%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD049-3 : 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 : n026.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 07:10:28 AM UTC 2026
% Result : Unsatisfiable 91.21s 23.74s
% Output : Refutation 87.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 34
% Syntax : Number of formulae : 1197 ( 295 unt; 0 typ; 0 def)
% Number of atoms : 4239 (1077 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 11754 (1873 ~;1718 |; 0 &;8163 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 1268 ( 0 ^;1268 !; 0 ?;1268 :)
% Comments :
%------------------------------------------------------------------------------
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(b_decl,type,
b: $i ).
thf(d_decl,type,
d: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(c_decl,type,
c: $i ).
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(defined_decl,type,
defined: $i > $o ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(19,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(68,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)],[19]) ).
thf(69,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)],[68]) ).
thf(14,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(58,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(59,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(cnf,[status(esa)],[58]) ).
thf(1,negated_conjecture,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
thf(35,plain,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(39,plain,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(1822,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,39]) ).
thf(1823,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[1822]) ).
thf(1824,plain,
( ~ ( b @ defined )
| ( b @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[1823:[bind(A,$thf( b ))]]) ).
thf(33,axiom,
b @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
thf(93,plain,
b @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(2173,plain,
( ~ $true
| ( b @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[1824,93]) ).
thf(2174,plain,
b @ multiplicative_inverse @ defined,
inference(simp,[status(thm)],[2173]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(62,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(2777,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2174,63]) ).
thf(2778,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2777]) ).
thf(2779,plain,
additive_identity @ ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2778:[bind(A,$thf( b @ multiplicative_inverse ))]]) ).
thf(10,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(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(5383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2779,52]) ).
thf(5384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5383]) ).
thf(5385,plain,
additive_identity @ ( b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5384:[bind(A,$thf( b @ multiplicative_inverse )),bind(B,$thf( b @ multiplicative_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(7,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)],[7]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(44,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[44]) ).
thf(125,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[46,45]) ).
thf(126,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[125]) ).
thf(127,plain,
multiplicative_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(94,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(95,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(12186,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[127,95]) ).
thf(12187,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12186]) ).
thf(12188,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12187:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(31,axiom,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(89,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(90,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[89]) ).
thf(15604,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12188,90]) ).
thf(15605,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15604]) ).
thf(15618,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[15605]) ).
thf(15628,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[15618]) ).
thf(20,axiom,
a @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(70,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(113,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[70,45]) ).
thf(114,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[113]) ).
thf(115,plain,
a @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( a ))]]) ).
thf(2610,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[115,63]) ).
thf(2611,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2610]) ).
thf(2612,plain,
additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2611:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(136,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[115,45]) ).
thf(137,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
a @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(2658,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,63]) ).
thf(2659,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2658]) ).
thf(2660,plain,
additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2659:[bind(A,$thf( a ))]]) ).
thf(3659,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)],[2660,52]) ).
thf(3660,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[3659]) ).
thf(3661,plain,
additive_identity @ ( a @ additive_inverse @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[3660:[bind(A,$thf( a )),bind(B,$thf( a @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(11,axiom,
c @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
thf(53,plain,
c @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(116,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,45]) ).
thf(117,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[116]) ).
thf(118,plain,
c @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( c ))]]) ).
thf(139,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[118,45]) ).
thf(140,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
c @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( c @ additive_inverse ))]]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(79,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(80,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(6283,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[141,80]) ).
thf(6284,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6283]) ).
thf(6285,plain,
c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6284:[bind(A,$thf( c @ additive_inverse @ additive_inverse ))]]) ).
thf(30,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(87,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(23,axiom,
d @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
thf(74,plain,
d @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,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(47,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)],[8]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( ( d @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[74,48]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( ( d @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( A )),bind(B,$thf( d ))]]) ).
thf(15812,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[74,156]) ).
thf(15813,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[15812]) ).
