%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD062-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 : n008.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 07:10:32 AM UTC 2026
% Result : Unsatisfiable 49.00s 10.76s
% Output : Refutation 42.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 30
% Syntax : Number of formulae : 147 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 462 ( 75 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1340 ( 249 ~; 223 |; 0 &; 868 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 231 ( 0 ^; 231 !; 0 ?; 231 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(defined_decl,type,
defined: $i > $o ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(27,axiom,
a @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(80,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(76,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(77,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[76]) ).
thf(95,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[80,77]) ).
thf(96,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[95]) ).
thf(97,plain,
a @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( a ))]]) ).
thf(133,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[97,77]) ).
thf(134,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
a @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(168,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[135,77]) ).
thf(169,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(56,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_addition) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(52,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ product ) ) )
| ~ ( A @ ( G @ ( D @ product ) ) )
| ~ ( C @ ( G @ ( F @ product ) ) )
| ~ ( F @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
thf(58,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ product ) ) )
| ~ ( A @ ( G @ ( D @ product ) ) )
| ~ ( C @ ( G @ ( F @ product ) ) )
| ~ ( F @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
multiplicative_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(36,plain,
multiplicative_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(98,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[36,77]) ).
thf(99,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
multiplicative_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(136,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[100,77]) ).
thf(137,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(1,negated_conjecture,
b @ ( a @ less_or_equal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
thf(31,plain,
b @ ( a @ less_or_equal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
~ ( a @ additive_inverse @ ( b @ additive_inverse @ less_or_equal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
thf(32,plain,
~ ( a @ additive_inverse @ ( b @ additive_inverse @ less_or_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
~ ( a @ additive_inverse @ ( b @ additive_inverse @ less_or_equal ) ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(86,plain,
( ( ( a @ additive_inverse @ ( b @ additive_inverse @ less_or_equal ) )
!= ( b @ ( a @ less_or_equal ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,33]) ).
thf(87,plain,
( ( a @ additive_inverse @ ( b @ additive_inverse @ less_or_equal ) )
!= ( b @ ( a @ less_or_equal ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
( ( ( a @ additive_inverse )
!= b )
| ( ( b @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[87]) ).
thf(10,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(47,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(101,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[47,77]) ).
thf(102,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
additive_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( additive_identity ))]]) ).
thf(139,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[103,77]) ).
thf(140,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
additive_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(287,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[141,77]) ).
thf(288,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ product ) ) )
| ~ ( C @ ( additive_identity @ less_or_equal ) )
| ~ ( B @ ( additive_identity @ less_or_equal ) )
| ( A @ ( additive_identity @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ product ) ) )
| ~ ( C @ ( additive_identity @ less_or_equal ) )
| ~ ( B @ ( additive_identity @ less_or_equal ) )
| ( A @ ( additive_identity @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
b @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
thf(85,plain,
b @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(89,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[85,77]) ).
thf(90,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
b @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( b ))]]) ).
thf(130,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[91,77]) ).
thf(131,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
b @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(74,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)],[24]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(18,axiom,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(62,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(63,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[62]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[38,63]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[205]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= multiplicative_identity )
| ( B != additive_identity )
| ( A != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[206]) ).
thf(272,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ ( additive_identity @ defined )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[264]) ).
thf(327,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[272]) ).
thf(328,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ $true ),
inference(rewrite,[status(thm)],[327,47]) ).
thf(329,plain,
( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[328]) ).
thf(3,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
thf(34,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(105,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,63]) ).
thf(106,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity ))]]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
!= ( C @ ( additive_identity @ ( B @ sum ) ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[128]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplicative_identity != C )
| ( C != additive_identity )
| ( A != B )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(162,plain,
! [A: $i] :
( ( additive_identity != multiplicative_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(340,plain,
! [A: $i] :
( ~ $true
| ( ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
!= ( additive_identity @ ( A @ ( A @ sum ) ) ) )
| ( additive_identity != multiplicative_identity )
| ~ ( additive_identity @ ( A @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[162]) ).
thf(342,plain,
( ( additive_identity != multiplicative_identity )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( additive_identity ))]]) ).
thf(600,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ( additive_identity != multiplicative_identity )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[38,342]) ).
thf(601,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ( additive_identity != multiplicative_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[600]) ).
