%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ROB014-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 : Sun Sep 27 08:26:46 AM UTC 2026
% Result : Unsatisfiable 16.81s 4.82s
% Output : Refutation 16.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 90 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 114 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1047 ( 89 ~; 64 |; 0 &; 894 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 0 ^; 85 !; 0 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(negate_decl,type,
negate: $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(e_decl,type,
e: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(d_decl,type,
d: $i ).
thf(positive_integer_decl,type,
positive_integer: $i > $o ).
thf(successor_decl,type,
successor: $i > $i ).
thf(7,axiom,
one @ positive_integer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one) ).
thf(26,plain,
one @ positive_integer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ successor @ positive_integer )
| ~ ( A @ positive_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',next_integer) ).
thf(27,plain,
! [A: $i] :
( ( A @ successor @ positive_integer )
| ~ ( A @ positive_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,plain,
! [A: $i] :
( ( A @ successor @ positive_integer )
| ~ ( A @ positive_integer ) ),
inference(cnf,[status(esa)],[27]) ).
thf(1928,plain,
! [A: $i] :
( ( ( one @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(1929,plain,
! [A: $i] :
( ( ( one @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer ) ),
inference(simp,[status(thm)],[1928]) ).
thf(1930,plain,
one @ successor @ positive_integer,
inference(pattern_uni,[status(thm)],[1929:[bind(A,$thf( one ))]]) ).
thf(1933,plain,
! [A: $i] :
( ( ( one @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1930,28]) ).
thf(1934,plain,
! [A: $i] :
( ( ( one @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer ) ),
inference(simp,[status(thm)],[1933]) ).
thf(1935,plain,
one @ successor @ successor @ positive_integer,
inference(pattern_uni,[status(thm)],[1934:[bind(A,$thf( one @ successor ))]]) ).
thf(1940,plain,
! [A: $i] :
( ( ( one @ successor @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1935,28]) ).
thf(1941,plain,
! [A: $i] :
( ( ( one @ successor @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer ) ),
inference(simp,[status(thm)],[1940]) ).
thf(1942,plain,
one @ successor @ successor @ successor @ positive_integer,
inference(pattern_uni,[status(thm)],[1941:[bind(A,$thf( one @ successor @ successor ))]]) ).
thf(1947,plain,
! [A: $i] :
( ( ( one @ successor @ successor @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1942,28]) ).
thf(1948,plain,
! [A: $i] :
( ( ( one @ successor @ successor @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer ) ),
inference(simp,[status(thm)],[1947]) ).
thf(1949,plain,
one @ successor @ successor @ successor @ successor @ positive_integer,
inference(pattern_uni,[status(thm)],[1948:[bind(A,$thf( one @ successor @ successor @ successor ))]]) ).
thf(1954,plain,
! [A: $i] :
( ( ( one @ successor @ successor @ successor @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1949,28]) ).
thf(1955,plain,
! [A: $i] :
( ( ( one @ successor @ successor @ successor @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer ) ),
inference(simp,[status(thm)],[1954]) ).
thf(1956,plain,
one @ successor @ successor @ successor @ successor @ successor @ positive_integer,
inference(pattern_uni,[status(thm)],[1955:[bind(A,$thf( one @ successor @ successor @ successor @ successor ))]]) ).
thf(11,axiom,
( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
thf(36,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
= d ),
inference(lifteq,[status(thm)],[36]) ).
thf(1,negated_conjecture,
( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( one @ multiply ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_base_step) ).
thf(12,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( one @ multiply ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( one @ multiply ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( one @ multiply ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_times_x) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
inference(lifteq,[status(thm)],[21]) ).
thf(44,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ),
inference(rewrite,[status(thm)],[14,22]) ).
thf(47,plain,
( ( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
!= ( e @ negate ) )
| ( ( d @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ) ),
inference(paramod_ordered,[status(thm)],[37,44]) ).
thf(52,plain,
( ( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) )
!= e )
| ( ( d @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) )
!= e ) ),
inference(simp,[status(thm)],[47]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ negate @ ( A @ add ) @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',robbins_axiom) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ negate @ ( A @ add ) @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ negate @ ( A @ add ) @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ),
inference(lifteq,[status(thm)],[19]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
!= ( B @ negate @ ( A @ add ) @ negate ) )
| ( ( d @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ) ),
inference(paramod_ordered,[status(thm)],[37,20]) ).
thf(264,plain,
( ( d @ ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ add ) @ negate )
= ( e @ negate ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( e @ negate )),bind(B,$thf( e @ negate @ ( d @ add ) ))]]) ).
thf(406,plain,
( ( ( d @ ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ add ) @ negate )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) @ negate ) )
| ( ( e @ negate )
!= ( e @ negate ) ) ),
inference(paramod_ordered,[status(thm)],[264,44]) ).
thf(407,plain,
( ( d @ ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ add ) @ negate )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) @ negate ) ),
inference(simp,[status(thm)],[406]) ).