thf(15814,plain,
( ( d @ ( d @ less_or_equal ) )
| ( d @ ( d @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[15813:[bind(A,$thf( d ))]]) ).
thf(16092,plain,
d @ ( d @ less_or_equal ),
inference(simp,[status(thm)],[15814]) ).
thf(24,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(75,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)],[24]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(2,negated_conjecture,
~ ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_6) ).
thf(36,plain,
~ ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(40,plain,
~ ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(5166,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[76,40]) ).
thf(5167,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[5166]) ).
thf(5168,plain,
( ~ ( d @ ( additive_identity @ less_or_equal ) )
| ~ ( additive_identity @ ( d @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[5167:[bind(A,$thf( d )),bind(B,$thf( additive_identity ))]]) ).
thf(1877,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,40]) ).
thf(1878,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[1877]) ).
thf(1879,plain,
( ~ ( d @ defined )
| ( d @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[1878:[bind(A,$thf( d ))]]) ).
thf(2531,plain,
( ~ $true
| ( d @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[1879,74]) ).
thf(2532,plain,
d @ multiplicative_inverse @ defined,
inference(simp,[status(thm)],[2531]) ).
thf(2533,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2532,45]) ).
thf(2534,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2533]) ).
thf(2535,plain,
d @ multiplicative_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2534:[bind(A,$thf( d @ multiplicative_inverse ))]]) ).
thf(2570,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2535,45]) ).
thf(2571,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2570]) ).
thf(2572,plain,
d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2571:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(2844,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2572,45]) ).
thf(2845,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2844]) ).
thf(2846,plain,
d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2845:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(4391,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2846,45]) ).
thf(4392,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4391]) ).
thf(4393,plain,
d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4392:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(5818,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4393,45]) ).
thf(5819,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[5818]) ).
thf(5820,plain,
d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[5819:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2780,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[63,40]) ).
thf(2781,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[2780]) ).
thf(2806,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A != d )
| ( ( A @ additive_inverse )
!= additive_identity )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[2781]) ).
thf(2834,plain,
( ( ( d @ additive_inverse )
!= additive_identity )
| ~ ( d @ defined ) ),
inference(simp,[status(thm)],[2806]) ).
thf(3039,plain,
( ( ( d @ additive_inverse )
!= additive_identity )
| ~ $true ),
inference(rewrite,[status(thm)],[2834,74]) ).
thf(3040,plain,
( ( d @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[3039]) ).
thf(1758,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[46,59]) ).
thf(1759,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[1758]) ).
thf(1760,plain,
( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[1759:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(2097,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)],[1760,52]) ).
thf(2098,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2097]) ).
thf(2099,plain,
( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[2098:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(2175,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2174,45]) ).
thf(2176,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2175]) ).
thf(2177,plain,
b @ multiplicative_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2176:[bind(A,$thf( b @ multiplicative_inverse ))]]) ).
thf(2212,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2177,45]) ).
thf(2213,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2212]) ).
thf(2214,plain,
b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2213:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(2358,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2214,45]) ).
thf(2359,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2358]) ).
thf(2360,plain,
b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2359:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2395,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2360,45]) ).
thf(2396,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2395]) ).
thf(2397,plain,
b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2396:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( ( A @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ( B @ additive_inverse @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[45,45]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( A @ additive_inverse @ defined )
!= ( B @ defined ) )
| ( B @ additive_inverse @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse @ defined )
| ~ ( A @ defined ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( C )),bind(B,$thf( C @ additive_inverse ))]]) ).
thf(131,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[121]) ).
thf(14239,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2397,131]) ).
thf(14240,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14239]) ).
thf(14241,plain,
b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14240:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(6212,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[138,80]) ).
thf(6213,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6212]) ).
thf(6214,plain,
a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6213:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(21,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(71,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(122,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[71,45]) ).
thf(123,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[122]) ).
thf(124,plain,
additive_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( additive_identity ))]]) ).
thf(142,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[124,45]) ).
