%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD011-3 : 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 : n010.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 07:10:17 AM UTC 2026
% Result : Unsatisfiable 111.62s 26.97s
% Output : Refutation 112.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 29
% Syntax : Number of formulae : 566 ( 138 unt; 0 typ; 0 def)
% Number of atoms : 1969 ( 438 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 6048 ( 895 ~; 809 |; 0 &;4344 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 730 ( 0 ^; 730 !; 0 ?; 730 :)
% 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(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $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(multiply_decl,type,
multiply: $i > $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
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(69,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(17,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(60,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(36,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[36]) ).
thf(269,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[60,37]) ).
thf(270,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[269]) ).
thf(271,plain,
additive_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( additive_identity ))]]) ).
thf(29,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(83,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(84,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(15416,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[271,84]) ).
thf(15417,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15416]) ).
thf(15418,plain,
additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15417:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(9,axiom,
multiplicative_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(46,plain,
multiplicative_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(254,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[46,37]) ).
thf(255,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[254]) ).
thf(256,plain,
multiplicative_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(283,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[256,37]) ).
thf(284,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[283]) ).
thf(285,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(370,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[285,37]) ).
thf(371,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[370]) ).
thf(372,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[371:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(544,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[372,37]) ).
thf(545,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[544]) ).
thf(546,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[545:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(891,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)],[546,37]) ).
thf(892,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[891]) ).
thf(893,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[892:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(16,axiom,
a @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(59,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(257,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,37]) ).
thf(258,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[257]) ).
thf(259,plain,
a @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( a ))]]) ).
thf(289,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[259,37]) ).
thf(290,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[289]) ).
thf(291,plain,
a @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(518,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[291,37]) ).
thf(519,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[518]) ).
thf(520,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(557,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[520,37]) ).
thf(558,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[557]) ).
thf(559,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[558:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(911,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)],[559,37]) ).
thf(912,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[911]) ).
thf(913,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[912:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1419,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[913,37]) ).
thf(1420,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1419]) ).
thf(1421,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1420:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1593,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1421,37]) ).
thf(1594,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1593]) ).
thf(1595,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1594:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1925,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1595,37]) ).
thf(1926,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1925]) ).
thf(1927,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1926:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2425,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1927,37]) ).
thf(2426,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2425]) ).
thf(2427,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2426:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(15300,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,84]) ).
thf(15301,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15300]) ).
thf(15302,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15301:[bind(A,$thf( additive_identity ))]]) ).
thf(1,negated_conjecture,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).
thf(30,plain,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(32,plain,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(15761,plain,
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15302,32]) ).
thf(15762,plain,
( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15761]) ).
thf(15816,plain,
( ( additive_identity != additive_identity )
| ( a != additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[15762]) ).
thf(15844,plain,
a != additive_identity,
inference(simp,[status(thm)],[15816]) ).
thf(1108,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[893,37]) ).
thf(1109,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1108]) ).
thf(1110,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1109:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(10,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(47,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(cnf,[status(esa)],[47]) ).
thf(91,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)],[48,32]) ).
thf(92,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
( ~ ( a @ defined )
| ( a @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( a ))]]) ).
thf(101,plain,
( ~ $true
| ( a @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[93,59]) ).
thf(102,plain,
a @ multiplicative_inverse @ defined,
inference(simp,[status(thm)],[101]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(67,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(68,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(7674,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,68]) ).
thf(7675,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7674]) ).
thf(7676,plain,
a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7675:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
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(77,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(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(13108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7676,78]) ).
thf(13109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13108]) ).
thf(13110,plain,
a @ multiplicative_inverse @ ( multiplicative_identity @ ( a @ multiplicative_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[13109:[bind(A,$thf( a @ multiplicative_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a @ multiplicative_inverse ))]]) ).
thf(272,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[102,37]) ).
thf(273,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
a @ multiplicative_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
thf(301,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[274,37]) ).
thf(302,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[301]) ).
thf(303,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(51,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(2835,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[303,52]) ).
thf(2836,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2835]) ).
thf(2837,plain,
additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2836:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(15382,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[59,84]) ).
thf(15383,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15382]) ).
thf(15384,plain,
a @ ( a @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15383:[bind(A,$thf( a ))]]) ).
