termination reason: Instruction limit
% 2.73/1.08 % (521592)Termination phase: Saturation
% 2.73/1.08 % (521592)Time elapsed: 0.004 s
% 2.73/1.08 % (521592)Peak memory usage: 88 MB
% 2.73/1.08 % (521592)Instructions burned: 5 (million)
% 2.73/1.08 % (521591)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2222052631:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.73/1.08 % (521595)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1129301992:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.73/1.08 % (521589)Refutation not found, incomplete strategy
% 2.73/1.08 % (521589)------------------------------
% 2.73/1.08 % (521589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.08 % (521589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.08 % (521589)CaDiCaL version: 2.1.3
% 2.73/1.08 % (521589)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.08 % (521589)Time elapsed: 0.026 s
% 2.73/1.08 % (521589)Peak memory usage: 111 MB
% 2.73/1.08 % (521589)Instructions burned: 5 (million)
% 2.73/1.08 % (521591)Instruction limit reached!
% 2.73/1.08 % (521591)------------------------------
% 2.73/1.08 % (521591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.08 % (521591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.08 % (521591)CaDiCaL version: 2.1.3
% 2.73/1.08 % (521591)Termination reason: Instruction limit
% 2.73/1.08 % (521591)Termination phase: Saturation
% 2.73/1.08 % (521591)Time elapsed: 0.005 s
% 2.73/1.08 % (521591)Peak memory usage: 88 MB
% 2.73/1.08 % (521591)Instructions burned: 7 (million)
% 2.73/1.08 % (521590)Also succeeded, but the first one will report.
% 2.73/1.08 % (521588)Instruction limit reached!
% 2.73/1.08 % (521588)------------------------------
% 2.73/1.08 % (521588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.08 % (521588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.08 % (521588)CaDiCaL version: 2.1.3
% 2.73/1.08 % (521588)Termination reason: Instruction limit
% 2.73/1.08 % (521588)Termination phase: Saturation
% 2.73/1.08 % (521588)Time elapsed: 0.031 s
% 2.73/1.08 % (521588)Peak memory usage: 115 MB
% 2.73/1.08 % (521588)Instructions burned: 12 (million)
% 2.73/1.08 % (521595)Refutation not found, incomplete strategy
% 2.73/1.08 % (521595)------------------------------
% 2.73/1.08 % (521595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.08 % (521595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.08 % (521595)CaDiCaL version: 2.1.3
% 2.73/1.08 % (521595)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.08 % (521595)Time elapsed: 0.027 s
% 2.73/1.08 % (521595)Peak memory usage: 111 MB
% 2.73/1.08 % (521595)Instructions burned: 5 (million)
% 2.73/1.08 % (521596)Refutation found. Thanks to Tanya!
% 2.73/1.08 % SZS status Theorem for theBenchmark
% 2.73/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.08 % (521596)------------------------------
% 2.73/1.08 % (521596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.08 % (521596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.08 % (521596)CaDiCaL version: 2.1.3
% 2.73/1.08 % (521596)Termination reason: Refutation
% 2.73/1.08 % (521596)Time elapsed: 0.019 s
% 2.73/1.08 % (521596)Peak memory usage: 112 MB
% 2.73/1.08 % (521596)Instructions burned: 10 (million)
% 2.73/1.08 % (521596)------------------------------
% 2.73/1.08 % (521596)------------------------------
% 2.73/1.08 % (521500)Success in time 0.319 s
% 2.73/1.08 % Vampire exiting
%------------------------------------------------------------------------------