thf(143,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
additive_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(12087,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[144,95]) ).
thf(12088,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12087]) ).
thf(12089,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12088:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(2638,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,63]) ).
thf(2639,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2638]) ).
thf(2640,plain,
additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2639:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(2919,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2640,40]) ).
thf(2920,plain,
( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[2919]) ).
thf(2931,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != d )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[2920]) ).
thf(2953,plain,
( ( multiplicative_identity != d )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[2931]) ).
thf(2772,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[127,63]) ).
thf(2773,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2772]) ).
thf(2774,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2773:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(5295,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)],[2774,52]) ).
thf(5296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5295]) ).
thf(5297,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5296:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(329,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[141,45]) ).
thf(330,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[329]) ).
thf(331,plain,
c @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( c @ additive_inverse @ additive_inverse ))]]) ).
thf(629,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[331,45]) ).
thf(630,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[629]) ).
thf(631,plain,
c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[630:[bind(A,$thf( c @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1065,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[631,45]) ).
thf(1066,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1065]) ).
thf(1067,plain,
c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1066:[bind(A,$thf( c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1495,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1067,45]) ).
thf(1496,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1495]) ).
thf(1497,plain,
c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1496:[bind(A,$thf( c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ less_or_equal ) )
!= ( B @ ( A @ less_or_equal ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ less_or_equal ) ) ),
inference(eqfactor_ordered,[status(thm)],[48]) ).
thf(224,plain,
! [A: $i] :
( ~ ( A @ defined )
| ~ ( A @ defined )
| ( A @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( B ))]]) ).
thf(233,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(31576,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[127,233]) ).
thf(31577,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31576]) ).
thf(31578,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31577:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(13,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(56,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15587,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12188,40]) ).
thf(15588,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15587]) ).
thf(15621,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= additive_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= d )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[15588]) ).
thf(15632,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= additive_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= d ) ),
inference(simp,[status(thm)],[15621]) ).
thf(4191,plain,
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3661,40]) ).
thf(4192,plain,
( ( additive_identity @ ( a @ additive_inverse @ ( a @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4191]) ).
thf(4202,plain,
( ( additive_identity != additive_identity )
| ( ( a @ additive_inverse )
!= d )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[4192]) ).
thf(4220,plain,
( ( ( a @ additive_inverse )
!= d )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[4202]) ).
thf(2432,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2397,45]) ).
thf(2433,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2432]) ).
thf(2434,plain,
b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2433:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[124,48]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(174,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( additive_identity @ additive_inverse @ less_or_equal ) )
| ( additive_identity @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ additive_inverse ))]]) ).
thf(1778,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[70,59]) ).
thf(1779,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[1778]) ).
thf(1780,plain,
( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
| ( a @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[1779:[bind(A,$thf( a ))]]) ).
thf(5575,plain,
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( a @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1780,39]) ).
thf(5576,plain,
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ( a @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5575]) ).
thf(5610,plain,
( ( additive_identity != additive_identity )
| ( a != b )
| ( additive_identity != additive_identity )
| ( a @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5576]) ).
thf(5631,plain,
( ( a != b )
| ( a @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5610]) ).
thf(7942,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( a != b ) ),
inference(paramod_ordered,[status(thm)],[5631,45]) ).
thf(7943,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( a != b ) ),
inference(simp,[status(thm)],[7942]) ).
thf(7944,plain,
( ( a @ multiplicative_inverse @ additive_inverse @ defined )
| ( a != b ) ),
inference(pattern_uni,[status(thm)],[7943:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
thf(5,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(42,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)],[5]) ).
thf(240,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[127,45]) ).
thf(241,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[240]) ).
thf(242,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(501,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[242,45]) ).
thf(502,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[501]) ).
thf(503,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[502:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(31434,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[503,233]) ).
thf(31435,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31434]) ).
thf(31436,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31435:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2673,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[141,63]) ).