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(63,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(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[63]) ).
thf(15924,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[15384,64]) ).
thf(15925,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[15924]) ).
thf(15926,plain,
a @ ( additive_identity @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[15925:[bind(A,$thf( a )),bind(B,$thf( additive_identity )),bind(C,$thf( a ))]]) ).
thf(14,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(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(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,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)],[55]) ).
thf(295,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[271,37]) ).
thf(296,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[295]) ).
thf(297,plain,
additive_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[296:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(531,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[297,37]) ).
thf(532,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[531]) ).
thf(533,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[532:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(7685,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,68]) ).
thf(7686,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7685]) ).
thf(7687,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7686:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(13027,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7687,78]) ).
thf(13028,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13027]) ).
thf(13029,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[13028:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(7,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(42,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15335,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[256,84]) ).
thf(15336,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15335]) ).
thf(15337,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15336:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(16528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[15337,64]) ).
thf(16529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[16528]) ).
thf(16530,plain,
multiplicative_identity @ additive_inverse @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[16529:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(376,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[303,37]) ).
thf(377,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[376]) ).
thf(378,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[377:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(692,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[378,37]) ).
thf(693,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[692]) ).
thf(694,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[693:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(951,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[694,37]) ).
thf(952,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[951]) ).
thf(953,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[952:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1473,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[953,37]) ).
thf(1474,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1473]) ).
thf(1475,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1474:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2813,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[59,52]) ).
thf(2814,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2813]) ).
thf(2815,plain,
additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2814:[bind(A,$thf( a ))]]) ).
thf(6007,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2815,64]) ).
thf(6008,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[6007]) ).
thf(6009,plain,
additive_identity @ ( a @ additive_inverse @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[6008:[bind(A,$thf( a )),bind(B,$thf( a @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(286,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[256,48]) ).
thf(287,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(1500,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1110,37]) ).
thf(1501,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1500]) ).
thf(1502,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1501:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1898,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1502,37]) ).
thf(1899,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1898]) ).
thf(1900,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1899:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2398,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1900,37]) ).
thf(2399,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2398]) ).
thf(2400,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2399:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(7759,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[520,68]) ).
thf(7760,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7759]) ).
thf(7761,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7760:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2696,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[533,52]) ).
thf(2697,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2696]) ).
thf(2698,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2697:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(7650,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,68]) ).
thf(7651,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7650]) ).
thf(7652,plain,
multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7651:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(2769,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[256,52]) ).
thf(2770,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2769]) ).
thf(2771,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2770:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(6032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2771,64]) ).
thf(6033,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[6032]) ).
thf(6034,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[6033:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(15385,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[259,84]) ).
thf(15386,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15385]) ).
thf(15387,plain,
a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15386:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(1871,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1475,37]) ).
thf(1872,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1871]) ).
thf(1873,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1872:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2371,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1873,37]) ).
thf(2372,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2371]) ).
thf(2373,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2372:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(292,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[259,48]) ).
thf(293,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[292]) ).
thf(294,plain,
( ( additive_identity @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(2514,plain,
( ( ( additive_identity @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[294,32]) ).
thf(2515,plain,
( ( ( additive_identity @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2514]) ).
thf(2573,plain,
( ( additive_identity != additive_identity )
| ( ( a @ additive_inverse )
!= a )
| ( additive_identity != additive_identity )
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2515]) ).
thf(2602,plain,
( ( ( a @ additive_inverse )
!= a )
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2573]) ).
thf(2633,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( ( a @ additive_inverse )
!= a ) ),
inference(paramod_ordered,[status(thm)],[2602,37]) ).
thf(2634,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( ( a @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[2633]) ).
thf(2635,plain,
( ( a @ additive_inverse @ multiplicative_inverse @ additive_inverse @ defined )
| ( ( a @ additive_inverse )
!= a ) ),
inference(pattern_uni,[status(thm)],[2634:[bind(A,$thf( a @ additive_inverse @ multiplicative_inverse ))]]) ).
thf(7726,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[259,68]) ).
thf(7727,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7726]) ).
thf(7728,plain,
a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7727:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(15,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(57,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)],[15]) ).
thf(2723,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,52]) ).
thf(2724,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2723]) ).
thf(2725,plain,
additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2724:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(5955,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2725,64]) ).
thf(5956,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5955]) ).
thf(5957,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[5956:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( multiplicative_identity @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(2,negated_conjecture,
~ ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_3) ).
thf(31,plain,
~ ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
~ ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(152,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ~ $true
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,33]) ).
thf(153,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( a @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( a @ multiplicative_inverse @ multiplicative_inverse )),bind(C,$thf( a )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G ))]]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( a @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( a @ ( D @ ( C @ sum ) ) )
!= ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) )
| ~ ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[194]) ).
