%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD009-3 : 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 : n015.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 07:10:16 AM UTC 2026
% Result : Unsatisfiable 17.94s 5.21s
% Output : Refutation 15.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 142 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 468 ( 64 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1378 ( 248 ~; 242 |; 0 &; 888 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 255 ( 0 ^; 255 !; 0 ?; 255 :)
% Comments :
%------------------------------------------------------------------------------
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(a_decl,type,
a: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(defined_decl,type,
defined: $i > $o ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(16,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(59,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,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(46,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(47,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(cnf,[status(esa)],[46]) ).
thf(93,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,47]) ).
thf(94,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[93]) ).
thf(95,plain,
( ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) )
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( additive_identity ))]]) ).
thf(1,negated_conjecture,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
thf(31,plain,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(33,plain,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(132,plain,
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[95,33]) ).
thf(133,plain,
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[132]) ).
thf(136,plain,
( ( additive_identity != additive_identity )
| ( a != additive_identity )
| ( additive_identity != additive_identity )
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[133]) ).
thf(138,plain,
( ( a != additive_identity )
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[136]) ).
thf(14,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(56,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)],[14]) ).
thf(6,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(40,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)],[6]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(13,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(54,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)],[13]) ).
thf(20,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(66,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)],[20]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(38,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[37]) ).
thf(253,plain,
! [A: $i] :
( ( ( additive_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( a != additive_identity ) ),
inference(paramod_ordered,[status(thm)],[138,38]) ).
thf(254,plain,
! [A: $i] :
( ( ( additive_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
( ( additive_identity @ multiplicative_inverse @ additive_inverse @ defined )
| ( a != additive_identity ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( additive_identity @ multiplicative_inverse ))]]) ).
thf(23,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(72,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)],[23]) ).
thf(3,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(35,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)],[3]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(90,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[47,33]) ).
thf(91,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
( ~ ( a @ defined )
| ( a @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( a ))]]) ).
thf(15,axiom,
a @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(58,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(106,plain,
( ~ $true
| ( a @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[92,58]) ).
thf(107,plain,
a @ multiplicative_inverse @ defined,
inference(simp,[status(thm)],[106]) ).
thf(55,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(cnf,[status(esa)],[54]) ).
thf(2,negated_conjecture,
! [A: $i] :
~ ( b @ ( A @ ( a @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_4) ).
thf(32,plain,
! [A: $i] :
~ ( b @ ( A @ ( a @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,plain,
! [A: $i] :
~ ( b @ ( A @ ( a @ product ) ) ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(149,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( b @ ( H @ ( a @ product ) ) ) )
| ~ $true
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,34]) ).
thf(150,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( b @ ( H @ ( a @ product ) ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(151,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( b @ ( E @ ( D @ sum ) ) )
| ~ ( E @ ( A @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( C @ ( B @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( b )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( B ))]]) ).
thf(179,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( b @ ( E @ ( D @ sum ) ) )
| ~ ( E @ ( A @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( E @ ( A @ ( C @ product ) ) )
!= ( D @ ( A @ ( B @ product ) ) ) )
| ~ ( b @ ( E @ ( D @ sum ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( C @ ( B @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[179]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( b @ ( C @ ( C @ sum ) ) )
| ~ ( C @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( B @ ( B @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( A )),bind(B,$thf( C )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( b @ ( C @ ( C @ sum ) ) )
| ~ ( C @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( B @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(29,axiom,
b @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
thf(84,plain,
b @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(274,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[84,38]) ).
thf(275,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[274]) ).
thf(276,plain,
b @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( b ))]]) ).
thf(5,axiom,
multiplicative_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(39,plain,
multiplicative_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(280,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[39,38]) ).
thf(281,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[280]) ).
thf(282,plain,
multiplicative_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(306,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[282,38]) ).
thf(307,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(108,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[107,47]) ).
thf(109,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[108]) ).
thf(110,plain,
( ( additive_identity @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
thf(226,plain,
( ( ( additive_identity @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[110,33]) ).
thf(227,plain,
( ( ( additive_identity @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[226]) ).
thf(243,plain,
( ( additive_identity != additive_identity )
| ( ( a @ multiplicative_inverse )
!= a )
| ( additive_identity != additive_identity )
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[227]) ).
thf(247,plain,
( ( ( a @ multiplicative_inverse )
!= a )
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[243]) ).