thf(2674,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2673]) ).
thf(2675,plain,
additive_identity @ ( c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2674:[bind(A,$thf( c @ additive_inverse @ additive_inverse ))]]) ).
thf(30147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2675,52]) ).
thf(30148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[30147]) ).
thf(30149,plain,
additive_identity @ ( c @ additive_inverse @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[30148:[bind(A,$thf( c @ additive_inverse @ additive_inverse )),bind(B,$thf( c @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(3,negated_conjecture,
d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
thf(37,plain,
d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6289,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,80]) ).
thf(6290,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6289]) ).
thf(6291,plain,
additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6290:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(2641,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,63]) ).
thf(2642,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2641]) ).
thf(2643,plain,
additive_identity @ ( b @ ( b @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2642:[bind(A,$thf( b ))]]) ).
thf(2972,plain,
( ( ( additive_identity @ ( b @ ( b @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2643,39]) ).
thf(2973,plain,
( ( additive_identity @ ( b @ ( b @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[2972]) ).
thf(3015,plain,
( ( additive_identity != additive_identity )
| ( b != b )
| ( ( b @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[2973]) ).
thf(3029,plain,
( ( b @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[3015]) ).
thf(1790,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,59]) ).
thf(1791,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[1790]) ).
thf(1792,plain,
( ( additive_identity @ ( c @ ( additive_identity @ sum ) ) )
| ( c @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[1791:[bind(A,$thf( c ))]]) ).
thf(128,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[93,45]) ).
thf(129,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[128]) ).
thf(130,plain,
b @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( b ))]]) ).
thf(250,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[130,45]) ).
thf(251,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[250]) ).
thf(252,plain,
b @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(6272,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[252,80]) ).
thf(6273,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6272]) ).
thf(6274,plain,
b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6273:[bind(A,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(31591,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[2532,233]) ).
thf(31592,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31591]) ).
thf(31593,plain,
d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31592:[bind(A,$thf( d @ multiplicative_inverse ))]]) ).
thf(6421,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[242,80]) ).
thf(6422,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6421]) ).
thf(6423,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6422:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(12045,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,95]) ).
thf(12046,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12045]) ).
thf(12047,plain,
c @ ( c @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12046:[bind(A,$thf( c ))]]) ).
thf(12867,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( c @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12047,52]) ).
thf(12868,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( c @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12867]) ).
thf(12869,plain,
c @ ( additive_identity @ ( c @ sum ) ),
inference(pattern_uni,[status(thm)],[12868:[bind(A,$thf( c )),bind(B,$thf( additive_identity )),bind(C,$thf( c ))]]) ).
thf(6365,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[2535,80]) ).
thf(6366,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6365]) ).
thf(6367,plain,
d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6366:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(20470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6367,88]) ).
thf(20471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[20470]) ).
thf(20472,plain,
d @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ ( d @ multiplicative_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[20471:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( d @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(31540,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[2535,233]) ).
thf(31541,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31540]) ).
thf(31542,plain,
d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31541:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(12194,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2532,95]) ).
thf(12195,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12194]) ).
thf(12196,plain,
d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12195:[bind(A,$thf( d @ multiplicative_inverse ))]]) ).
thf(16174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12196,52]) ).
thf(16175,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[16174]) ).
thf(16176,plain,
d @ multiplicative_inverse @ ( additive_identity @ ( d @ multiplicative_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[16175:[bind(A,$thf( d @ multiplicative_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( d @ multiplicative_inverse ))]]) ).
thf(11984,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,95]) ).
thf(11985,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11984]) ).
thf(11986,plain,
multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[11985:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(15565,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12188,39]) ).
thf(15566,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15565]) ).
thf(15622,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= additive_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[15566]) ).
thf(15633,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= additive_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= b ) ),
inference(simp,[status(thm)],[15622]) ).
thf(12130,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[130,95]) ).
thf(12131,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12130]) ).