thf(223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a @ ( D @ ( C @ sum ) ) )
!= ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) )
| ~ ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
!= ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) ) )
| ( ( a @ ( D @ ( C @ sum ) ) )
!= ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) )
| ~ ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[223]) ).
thf(620,plain,
! [B: $i,A: $i] :
( ( ( a @ ( B @ ( B @ sum ) ) )
!= ( multiplicative_identity @ ( A @ ( A @ sum ) ) ) )
| ~ ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[619:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(646,plain,
! [B: $i,A: $i] :
( ( ( a @ ( B @ ( B @ sum ) ) )
!= ( multiplicative_identity @ ( A @ ( A @ sum ) ) ) )
| ~ ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[620]) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
!= ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) ) )
| ~ ( a @ ( D @ ( C @ sum ) ) )
| ~ ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[194]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( B @ ( B @ sum ) ) )
| ~ ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( B @ ( B @ sum ) ) )
| ~ ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(7723,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[59,68]) ).
thf(7724,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7723]) ).
thf(7725,plain,
a @ ( a @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7724:[bind(A,$thf( a ))]]) ).
thf(13011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7725,78]) ).
thf(13012,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13011]) ).
thf(13013,plain,
a @ ( multiplicative_identity @ ( a @ product ) ),
inference(pattern_uni,[status(thm)],[13012:[bind(A,$thf( a )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a ))]]) ).
thf(12996,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7728,78]) ).
thf(12997,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[12996]) ).
thf(12998,plain,
a @ additive_inverse @ ( multiplicative_identity @ ( a @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[12997:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a @ additive_inverse ))]]) ).
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(61,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(8,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(44,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)],[8]) ).
thf(45,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)],[44]) ).
thf(27,axiom,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(79,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(80,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[79]) ).
thf(1741,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)],[45,80]) ).
thf(1742,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)],[1741]) ).
thf(1743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[1742:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity ))]]) ).
thf(1796,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)],[1743]) ).
thf(7720,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[291,68]) ).
thf(7721,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7720]) ).
thf(7722,plain,
a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7721:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
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(73,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(74,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(3965,plain,
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2771,32]) ).
thf(3966,plain,
( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[3965]) ).
thf(4025,plain,
( ( additive_identity != additive_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= a )
| ( ( multiplicative_identity @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3966]) ).
thf(4065,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= a )
| ( ( multiplicative_identity @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4025]) ).
thf(2074,plain,
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[288,32]) ).
thf(2075,plain,
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2074]) ).
thf(2135,plain,
( ( additive_identity != additive_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= a )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2075]) ).
thf(2164,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= a )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2135]) ).
thf(7690,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[256,68]) ).
thf(7691,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7690]) ).
thf(7692,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7691:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplicative_identity != a )
| ( D != B )
| ( C != A )
| ~ ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( multiplicative_identity != a )
| ~ ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(357,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
!= ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) ) )
| ( multiplicative_identity != a )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[231]) ).
thf(359,plain,
! [A: $i] :
( ( multiplicative_identity != a )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( B ))]]) ).
thf(364,plain,
! [A: $i] :
( ( multiplicative_identity != a )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(570,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( H @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( H @ product ) ) ) )
| ( multiplicative_identity != a )
| ~ $true
| ~ ( multiplicative_identity @ ( H @ ( H @ sum ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,364]) ).
thf(571,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( H @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( H @ product ) ) ) )
| ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( H @ ( H @ sum ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[570]) ).
thf(572,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ~ ( E @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( C @ product ) ) )
| ~ ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( A @ ( C @ ( B @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[571:[bind(A,$thf( C )),bind(B,$thf( a @ multiplicative_inverse @ multiplicative_inverse )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( C ))]]) ).
thf(589,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ~ ( E @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( C @ product ) ) )
| ~ ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( A @ ( C @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(1080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( multiplicative_identity @ ( A @ ( A @ sum ) ) )
!= ( A @ ( C @ ( B @ sum ) ) ) )
| ( multiplicative_identity != a )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ~ ( E @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( C @ product ) ) )
| ~ ( D @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( A @ ( C @ ( B @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[589]) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) )
| ~ ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[1080:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity ))]]) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) )
| ~ ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[1088]) ).
thf(1550,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( multiplicative_identity @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) )
| ( multiplicative_identity != a )
| ~ ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1090]) ).
thf(1559,plain,
( ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[1550:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( multiplicative_identity ))]]) ).
thf(1570,plain,
( ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[1559]) ).
thf(8106,plain,
( ( ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( a @ ( a @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7725,33]) ).
thf(8107,plain,
( ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( a @ ( a @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[8106]) ).
thf(8172,plain,
( ( a != a )
| ( ( a @ multiplicative_inverse @ multiplicative_inverse )
!= a )
| ( multiplicative_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[8107]) ).
thf(8199,plain,
( ( a @ multiplicative_inverse @ multiplicative_inverse )
!= a ),
inference(simp,[status(thm)],[8172]) ).
thf(5,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(38,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)],[5]) ).