thf(420,plain,
( ( d @ ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ add ) )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) ) ),
inference(simp,[status(thm)],[407]) ).
thf(48,plain,
( ( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
!= ( e @ negate @ ( d @ add ) @ negate ) )
| ( ( d @ ( d @ add ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ) ),
inference(paramod_ordered,[status(thm)],[37,44]) ).
thf(55,plain,
( ( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) )
!= ( e @ negate @ ( d @ add ) ) )
| ( ( d @ ( d @ add ) @ ( e @ add ) )
!= e ) ),
inference(simp,[status(thm)],[48]) ).
thf(99,plain,
( ( ( e @ negate @ ( d @ add ) @ negate )
!= ( e @ negate ) )
| ( ( e @ negate )
!= d )
| ( ( d @ ( d @ add ) @ ( e @ add ) )
!= e ) ),
inference(simp,[status(thm)],[55]) ).
thf(126,plain,
( ( ( e @ negate @ ( d @ add ) )
!= e )
| ( ( e @ negate )
!= d )
| ( ( d @ ( d @ add ) @ ( e @ add ) )
!= e ) ),
inference(simp,[status(thm)],[99]) ).
thf(602,plain,
( ( e != e )
| ( ( e @ negate @ ( d @ add ) )
!= ( d @ ( d @ add ) @ ( e @ add ) ) )
| ( ( e @ negate )
!= d )
| ( ( d @ ( d @ add ) @ ( e @ add ) )
!= e ) ),
inference(eqfactor_ordered,[status(thm)],[126]) ).
thf(605,plain,
( ( ( e @ negate @ ( d @ add ) )
!= ( d @ ( d @ add ) @ ( e @ add ) ) )
| ( ( e @ negate )
!= d )
| ( ( d @ ( d @ add ) @ ( e @ add ) )
!= e ) ),
inference(simp,[status(thm)],[602]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= ( d @ ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ add ) ) )
| ( ( A @ ( B @ add ) @ negate )
= ( e @ negate ) ) ),
inference(paramod_ordered,[status(thm)],[16,264]) ).
thf(391,plain,
( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ ( d @ add ) @ negate )
= ( e @ negate ) ),
inference(pattern_uni,[status(thm)],[390:[bind(A,$thf( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate )),bind(B,$thf( d ))]]) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ ( d @ add ) @ negate )
!= ( B @ negate @ ( A @ add ) @ negate ) )
| ( ( e @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ) ),
inference(paramod_ordered,[status(thm)],[391,20]) ).
thf(478,plain,
( ( e @ negate @ ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ ( d @ add ) @ negate @ add ) @ negate )
= d ),
inference(pattern_uni,[status(thm)],[477:[bind(A,$thf( d )),bind(B,$thf( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) ))]]) ).
thf(850,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= ( e @ negate @ ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ ( d @ add ) @ negate @ add ) ) )
| ( ( A @ ( B @ add ) @ negate )
= d ) ),
inference(paramod_ordered,[status(thm)],[16,478]) ).
thf(851,plain,
( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
= d ),
inference(pattern_uni,[status(thm)],[850:[bind(A,$thf( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ ( d @ add ) @ negate )),bind(B,$thf( e @ negate ))]]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) )
| ~ ( A @ positive_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_by_adding) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) )
| ~ ( A @ positive_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) )
| ~ ( A @ positive_integer ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( A @ positive_integer )
| ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(606,plain,
( ( ( d @ ( d @ add ) )
!= ( e @ negate ) )
| ( d != e )
| ( ( e @ negate )
!= d )
| ( ( d @ ( d @ add ) @ ( e @ add ) )
!= e ) ),
inference(simp,[status(thm)],[602]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( C @ ( B @ add ) @ negate @ ( A @ add ) @ negate )
!= ( C @ ( A @ add ) @ negate @ ( B @ add ) @ negate ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_2) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( C @ ( B @ add ) @ negate @ ( A @ add ) @ negate )
!= ( C @ ( A @ add ) @ negate @ ( B @ add ) @ negate ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ add ) @ ( D @ multiply ) @ ( B @ add ) @ negate @ ( A @ add ) @ negate )
= C )
| ~ ( D @ positive_integer )
| ( ( B @ negate @ ( A @ add ) @ negate )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_4) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ add ) @ ( D @ multiply ) @ ( B @ add ) @ negate @ ( A @ add ) @ negate )
= C )
| ~ ( D @ positive_integer )
| ( ( B @ negate @ ( A @ add ) @ negate )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) )
!= e ),
inference(simp,[status(thm)],[44]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(46,plain,
( ( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) @ negate ) )
| ( ( e @ negate )
!= d ) ),
inference(paramod_ordered,[status(thm)],[37,44]) ).
thf(49,plain,
( ( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) ) )
| ( ( e @ negate )
!= d ) ),
inference(simp,[status(thm)],[46]) ).
