%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD065-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 07:10:33 AM UTC 2026
% Result : Unsatisfiable 22.01s 10.71s
% Output : Refutation 22.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 143 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 427 ( 65 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1210 ( 214 ~; 190 |; 0 &; 806 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 176 ( 0 ^; 176 !; 0 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(defined_decl,type,
defined: $i > $o ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( additive_identity @ less_or_equal ) )
| ~ ( A @ ( additive_identity @ less_or_equal ) )
| ( B @ ( A @ multiply ) @ ( additive_identity @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( additive_identity @ less_or_equal ) )
| ~ ( A @ ( additive_identity @ less_or_equal ) )
| ( B @ ( A @ multiply ) @ ( additive_identity @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(8,axiom,
multiplicative_identity @ defined,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(44,plain,
multiplicative_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(63,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(64,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[63]) ).
thf(138,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[44,64]) ).
thf(139,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[138]) ).
thf(140,plain,
multiplicative_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(187,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[140,64]) ).
thf(188,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[187]) ).
thf(189,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(241,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[189,64]) ).
thf(242,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[241]) ).
thf(243,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(351,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[243,64]) ).
thf(352,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[351]) ).
thf(353,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[352:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(30,axiom,
~ ( multiplicative_identity @ ( additive_identity @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
thf(85,plain,
~ ( multiplicative_identity @ ( additive_identity @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ equalish ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ equalish ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(20,axiom,
a @ defined,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
thf(67,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(38,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(39,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(661,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[67,39]) ).
thf(662,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(simp,[status(thm)],[661]) ).
thf(663,plain,
a @ ( a @ ( multiplicative_identity @ multiply ) @ equalish ),
inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( a ))]]) ).
thf(21,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(68,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(141,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[68,64]) ).
thf(142,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[141]) ).
thf(143,plain,
additive_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( additive_identity ))]]) ).
thf(205,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[143,64]) ).
thf(206,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
additive_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(307,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[207,64]) ).
thf(308,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[307]) ).
thf(309,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(414,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[309,64]) ).
thf(415,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[414]) ).
thf(416,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[415:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(480,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[416,64]) ).
thf(481,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[480]) ).
thf(482,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ less_or_equal ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ less_or_equal ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_equality) ).
thf(42,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ equalish ) )
| ~ ( C @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ equalish ) )
| ~ ( C @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ equalish ) )
| ~ ( C @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(617,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[44,39]) ).
thf(618,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(simp,[status(thm)],[617]) ).
thf(619,plain,
multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ multiply ) @ equalish ),
inference(pattern_uni,[status(thm)],[618:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(1,negated_conjecture,
additive_identity @ ( a @ additive_inverse @ less_or_equal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_2) ).
thf(31,plain,
additive_identity @ ( a @ additive_inverse @ less_or_equal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
~ ( a @ ( additive_identity @ less_or_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_3) ).
thf(32,plain,
~ ( a @ ( additive_identity @ less_or_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
~ ( a @ ( additive_identity @ less_or_equal ) ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(123,plain,
( ( ( additive_identity @ ( a @ additive_inverse @ less_or_equal ) )
!= ( a @ ( additive_identity @ less_or_equal ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,33]) ).
thf(124,plain,
( ( additive_identity @ ( a @ additive_inverse @ less_or_equal ) )
!= ( a @ ( additive_identity @ less_or_equal ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
( ( additive_identity != a )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[124]) ).
thf(458,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[353,64]) ).
thf(459,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[458]) ).
thf(460,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[459:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ multiply ) @ multiply ) @ ( C @ ( B @ multiply ) @ ( A @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ multiply ) @ multiply ) @ ( C @ ( B @ multiply ) @ ( A @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(86,plain,
~ ( multiplicative_identity @ ( additive_identity @ equalish ) ),
inference(polarity_switch,[status(thm)],[85]) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true
| ~ ( B @ ( C @ equalish ) )
| ~ ( C @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[37,86]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ ( B @ ( C @ equalish ) )
| ~ ( C @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[376]) ).
thf(378,plain,
! [A: $i] :
( ~ ( multiplicative_identity @ ( A @ equalish ) )
| ~ ( A @ ( additive_identity @ equalish ) ) ),
inference(pattern_uni,[status(thm)],[377:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity ))]]) ).
thf(401,plain,
! [A: $i] :
( ~ ( multiplicative_identity @ ( A @ equalish ) )
| ~ ( A @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[378]) ).
thf(507,plain,
! [A: $i] :
( ~ $true
| ( ( multiplicative_identity @ ( A @ equalish ) )
!= ( A @ ( additive_identity @ equalish ) ) )
| ~ ( A @ ( additive_identity @ equalish ) ) ),
inference(eqfactor_ordered,[status(thm)],[401]) ).
thf(510,plain,
! [A: $i] :
( ( multiplicative_identity != A )
| ( A != additive_identity )
| ~ ( A @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[507]) ).
thf(519,plain,
( ( multiplicative_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[510]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(144,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[67,64]) ).
thf(145,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[144]) ).
thf(146,plain,
a @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( a ))]]) ).
thf(223,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[146,64]) ).
thf(224,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[223]) ).