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(cnf,[status(esa)],[69]) ).
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(65,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(7608,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[285,68]) ).
thf(7609,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7608]) ).
thf(7610,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7609:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(13021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7610,78]) ).
thf(13022,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13021]) ).
thf(13023,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[13022:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(2838,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[271,52]) ).
thf(2839,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2838]) ).
thf(2840,plain,
additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2839:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(8999,plain,
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7728,33]) ).
thf(9000,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[8999]) ).
thf(9048,plain,
( ( ( a @ additive_inverse )
!= a )
| ( ( a @ additive_inverse )
!= ( a @ multiplicative_inverse @ multiplicative_inverse ) )
| ( multiplicative_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[9000]) ).
thf(9073,plain,
( ( ( a @ additive_inverse )
!= a )
| ( ( a @ additive_inverse )
!= ( a @ multiplicative_inverse @ multiplicative_inverse ) ) ),
inference(simp,[status(thm)],[9048]) ).
thf(13,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(53,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2810,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[291,52]) ).
thf(2811,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2810]) ).
thf(2812,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2811:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(5949,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2812,64]) ).
thf(5950,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5949]) ).
thf(5951,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5950:[bind(A,$thf( a @ additive_inverse @ additive_inverse )),bind(B,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(15273,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,84]) ).
thf(15274,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15273]) ).
thf(15275,plain,
multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15274:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(666,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[533,37]) ).
thf(667,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[666]) ).
thf(668,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[667:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(931,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)],[668,37]) ).
thf(932,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[931]) ).
thf(933,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[932:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(85,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[46,48]) ).
thf(86,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[85]) ).
thf(87,plain,
( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(124,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[87,32]) ).
thf(125,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[124]) ).
thf(128,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != a )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[125]) ).
thf(130,plain,
( ( multiplicative_identity != a )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[128]) ).
thf(275,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(paramod_ordered,[status(thm)],[130,37]) ).
thf(276,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( multiplicative_identity @ multiplicative_inverse ))]]) ).
thf(679,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(paramod_ordered,[status(thm)],[277,37]) ).
thf(680,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[679]) ).
thf(681,plain,
( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(pattern_uni,[status(thm)],[680:[bind(A,$thf( multiplicative_identity @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(1148,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(paramod_ordered,[status(thm)],[681,37]) ).
thf(1149,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[1148]) ).
thf(1150,plain,
( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
| ( multiplicative_identity != a ) ),
inference(pattern_uni,[status(thm)],[1149:[bind(A,$thf( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1446,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[933,37]) ).
thf(1447,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1446]) ).
thf(1448,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1447:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1829,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1448,37]) ).
thf(1830,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1829]) ).
thf(1831,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1830:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(15320,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,84]) ).
thf(15321,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15320]) ).
thf(15322,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15321:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(7747,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,68]) ).
thf(7748,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7747]) ).
thf(7749,plain,
a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7748:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse ))]]) ).
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(40,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(cnf,[status(esa)],[40]) ).
thf(2746,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,52]) ).
thf(2747,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2746]) ).
thf(2748,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2747:[bind(A,$thf( additive_identity ))]]) ).
thf(5918,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2748,64]) ).
thf(5919,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5918]) ).
thf(5920,plain,
additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[5919:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(6077,plain,
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5920,32]) ).
thf(6078,plain,
( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[6077]) ).
thf(6138,plain,
( ( additive_identity != additive_identity )
| ( ( additive_identity @ additive_inverse )
!= a )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[6078]) ).
thf(6186,plain,
( ( additive_identity @ additive_inverse )
!= a ),
inference(simp,[status(thm)],[6138]) ).
thf(13024,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7749,78]) ).
thf(13025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13024]) ).
thf(13026,plain,
a @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ ( a @ multiplicative_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[13025:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(8215,plain,
( ( ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7676,33]) ).