thf(12132,plain,
b @ additive_inverse @ ( b @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12131:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(15304,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ additive_inverse @ ( b @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12132,52]) ).
thf(15305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ additive_inverse @ ( b @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[15304]) ).
thf(15306,plain,
b @ additive_inverse @ ( additive_identity @ ( b @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[15305:[bind(A,$thf( b @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( b @ additive_inverse ))]]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( c @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[53,48]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( ( c @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(168,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( A )),bind(B,$thf( c ))]]) ).
thf(17543,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[93,168]) ).
thf(17544,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[17543]) ).
thf(17545,plain,
( ( b @ ( c @ less_or_equal ) )
| ( c @ ( b @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[17544:[bind(A,$thf( b ))]]) ).
thf(18373,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( additive_identity @ additive_inverse @ less_or_equal ) )
| ( additive_identity @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[124,174]) ).
thf(18374,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( additive_identity @ additive_inverse @ less_or_equal ) )
| ( additive_identity @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[18373]) ).
thf(18375,plain,
( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ less_or_equal ) )
| ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[18374:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(18624,plain,
additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ less_or_equal ),
inference(simp,[status(thm)],[18375]) ).
thf(663,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[503,45]) ).
thf(664,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[663]) ).
thf(665,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[664:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1113,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)],[665,45]) ).
thf(1114,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1113]) ).
thf(1115,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1114:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(12021,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,95]) ).
thf(12022,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12021]) ).
thf(12023,plain,
a @ ( a @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12022:[bind(A,$thf( a ))]]) ).
thf(12783,plain,
( ( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12023,39]) ).
thf(12784,plain,
( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12783]) ).
thf(12841,plain,
( ( a != additive_identity )
| ( a != b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12784]) ).
thf(12864,plain,
( ( a != additive_identity )
| ( a != b ) ),
inference(simp,[status(thm)],[12841]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(cnf,[status(esa)],[56]) ).
thf(25,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(77,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)],[25]) ).
thf(78,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)],[77]) ).
thf(31473,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[144,233]) ).
thf(31474,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31473]) ).
thf(31475,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31474:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(270,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[138,45]) ).
thf(271,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(555,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[272,45]) ).
thf(556,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[555]) ).
thf(557,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[556:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1041,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)],[557,45]) ).
thf(1042,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1041]) ).
thf(1043,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1042:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1464,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)],[1043,45]) ).
thf(1465,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1464]) ).
thf(1466,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1465:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2005,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)],[1466,45]) ).
thf(2006,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2005]) ).
thf(2007,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2006:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[46,48]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(216,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( multiplicative_identity @ less_or_equal ) )
| ( multiplicative_identity @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( A )),bind(B,$thf( multiplicative_identity ))]]) ).
thf(19641,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6285,88]) ).
thf(19642,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[19641]) ).
thf(19643,plain,
c @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( c @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[19642:[bind(A,$thf( c @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( c @ additive_inverse @ additive_inverse ))]]) ).
thf(15800,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[46,156]) ).
thf(15801,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[15800]) ).
thf(15802,plain,
( ( multiplicative_identity @ ( d @ less_or_equal ) )
| ( d @ ( multiplicative_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[15801:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(12150,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2535,95]) ).
thf(12151,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12150]) ).
thf(12152,plain,
d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12151:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(23998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12152,52]) ).
thf(23999,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[23998]) ).
thf(24000,plain,
d @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ ( d @ multiplicative_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[23999:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( d @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(18,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_2) ).
thf(66,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(67,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)],[66]) ).
thf(4,negated_conjecture,
~ ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_8) ).
thf(38,plain,
~ ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(41,plain,
~ ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ),
inference(polarity_switch,[status(thm)],[38]) ).
thf(286,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) )
| ~ $true
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[67,41]) ).
thf(287,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c @ ( b @ multiply ) @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( d @ ( B @ product ) ) )
| ~ ( C @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( a )),bind(B,$thf( d )),bind(C,$thf( c @ ( b @ multiply ) )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G ))]]) ).