thf(225,plain,
a @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(26,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ equalish ) )
| ~ ( A @ defined )
| ( multiplicative_identity @ ( A @ multiplicative_inverse @ ( A @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(77,plain,
! [A: $i] :
( ( additive_identity @ ( A @ equalish ) )
| ~ ( A @ defined )
| ( multiplicative_identity @ ( A @ multiplicative_inverse @ ( A @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(640,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[68,39]) ).
thf(641,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(simp,[status(thm)],[640]) ).
thf(642,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ equalish ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( additive_identity ))]]) ).
thf(24,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ equalish ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(73,plain,
! [A: $i] :
( ( additive_identity @ ( A @ equalish ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(695,plain,
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ multiply ) @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[619,86]) ).
thf(696,plain,
( ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ multiply ) @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[695]) ).
thf(713,plain,
( ( multiplicative_identity != multiplicative_identity )
| ( ( multiplicative_identity @ ( multiplicative_identity @ multiply ) )
!= additive_identity ) ),
inference(simp,[status(thm)],[696]) ).
thf(718,plain,
( ( multiplicative_identity @ ( multiplicative_identity @ multiply ) )
!= additive_identity ),
inference(simp,[status(thm)],[713]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(81,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(329,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[225,64]) ).
thf(330,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[329]) ).
thf(331,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(436,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[331,64]) ).
thf(437,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[436]) ).
thf(438,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[437:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true
| ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined ) ),
inference(paramod_ordered,[status(thm)],[35,86]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined ) ),
inference(simp,[status(thm)],[160]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ add ) )
!= multiplicative_identity )
| ( ( B @ ( A @ add ) )
!= additive_identity )
| ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined ) ),
inference(simp,[status(thm)],[161]) ).
thf(274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ( ( B @ ( C @ add ) )
!= multiplicative_identity )
| ( ( B @ ( A @ add ) )
!= additive_identity )
| ~ ( C @ ( A @ equalish ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68,171]) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ( ( B @ ( C @ add ) )
!= multiplicative_identity )
| ( ( B @ ( A @ add ) )
!= additive_identity )
| ~ ( C @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( B @ add ) )
!= multiplicative_identity )
| ( ( additive_identity @ ( A @ add ) )
!= additive_identity )
| ~ ( B @ ( A @ equalish ) ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( A )),bind(B,$thf( additive_identity ))]]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( B @ add ) )
!= multiplicative_identity )
| ( ( additive_identity @ ( A @ add ) )
!= additive_identity )
| ~ ( B @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(705,plain,
! [A: $i] :
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ multiply ) @ equalish ) )
!= ( multiplicative_identity @ ( A @ equalish ) ) )
| ~ $true
| ~ ( A @ ( additive_identity @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[619,401]) ).
thf(706,plain,
! [A: $i] :
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ multiply ) @ equalish ) )
!= ( multiplicative_identity @ ( A @ equalish ) ) )
| ~ ( A @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[705]) ).
thf(707,plain,
~ ( multiplicative_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ equalish ) ),
inference(pattern_uni,[status(thm)],[706:[bind(A,$thf( multiplicative_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( C @ defined )
| ~ ( A @ defined )
| ( B @ ( C @ ( A @ add ) @ multiply ) @ ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( C @ defined )
| ~ ( A @ defined )
| ( B @ ( C @ ( A @ add ) @ multiply ) @ ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(75,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5733,plain,
$false,
inference(e,[status(thm)],[69,56,353,85,65,140,663,143,482,79,42,37,619,125,460,189,416,57,61,243,38,33,519,53,225,77,642,73,718,45,64,32,34,44,59,71,49,86,81,39,438,35,63,282,707,67,331,31,40,55,401,171,75,207,36,146,51,47,68,83,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD065-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/5.41 % Computer : n017.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.42 % DateTime : Sun Sep 27 02:29:11 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/6.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/6.23 % [INFO] Parsing done (201ms).
% 1.31/6.25 % [INFO] Running in sequential loop mode.
% 2.04/6.66 % [INFO] eprover registered as external prover.
% 2.04/6.67 % [INFO] Scanning for conjecture ...
% 2.25/6.77 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 2.44/6.84 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.44/6.88 % [INFO] Problem is propositional (TPTP CNF).
% 2.44/6.89 % [INFO] Type checking passed.
% 2.44/6.89 % [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 ...
% 22.01/10.70 % External prover 'e' found a proof!
% 22.01/10.70 % [INFO] Killing All external provers ...
% 22.01/10.70 % Time passed: 5144ms (effective reasoning time: 4450ms)
% 22.01/10.71 % Axioms used in derivation (28): existence_of_identity_multiplication, transitivity_of_order_relation, associativity_multiplication, well_definedness_of_additive_identity, compatibility_of_order_relation_and_multiplication, well_definedness_of_multiplication, existence_of_identity_addition, transitivity_of_equality, reflexivity_of_equality, totality_of_order_relation, commutativity_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, distributivity, compatibility_of_equality_and_multiplication, a_is_defined, antisymmetry_of_order_relation, associativity_addition, compatibility_of_equality_and_addition, existence_of_inverse_multiplication, well_definedness_of_multiplicative_identity, well_definedness_of_additive_inverse, symmetry_of_equality, different_identities, well_definedness_of_multiplicative_inverse, compatibility_of_equality_and_order_relation, compatibility_of_order_relation_and_addition
% 22.01/10.71 % No. of inferences in proof: 143
% 22.01/10.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5144 ms resp. 4450 ms w/o parsing
% 22.01/10.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.01/10.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------