thf(7,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(42,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,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(52,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,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(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(259,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,38]) ).
thf(260,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[259]) ).
thf(261,plain,
additive_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( additive_identity ))]]) ).
thf(268,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[107,38]) ).
thf(269,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[268]) ).
thf(270,plain,
a @ multiplicative_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
thf(374,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[270,38]) ).
thf(375,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[374]) ).
thf(376,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(87,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[84,47]) ).
thf(88,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[87]) ).
thf(89,plain,
( ( additive_identity @ ( b @ ( additive_identity @ sum ) ) )
| ( b @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( b ))]]) ).
thf(24,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(74,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17,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(60,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)],[17]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(85,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(300,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[276,38]) ).
thf(301,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[300]) ).
thf(302,plain,
b @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(22,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(70,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)],[22]) ).
thf(19,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(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(265,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[58,38]) ).
thf(266,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[265]) ).
thf(267,plain,
a @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( a ))]]) ).
thf(294,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[267,38]) ).
thf(295,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[294]) ).
thf(296,plain,
a @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( a @ additive_inverse ))]]) ).
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(44,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,axiom,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(80,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(81,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[80]) ).
thf(25,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(76,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)],[25]) ).
thf(204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( b @ ( E @ ( D @ sum ) ) )
!= ( a @ ( C @ ( B @ sum ) ) ) )
| ~ ( E @ ( A @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( C @ ( B @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[179]) ).
thf(208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( b @ ( E @ ( D @ sum ) ) )
!= ( a @ ( C @ ( B @ sum ) ) ) )
| ~ ( E @ ( A @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(10,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(48,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)],[10]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(50,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(121,plain,
( ( ( additive_identity @ ( b @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( b @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[89,33]) ).
thf(122,plain,
( ( ( additive_identity @ ( b @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ( b @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[121]) ).
thf(125,plain,
( ( additive_identity != additive_identity )
| ( b != a )
| ( additive_identity != additive_identity )
| ( b @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[122]) ).
thf(127,plain,
( ( b != a )
| ( b @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[125]) ).
thf(28,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(82,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)],[28]) ).
thf(209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( b != a )
| ( E != C )
| ( D != B )
| ~ ( E @ ( A @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( b != a )
| ~ ( C @ ( A @ ( C @ product ) ) )
| ~ ( B @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(288,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[261,38]) ).
thf(289,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[288]) ).
thf(290,plain,
additive_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(68,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,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(62,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)],[18]) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( A @ ( C @ product ) ) )
!= ( B @ ( A @ ( B @ product ) ) ) )
| ( b != a )
| ~ ( B @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( C @ ( B @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[214]) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( b != a )
| ~ ( B @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( B @ ( B @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[358:[bind(A,$thf( A )),bind(B,$thf( C ))]]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( b != a )
| ~ ( B @ ( A @ ( B @ product ) ) )
| ~ ( a @ ( B @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(2853,plain,
$false,
inference(e,[status(thm)],[138,56,41,54,66,255,72,36,107,215,276,308,247,42,37,52,110,46,78,261,179,376,84,89,74,60,270,85,302,38,70,33,64,296,32,34,44,59,81,76,39,208,267,80,35,48,282,95,50,127,31,40,55,82,214,290,58,47,68,62,369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD009-3 : 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
% 0.15/0.62 % Computer : n015.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Sun Sep 27 02:24:31 UTC 2026
% 0.18/0.63 % CPUTime :
% 0.18/0.63 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
% 1.00/1.22 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.41 % [INFO] Parsing done (195ms).
% 1.33/1.43 % [INFO] Running in sequential loop mode.
% 2.08/1.83 % [INFO] eprover registered as external prover.
% 2.08/1.83 % [INFO] Scanning for conjecture ...
% 2.27/1.93 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 2.27/2.00 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.49/2.05 % [INFO] Problem is propositional (TPTP CNF).
% 2.49/2.06 % [INFO] Type checking passed.
% 2.49/2.06 % [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 ...
% 17.69/5.20 % External prover 'e' found a proof!
% 17.69/5.20 % [INFO] Killing All external provers ...
% 17.94/5.21 % Time passed: 4435ms (effective reasoning time: 3770ms)
% 17.94/5.21 % 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
% 17.94/5.21 % No. of inferences in proof: 142
% 17.94/5.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4435 ms resp. 3770 ms w/o parsing
% 15.94/5.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.94/5.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------