thf(299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c @ ( b @ multiply ) @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( d @ ( B @ product ) ) )
| ~ ( C @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( d @ ( B @ product ) ) )
!= ( C @ ( d @ ( A @ product ) ) ) )
| ~ ( c @ ( b @ multiply ) @ ( D @ ( C @ sum ) ) )
| ~ ( C @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[299]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ~ ( c @ ( b @ multiply ) @ ( B @ ( B @ sum ) ) )
| ~ ( B @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( A @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ~ ( c @ ( b @ multiply ) @ ( B @ ( B @ sum ) ) )
| ~ ( B @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[318]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ) )
!= ( B @ ( d @ ( A @ product ) ) ) )
| ~ ( c @ ( b @ multiply ) @ ( B @ ( B @ sum ) ) )
| ~ $true
| ~ ( a @ ( A @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,327]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ) )
!= ( B @ ( d @ ( A @ product ) ) ) )
| ~ ( c @ ( b @ multiply ) @ ( B @ ( B @ sum ) ) )
| ~ ( a @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[339]) ).
thf(344,plain,
! [B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= B )
| ( ( b @ multiplicative_inverse )
!= d )
| ( a != A )
| ~ ( c @ ( b @ multiply ) @ ( B @ ( B @ sum ) ) )
| ~ ( a @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(346,plain,
( ( ( b @ multiplicative_inverse )
!= d )
| ~ ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
| ~ ( a @ ( a @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[344]) ).
thf(347,plain,
( ~ $true
| ( ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
!= ( a @ ( a @ ( a @ sum ) ) ) )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( a @ ( a @ ( a @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[346]) ).
thf(348,plain,
( ( ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
!= ( a @ ( a @ ( a @ sum ) ) ) )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( a @ ( a @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(28,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(83,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)],[28]) ).
thf(84,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(11969,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[115,95]) ).
thf(11970,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11969]) ).
thf(11971,plain,
a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[11970:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(15,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(60,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)],[15]) ).
thf(61,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)],[60]) ).
thf(12081,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[118,95]) ).
thf(12082,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12081]) ).
thf(12083,plain,
c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12082:[bind(A,$thf( c @ additive_inverse ))]]) ).
thf(14810,plain,
( ( ( c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12083,39]) ).
thf(14811,plain,
( ( c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[14810]) ).
thf(14855,plain,
( ( ( c @ additive_inverse )
!= additive_identity )
| ( ( c @ additive_inverse )
!= b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[14811]) ).
thf(14874,plain,
( ( ( c @ additive_inverse )
!= additive_identity )
| ( ( c @ additive_inverse )
!= b ) ),
inference(simp,[status(thm)],[14855]) ).
thf(2797,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2177,63]) ).
thf(2798,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2797]) ).
thf(2799,plain,
additive_identity @ ( b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2798:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(12,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(54,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( c @ ( b @ multiply ) @ ( D @ ( C @ sum ) ) )
!= ( a @ ( B @ ( A @ sum ) ) ) )
| ~ ( D @ ( d @ ( B @ product ) ) )
| ~ ( C @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[299]) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c @ ( b @ multiply ) )
!= a )
| ( D != B )
| ( C != A )
| ~ ( D @ ( d @ ( B @ product ) ) )
| ~ ( C @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( B @ ( d @ ( B @ product ) ) )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(582,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( d @ ( B @ product ) ) )
!= ( A @ ( d @ ( A @ product ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[323]) ).
thf(583,plain,
! [A: $i] :
( ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( A @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[582:[bind(A,$thf( B ))]]) ).
thf(588,plain,
! [A: $i] :
( ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[583]) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( a @ ( C @ ( C @ sum ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( C @ ( d @ ( C @ product ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[55,588]) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( a @ ( C @ ( C @ sum ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( C @ ( d @ ( C @ product ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[951]) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= a )
| ( B != C )
| ( A != C )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( C @ ( d @ ( C @ product ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[952]) ).