thf(516,plain,
( ( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ ( d @ add ) @ negate )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) @ negate ) )
| ( ( e @ negate )
!= ( e @ negate ) ) ),
inference(paramod_ordered,[status(thm)],[391,44]) ).
thf(517,plain,
( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ ( d @ add ) @ negate )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) @ negate ) ),
inference(simp,[status(thm)],[516]) ).
thf(532,plain,
( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ ( d @ add ) )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( e @ add ) ) ),
inference(simp,[status(thm)],[517]) ).
thf(1798,plain,
( ( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate )
!= ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) ) )
| ( d != e ) ),
inference(simp,[status(thm)],[532]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( C @ ( B @ add ) @ negate @ ( A @ add ) @ negate )
!= ( C @ ( A @ add ) @ negate @ ( B @ add ) @ negate ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( C @ ( B @ add ) @ negate @ ( A @ add ) @ negate )
!= ( C @ ( A @ add ) @ negate @ ( B @ add ) @ negate ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ ( d @ add ) @ negate )
!= ( B @ ( A @ add ) @ negate ) )
| ( ( B @ negate @ ( A @ add ) @ negate @ ( e @ negate @ add ) @ negate )
= A ) ),
inference(paramod_ordered,[status(thm)],[391,20]) ).
thf(482,plain,
( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
= d ),
inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( d )),bind(B,$thf( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate ))]]) ).
thf(1308,plain,
( ( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) )
!= d )
| ( ( e @ negate @ ( d @ add ) @ ( e @ negate @ add ) @ negate )
!= e ) ),
inference(simp,[status(thm)],[420]) ).
thf(2064,plain,
! [A: $i] :
( ( ( one @ successor @ successor @ successor @ successor @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1956,28]) ).
thf(2065,plain,
! [A: $i] :
( ( ( one @ successor @ successor @ successor @ successor @ successor @ positive_integer )
!= ( A @ positive_integer ) )
| ( A @ successor @ positive_integer ) ),
inference(simp,[status(thm)],[2064]) ).
thf(2066,plain,
one @ successor @ successor @ successor @ successor @ successor @ successor @ positive_integer,
inference(pattern_uni,[status(thm)],[2065:[bind(A,$thf( one @ successor @ successor @ successor @ successor @ successor ))]]) ).
thf(812,plain,
! [B: $i,A: $i] :
( ( ( one @ positive_integer )
!= ( A @ positive_integer ) )
| ~ $true
| ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,25]) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( ( one @ positive_integer )
!= ( A @ positive_integer ) )
| ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) ) ),
inference(simp,[status(thm)],[812]) ).
thf(814,plain,
! [A: $i] :
( ( one @ ( A @ successor @ multiply ) )
= ( one @ ( A @ multiply ) @ ( one @ add ) ) ),
inference(pattern_uni,[status(thm)],[813:[bind(A,$thf( one ))]]) ).
thf(818,plain,
! [A: $i] :
( ( one @ ( A @ successor @ multiply ) )
= ( one @ ( A @ multiply ) @ ( one @ add ) ) ),
inference(simp,[status(thm)],[814]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
!= ( B @ ( A @ add ) @ negate ) )
| ( ( B @ negate @ ( A @ add ) @ negate @ ( d @ add ) @ negate )
= A ) ),
inference(paramod_ordered,[status(thm)],[37,20]) ).
thf(268,plain,
( ( e @ negate @ ( d @ add ) @ negate @ negate @ ( e @ negate @ add ) @ negate @ ( d @ add ) @ negate )
= ( e @ negate ) ),
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( e @ negate )),bind(B,$thf( e @ negate @ ( d @ add ) @ negate ))]]) ).
thf(3179,plain,
$false,
inference(e,[status(thm)],[1956,52,420,1942,605,851,1935,37,25,20,606,29,28,21,32,264,45,17,22,44,27,391,12,49,1798,18,16,31,99,1949,482,26,55,23,1308,2066,478,36,818,19,126,268,532,1930,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB014-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n007.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 06:12:54 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.18 % [INFO] Parsing done (197ms).
% 1.27/1.19 % [INFO] Running in sequential loop mode.
% 1.97/1.60 % [INFO] eprover registered as external prover.
% 2.18/1.60 % [INFO] Scanning for conjecture ...
% 2.18/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.38/1.73 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.38/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.38/1.76 % [INFO] Type checking passed.
% 2.38/1.77 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 16.81/4.81 % External prover 'e' found a proof!
% 16.81/4.81 % [INFO] Killing All external provers ...
% 16.81/4.81 % Time passed: 4282ms (effective reasoning time: 3616ms)
% 16.81/4.82 % Axioms used in derivation (10): next_integer, times_by_adding, condition, lemma_3_4, one, robbins_axiom, one_times_x, lemma_3_2, associativity_of_add, commutativity_of_add
% 16.81/4.82 % No. of inferences in proof: 90
% 16.81/4.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4282 ms resp. 3616 ms w/o parsing
% 16.81/4.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.81/4.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------