thf(8216,plain,
( ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[8215]) ).
thf(8284,plain,
( ( ( a @ multiplicative_inverse )
!= a )
| ( ( a @ multiplicative_inverse @ multiplicative_inverse )
!= ( a @ multiplicative_inverse ) )
| ( multiplicative_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[8216]) ).
thf(8308,plain,
( ( ( a @ multiplicative_inverse )
!= a )
| ( ( a @ multiplicative_inverse @ multiplicative_inverse )
!= ( a @ multiplicative_inverse ) ) ),
inference(simp,[status(thm)],[8284]) ).
thf(11939,plain,
( ( ( a @ multiplicative_inverse )
!= a )
| ( ( a @ multiplicative_inverse )
!= a ) ),
inference(simp,[status(thm)],[8308]) ).
thf(11940,plain,
( ( a @ multiplicative_inverse )
!= a ),
inference(simp,[status(thm)],[11939]) ).
thf(16988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[15418,64]) ).
thf(16989,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[16988]) ).
thf(16990,plain,
additive_identity @ additive_inverse @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[16989:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ additive_inverse ))]]) ).
thf(7644,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[372,68]) ).
thf(7645,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7644]) ).
thf(7646,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7645:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(103,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)],[102,48]) ).
thf(104,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
( ( additive_identity @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(5308,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[62,32]) ).
thf(5309,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[5308]) ).
thf(5310,plain,
( ~ ( a @ ( additive_identity @ less_or_equal ) )
| ~ ( additive_identity @ ( a @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[5309:[bind(A,$thf( a )),bind(B,$thf( additive_identity ))]]) ).
thf(7753,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[271,68]) ).
thf(7754,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7753]) ).
thf(7755,plain,
additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7754:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(13120,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7755,78]) ).
thf(13121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13120]) ).
thf(13122,plain,
additive_identity @ additive_inverse @ ( multiplicative_identity @ ( additive_identity @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[13121:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ additive_inverse ))]]) ).
thf(15332,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[285,84]) ).
thf(15333,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15332]) ).
thf(15334,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15333:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(373,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[285,48]) ).
thf(374,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[373]) ).
thf(375,plain,
( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[374:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
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(34,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(5921,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) )
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[105,64]) ).
thf(5922,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) )
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5921]) ).
thf(5923,plain,
( ( additive_identity @ ( additive_identity @ ( a @ multiplicative_inverse @ sum ) ) )
| ( a @ multiplicative_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[5922:[bind(A,$thf( a @ multiplicative_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(7620,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[533,68]) ).
thf(7621,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7620]) ).
thf(7622,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7621:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2191,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( ( multiplicative_identity @ additive_inverse )
!= a ) ),
inference(paramod_ordered,[status(thm)],[2164,37]) ).
thf(2192,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( ( multiplicative_identity @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[2191]) ).
thf(2193,plain,
( ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ additive_inverse @ defined )
| ( ( multiplicative_identity @ additive_inverse )
!= a ) ),
inference(pattern_uni,[status(thm)],[2192:[bind(A,$thf( multiplicative_identity @ additive_inverse @ multiplicative_inverse ))]]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(11,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(49,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)],[11]) ).
thf(5995,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[87,64]) ).
thf(5996,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5995]) ).
thf(5997,plain,
( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[5996:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(2991,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2725,32]) ).
thf(2992,plain,
( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[2991]) ).
thf(3058,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != a )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[2992]) ).
thf(3091,plain,
( ( multiplicative_identity != a )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3058]) ).
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(71,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(10846,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[74,32]) ).
thf(10847,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[10846]) ).
thf(11076,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= additive_identity )
| ( B != a )
| ( A != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[10847]) ).
thf(11126,plain,
( ( ( a @ ( additive_identity @ add ) )
!= additive_identity )
| ~ ( a @ defined )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[11076]) ).
thf(13951,plain,
( ( ( a @ ( additive_identity @ add ) )
!= additive_identity )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[11126,59,60]) ).
thf(13952,plain,
( ( a @ ( additive_identity @ add ) )
!= additive_identity ),
inference(simp,[status(thm)],[13951]) ).
thf(5878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2840,64]) ).
thf(5879,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5878]) ).
thf(5880,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5879:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(6499,plain,
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5880,32]) ).
thf(6500,plain,
( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[6499]) ).