thf(1021,plain,
! [A: $i] :
( ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ ( A @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[978]) ).
thf(1600,plain,
! [A: $i] :
( ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[1021]) ).
thf(14158,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4393,131]) ).
thf(14159,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14158]) ).
thf(14160,plain,
d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14159:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2694,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[118,63]) ).
thf(2695,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2694]) ).
thf(2696,plain,
additive_identity @ ( c @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2695:[bind(A,$thf( c @ additive_inverse ))]]) ).
thf(4922,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( c @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2696,52]) ).
thf(4923,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( c @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[4922]) ).
thf(4924,plain,
additive_identity @ ( c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4923:[bind(A,$thf( c @ additive_inverse )),bind(B,$thf( c @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(29,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(85,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)],[29]) ).
thf(30683,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2799,52]) ).
thf(30684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[30683]) ).
thf(30685,plain,
additive_identity @ ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[30684:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse )),bind(B,$thf( b @ multiplicative_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(4962,plain,
( ( ( additive_identity @ ( c @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2696,40]) ).
thf(4963,plain,
( ( additive_identity @ ( c @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4962]) ).
thf(4979,plain,
( ( additive_identity != additive_identity )
| ( ( c @ additive_inverse )
!= d )
| ( ( c @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4963]) ).
thf(4999,plain,
( ( ( c @ additive_inverse )
!= d )
| ( ( c @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4979]) ).
thf(16203,plain,
( ( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12196,39]) ).
thf(16204,plain,
( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[16203]) ).
thf(16245,plain,
( ( ( d @ multiplicative_inverse )
!= additive_identity )
| ( ( d @ multiplicative_inverse )
!= b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[16204]) ).
thf(16279,plain,
( ( ( d @ multiplicative_inverse )
!= additive_identity )
| ( ( d @ multiplicative_inverse )
!= b ) ),
inference(simp,[status(thm)],[16245]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[127,48]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(248,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( multiplicative_identity @ additive_inverse @ less_or_equal ) )
| ( multiplicative_identity @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( A )),bind(B,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(2724,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[130,63]) ).
thf(2725,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2724]) ).
thf(2726,plain,
additive_identity @ ( b @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2725:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(5010,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2726,52]) ).
thf(5011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5010]) ).
thf(5012,plain,
additive_identity @ ( b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5011:[bind(A,$thf( b @ additive_inverse )),bind(B,$thf( b @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(12098,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,95]) ).
thf(12099,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12098]) ).
thf(12100,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12099:[bind(A,$thf( additive_identity ))]]) ).
thf(6158,plain,
( ( ( additive_identity @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( c @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1792,40]) ).
thf(6159,plain,
( ( ( additive_identity @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[6158]) ).
thf(6182,plain,
( ( additive_identity != additive_identity )
| ( c != d )
| ( additive_identity != additive_identity )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[6159]) ).
thf(6200,plain,
( ( c != d )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[6182]) ).
thf(484,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[144,45]) ).
thf(485,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[484]) ).
thf(486,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(646,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[486,45]) ).
thf(647,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[646]) ).
thf(648,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[647:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1089,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)],[648,45]) ).
thf(1090,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1089]) ).
thf(1091,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1090:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[115,48]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( a @ additive_inverse @ less_or_equal ) )
| ( a @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( A )),bind(B,$thf( a @ additive_inverse ))]]) ).
thf(14908,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( a @ additive_inverse @ less_or_equal ) )
| ( a @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[115,150]) ).
thf(14909,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( a @ additive_inverse @ less_or_equal ) )
| ( a @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[14908]) ).
thf(14910,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ less_or_equal ) )
| ( a @ additive_inverse @ ( a @ additive_inverse @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[14909:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(15206,plain,
a @ additive_inverse @ ( a @ additive_inverse @ less_or_equal ),
inference(simp,[status(thm)],[14910]) ).