thf(605,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= additive_identity )
| ( B != additive_identity )
| ( A != additive_identity )
| ( additive_identity != multiplicative_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[601]) ).
thf(607,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= additive_identity )
| ( additive_identity != multiplicative_identity )
| ~ ( additive_identity @ defined )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[605]) ).
thf(608,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= additive_identity )
| ( additive_identity != multiplicative_identity )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[607]) ).
thf(609,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= additive_identity )
| ( additive_identity != multiplicative_identity )
| ~ $true ),
inference(rewrite,[status(thm)],[608,47]) ).
thf(610,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= additive_identity )
| ( additive_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[609]) ).
thf(171,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[138,77]) ).
thf(172,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(7,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(41,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(165,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[132,77]) ).
thf(166,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(297,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[167,77]) ).
thf(298,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(358,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[299,77]) ).
thf(359,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[358]) ).
thf(360,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(9,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( A @ ( E @ ( D @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
thf(45,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( A @ ( E @ ( D @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_multiplication) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ sum ) ) )
| ~ ( B @ ( F @ ( D @ sum ) ) )
| ~ ( E @ ( D @ ( A @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
thf(54,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ sum ) ) )
| ~ ( B @ ( F @ ( D @ sum ) ) )
| ~ ( E @ ( D @ ( A @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(348,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[289,77]) ).
thf(349,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[348]) ).
thf(350,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[349:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(81,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_2) ).
thf(66,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ product ) ) )
| ~ ( B @ ( F @ ( D @ product ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
thf(50,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ product ) ) )
| ~ ( B @ ( F @ ( D @ product ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(307,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[170,77]) ).
thf(308,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[307]) ).
thf(309,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(368,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[309,77]) ).
thf(369,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[368]) ).
thf(370,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(72,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(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(317,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[173,77]) ).
thf(318,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[317]) ).
thf(319,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(cnf,[status(esa)],[39]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(68,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ sum ) ) )
| ~ ( A @ ( E @ ( C @ sum ) ) )
| ~ ( D @ ( C @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(83,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ sum ) ) )
| ~ ( A @ ( E @ ( C @ sum ) ) )
| ~ ( D @ ( C @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(8169,plain,
$false,
inference(e,[status(thm)],[170,56,37,52,77,58,36,138,88,289,78,132,74,60,85,38,70,33,97,329,141,610,173,41,128,360,45,64,32,34,54,350,81,76,39,103,91,66,135,299,80,167,35,162,342,48,63,50,370,31,72,43,319,40,47,68,62,83,309,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD062-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % 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
% 0.13/0.39 % Computer : n008.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 02:33:54 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 1.26/1.25 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.51 % [INFO] Parsing done (253ms).
% 1.85/1.53 % [INFO] Running in sequential loop mode.
% 2.97/2.16 % [INFO] eprover registered as external prover.
% 2.97/2.17 % [INFO] Scanning for conjecture ...
% 3.22/2.31 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 3.22/2.37 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 3.45/2.41 % [INFO] Problem is propositional (TPTP CNF).
% 3.45/2.42 % [INFO] Type checking passed.
% 3.45/2.42 % [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 ...
% 49.00/10.75 % External prover 'e' found a proof!
% 49.00/10.75 % [INFO] Killing All external provers ...
% 49.00/10.75 % Time passed: 10152ms (effective reasoning time: 9212ms)
% 49.00/10.76 % Axioms used in derivation (28): associativity_addition_1, existence_of_identity_multiplication, transitivity_of_order_relation, totality_of_multiplication, well_definedness_of_additive_identity, compatibility_of_order_relation_and_multiplication, a_is_defined, well_definedness_of_multiplication, existence_of_identity_addition, associativity_multiplication_1, antisymmetry_of_order_relation, totality_of_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_order_relation_and_addition, distributivity_2, b_is_defined, totality_of_order_relation, existence_of_inverse_multiplication, well_definedness_of_multiplicative_identity, well_definedness_of_additive_inverse, distributivity_1, associativity_addition_2, commutativity_addition, associativity_multiplication_2, different_identities, well_definedness_of_multiplicative_inverse
% 49.00/10.76 % No. of inferences in proof: 147
% 49.00/10.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10152 ms resp. 9212 ms w/o parsing
% 42.55/10.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 42.55/10.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------