thf(6554,plain,
( ( additive_identity != additive_identity )
| ( ( additive_identity @ additive_inverse @ additive_inverse )
!= a )
| ( ( additive_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[6500]) ).
thf(6585,plain,
( ( ( additive_identity @ additive_inverse @ additive_inverse )
!= a )
| ( ( additive_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[6554]) ).
thf(2344,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1831,37]) ).
thf(2345,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2344]) ).
thf(2346,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2345:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
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(81,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(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(75,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(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(cnf,[status(esa)],[75]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(2816,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[259,52]) ).
thf(2817,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2816]) ).
thf(2818,plain,
additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2817:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(5992,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2818,64]) ).
thf(5993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5992]) ).
thf(5994,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5993:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( a @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(2755,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,52]) ).
thf(2756,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2755]) ).
thf(2757,plain,
additive_identity @ ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2756:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
thf(5952,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2757,64]) ).
thf(5953,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5952]) ).
thf(5954,plain,
additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5953:[bind(A,$thf( a @ multiplicative_inverse )),bind(B,$thf( a @ multiplicative_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(6636,plain,
( ( ( additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5954,32]) ).
thf(6637,plain,
( ( additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[6636]) ).
thf(6693,plain,
( ( additive_identity != additive_identity )
| ( ( a @ multiplicative_inverse @ additive_inverse )
!= a )
| ( ( a @ multiplicative_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[6637]) ).
thf(6725,plain,
( ( ( a @ multiplicative_inverse @ additive_inverse )
!= a )
| ( ( a @ multiplicative_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[6693]) ).
thf(7884,plain,
( ( ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7652,33]) ).
thf(7885,plain,
( ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7884]) ).
thf(7931,plain,
( ( multiplicative_identity != a )
| ( ( a @ multiplicative_inverse @ multiplicative_inverse )
!= multiplicative_identity )
| ( multiplicative_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[7885]) ).
thf(7978,plain,
( ( multiplicative_identity != a )
| ( ( a @ multiplicative_inverse @ multiplicative_inverse )
!= multiplicative_identity ) ),
inference(simp,[status(thm)],[7931]) ).
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(cnf,[status(esa)],[65]) ).
thf(13008,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7722,78]) ).
thf(13009,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13008]) ).
thf(13010,plain,
a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( a @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[13009:[bind(A,$thf( a @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(304,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[274,48]) ).
thf(305,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[304]) ).
thf(306,plain,
( ( additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( a @ multiplicative_inverse @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse ))]]) ).
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(cnf,[status(esa)],[34]) ).
thf(2832,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[274,52]) ).
thf(2833,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2832]) ).
thf(2834,plain,
additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2833:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(6027,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2834,64]) ).
thf(6028,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[6027]) ).
thf(6029,plain,
additive_identity @ ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[6028:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse )),bind(B,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(1549,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1090]) ).
thf(1551,plain,
! [A: $i] :
( ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[1549:[bind(A,$thf( B ))]]) ).
thf(1562,plain,
! [A: $i] :
( ( multiplicative_identity != a )
| ~ ( multiplicative_identity @ ( A @ ( A @ sum ) ) )
| ~ ( A @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ~ ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[1551]) ).
thf(7054,plain,
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6034,32]) ).
thf(7055,plain,
( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[7054]) ).
thf(7126,plain,
( ( additive_identity != additive_identity )
| ( ( multiplicative_identity @ additive_inverse @ additive_inverse )
!= a )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[7055]) ).
thf(7154,plain,
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse )
!= a )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[7126]) ).
thf(15306,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[102,84]) ).
thf(15307,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15306]) ).
thf(15308,plain,
a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15307:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
thf(16375,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[15308,64]) ).
thf(16376,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ multiplicative_inverse @ ( a @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[16375]) ).
thf(16377,plain,
a @ multiplicative_inverse @ ( additive_identity @ ( a @ multiplicative_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[16376:[bind(A,$thf( a @ multiplicative_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( a @ multiplicative_inverse ))]]) ).
thf(7771,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) )
| ( multiplicative_identity != a ) ),
inference(paramod_ordered,[status(thm)],[130,68]) ).
thf(7772,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[7771]) ).
thf(7773,plain,
( ( multiplicative_identity @ multiplicative_inverse @ ( multiplicative_identity @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
| ( multiplicative_identity != a ) ),
inference(pattern_uni,[status(thm)],[7772:[bind(A,$thf( multiplicative_identity @ multiplicative_inverse ))]]) ).
thf(2766,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,52]) ).
thf(2767,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2766]) ).
thf(2768,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2767:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(6010,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2768,64]) ).
thf(6011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[6010]) ).
thf(6012,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[6011:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(15606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[15275,64]) ).
thf(15607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[15606]) ).
thf(15608,plain,
multiplicative_identity @ ( additive_identity @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[15607:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity ))]]) ).
thf(4095,plain,
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2818,32]) ).
thf(4096,plain,
( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4095]) ).
thf(4158,plain,
( ( additive_identity != additive_identity )
| ( ( a @ additive_inverse )
!= a )
| ( ( a @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4096]) ).
thf(4200,plain,
( ( ( a @ additive_inverse )
!= a )
| ( ( a @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4158]) ).
thf(50,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(cnf,[status(esa)],[49]) ).
thf(7665,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,68]) ).
thf(7666,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7665]) ).
thf(7667,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7666:[bind(A,$thf( additive_identity ))]]) ).
thf(7750,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[303,68]) ).
thf(7751,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7750]) ).
thf(7752,plain,
a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ ( a @ multiplicative_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7751:[bind(A,$thf( a @ multiplicative_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(5345,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[62,80]) ).
thf(5346,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[5345]) ).
thf(5347,plain,
( ~ ( additive_identity @ ( multiplicative_identity @ less_or_equal ) )
| ~ ( multiplicative_identity @ ( additive_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[5346:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity ))]]) ).
thf(2841,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[520,52]) ).
thf(2842,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2841]) ).
thf(2843,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2842:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(72,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(cnf,[status(esa)],[42]) ).
thf(8888,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7692,33]) ).
thf(8889,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( a @ ( a @ multiplicative_inverse @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[8888]) ).
thf(8957,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= a )
| ( ( multiplicative_identity @ additive_inverse )
!= ( a @ multiplicative_inverse @ multiplicative_inverse ) )
| ( multiplicative_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[8889]) ).
thf(8987,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= a )
| ( ( multiplicative_identity @ additive_inverse )
!= ( a @ multiplicative_inverse @ multiplicative_inverse ) ) ),
inference(simp,[status(thm)],[8957]) ).
thf(16683,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[15387,64]) ).
thf(16684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[16683]) ).
thf(16685,plain,
a @ additive_inverse @ ( additive_identity @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[16684:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( a @ additive_inverse ))]]) ).
thf(2678,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[285,52]) ).
thf(2679,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2678]) ).
thf(2680,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2679:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(6001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2680,64]) ).
thf(6002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[6001]) ).
thf(6003,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[6002:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(13078,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ ( multiplicative_identity @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) )
| ( multiplicative_identity != a ) ),
inference(paramod_ordered,[status(thm)],[7773,78]) ).
thf(13079,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ ( multiplicative_identity @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[13078]) ).
thf(13080,plain,
( ( multiplicative_identity @ multiplicative_inverse @ ( multiplicative_identity @ ( multiplicative_identity @ multiplicative_inverse @ product ) ) )
| ( multiplicative_identity != a ) ),
inference(pattern_uni,[status(thm)],[13079:[bind(A,$thf( multiplicative_identity @ multiplicative_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity @ multiplicative_inverse ))]]) ).
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(cnf,[status(esa)],[81]) ).
thf(117,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_or_equal ) )
!= ( E @ ( F @ less_or_equal ) ) )
| ~ $true
| ~ ( F @ ( D @ less_or_equal ) )
| ( E @ ( D @ less_or_equal ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[35,35]) ).
thf(118,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_or_equal ) )
!= ( E @ ( F @ less_or_equal ) ) )
| ~ ( F @ ( D @ less_or_equal ) )
| ( E @ ( D @ less_or_equal ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ less_or_equal ) )
| ( B @ ( D @ less_or_equal ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(58,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(cnf,[status(esa)],[57]) ).
thf(2022,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)],[1796]) ).
thf(2029,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)],[2022]) ).
thf(2040,plain,
! [A: $i] :
( ( multiplicative_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[2029]) ).
thf(2474,plain,
! [A: $i] :
( ~ $true
| ( ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
!= ( additive_identity @ ( A @ ( A @ sum ) ) ) )
| ( multiplicative_identity != additive_identity )
| ~ ( additive_identity @ ( A @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[2040]) ).
thf(2480,plain,
( ( multiplicative_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[2474:[bind(A,$thf( additive_identity ))]]) ).
thf(15560,plain,
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity != additive_identity )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15275,2480]) ).
thf(15561,plain,
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity != additive_identity ) ),
inference(simp,[status(thm)],[15560]) ).
thf(15683,plain,
( ( multiplicative_identity != additive_identity )
| ( multiplicative_identity != additive_identity )
| ( additive_identity != additive_identity )
| ( multiplicative_identity != additive_identity ) ),
inference(simp,[status(thm)],[15561]) ).
thf(15690,plain,
multiplicative_identity != additive_identity,
inference(simp,[status(thm)],[15683]) ).
thf(2717,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[372,52]) ).
thf(2718,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2717]) ).
thf(2719,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2718:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(13099,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7667,78]) ).
thf(13100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13099]) ).
thf(13101,plain,
additive_identity @ ( multiplicative_identity @ ( additive_identity @ product ) ),
inference(pattern_uni,[status(thm)],[13100:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(3257,plain,
( ( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2815,32]) ).
thf(3258,plain,
( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[3257]) ).
thf(3304,plain,
( ( additive_identity != additive_identity )
| ( a != a )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3258]) ).
thf(3341,plain,
( ( a @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[3304]) ).
thf(5889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[288,64]) ).
thf(5890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5889]) ).
thf(5891,plain,
( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[5890:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(13014,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7692,78]) ).
thf(13015,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[13014]) ).
thf(13016,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[13015:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(36128,plain,
$false,
inference(e,[status(thm)],[69,15418,893,2427,15844,1110,13110,2837,15926,56,533,913,15384,13029,42,16530,1475,37,6009,288,2400,7761,52,2698,372,7652,6034,15387,559,46,2373,2635,7728,57,78,5957,646,238,13013,84,12998,61,1796,7722,74,4065,60,2164,102,546,7725,1900,1502,7692,33,1570,8199,38,297,70,65,13023,285,15302,2840,9073,7610,53,5951,256,15275,933,77,1150,1831,15322,7749,41,6186,73,13026,7687,11940,2748,16990,953,7646,105,5310,13122,1927,45,1595,15334,375,32,34,64,2602,694,44,5923,291,59,259,7622,2193,54,49,1090,5997,3091,71,13952,6585,2346,681,274,81,5880,76,39,303,271,2812,5920,5994,6725,2757,668,7978,520,66,130,13010,2725,223,306,35,80,6029,1562,7154,16377,1873,589,7773,194,6012,15308,48,63,15608,4200,50,67,7667,31,7752,5347,2843,72,43,7676,8987,2818,87,1448,16685,1421,231,40,6003,55,13080,75,2680,82,119,58,378,15337,30,2815,2768,15690,36,2719,5954,51,294,13101,79,47,7755,62,277,3341,5891,68,13016,83,2834,364,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD011-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.23/0.71 % Computer : n010.cluster.edu
% 0.23/0.71 % Model : x86_64 x86_64
% 0.23/0.71 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.71 % Memory : 8046.5625MB
% 0.23/0.71 % OS : Linux 6.8.0-71-generic
% 0.23/0.71 % CPULimit : 300
% 0.23/0.71 % WCLimit : 300
% 0.23/0.71 % DateTime : Sun Sep 27 02:22:16 UTC 2026
% 0.23/0.71 % CPUTime :
% 0.23/0.71 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
% 1.50/1.63 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.98/1.95 % [INFO] Parsing done (316ms).
% 1.98/1.97 % [INFO] Running in sequential loop mode.
% 3.22/2.62 % [INFO] eprover registered as external prover.
% 3.22/2.63 % [INFO] Scanning for conjecture ...
% 3.40/2.78 % [INFO] Found a conjecture (or negated_conjecture) and 27 axioms. Running axiom selection ...
% 3.55/2.88 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 3.74/2.96 % [INFO] Problem is propositional (TPTP CNF).
% 3.74/2.97 % [INFO] Type checking passed.
% 3.74/2.98 % [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 ...
% 111.62/26.96 % External prover 'e' found a proof!
% 111.62/26.96 % [INFO] Killing All external provers ...
% 111.62/26.96 % Time passed: 26022ms (effective reasoning time: 24978ms)
% 111.62/26.96 % Axioms used in derivation (27): 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_order_relation, totality_of_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_order_relation_and_addition, distributivity_2, 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
% 111.62/26.96 % No. of inferences in proof: 566
% 111.62/26.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 26022 ms resp. 24978 ms w/o parsing
% 112.78/27.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 112.78/27.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------