thf(596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( a @ ( E @ ( D @ sum ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( E @ ( d @ ( E @ product ) ) )
| ~ ( D @ ( d @ ( D @ product ) ) )
| ~ $true
| ~ ( C @ ( A @ ( B @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,323]) ).
thf(597,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( a @ ( E @ ( D @ sum ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( E @ ( d @ ( E @ product ) ) )
| ~ ( D @ ( d @ ( D @ product ) ) )
| ~ ( C @ ( A @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[596]) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( B @ ( d @ ( B @ product ) ) )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( A @ ( B @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( a )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(16242,plain,
( ( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12196,90]) ).
thf(16243,plain,
( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[16242]) ).
thf(16257,plain,
( ( ( d @ multiplicative_inverse )
!= multiplicative_identity )
| ( ( d @ multiplicative_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[16243]) ).
thf(16264,plain,
( ( ( d @ multiplicative_inverse )
!= multiplicative_identity )
| ( ( d @ multiplicative_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[16257]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[71,48]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( A )),bind(B,$thf( additive_identity ))]]) ).
thf(2702,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,63]) ).
thf(2703,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2702]) ).
thf(2704,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2703:[bind(A,$thf( additive_identity ))]]) ).
thf(3814,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)],[2704,52]) ).
thf(3815,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[3814]) ).
thf(3816,plain,
additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[3815:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( ( b @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[93,48]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( ( b @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(222,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( b @ less_or_equal ) )
| ( b @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( A )),bind(B,$thf( b ))]]) ).
thf(24914,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( b @ less_or_equal ) )
| ( b @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[93,222]) ).
thf(24915,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( b @ less_or_equal ) )
| ( b @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[24914]) ).
thf(24916,plain,
( ( b @ ( b @ less_or_equal ) )
| ( b @ ( b @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[24915:[bind(A,$thf( b ))]]) ).
thf(25212,plain,
b @ ( b @ less_or_equal ),
inference(simp,[status(thm)],[24916]) ).
thf(5599,plain,
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( a @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1780,40]) ).
thf(5600,plain,
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ( a @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5599]) ).
thf(5613,plain,
( ( additive_identity != additive_identity )
| ( a != d )
| ( additive_identity != additive_identity )
| ( a @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5600]) ).
thf(5634,plain,
( ( a != d )
| ( a @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[5613]) ).
thf(7992,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( a != d ) ),
inference(paramod_ordered,[status(thm)],[5634,45]) ).
thf(7993,plain,
! [A: $i] :
( ( ( a @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( a != d ) ),
inference(simp,[status(thm)],[7992]) ).
thf(7994,plain,
( ( a @ multiplicative_inverse @ additive_inverse @ defined )
| ( a != d ) ),
inference(pattern_uni,[status(thm)],[7993:[bind(A,$thf( a @ multiplicative_inverse ))]]) ).
thf(2888,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)],[2640,52]) ).
thf(2889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[2888]) ).
thf(2890,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[2889:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( multiplicative_identity @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(2676,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,63]) ).
thf(2677,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2676]) ).
thf(2678,plain,
additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2677:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(4834,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)],[2678,52]) ).
thf(4835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[4834]) ).
thf(4836,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4835:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(32,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(91,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)],[32]) ).
thf(92,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)],[91]) ).
thf(2661,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[252,63]) ).
thf(2662,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2661]) ).
thf(2663,plain,
additive_identity @ ( b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2662:[bind(A,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(110,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[74,45]) ).
thf(111,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
d @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( d ))]]) ).
thf(12158,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,95]) ).
thf(12159,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12158]) ).
thf(12160,plain,
d @ additive_inverse @ ( d @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12159:[bind(A,$thf( d @ additive_inverse ))]]) ).
thf(15420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ additive_inverse @ ( d @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12160,52]) ).
thf(15421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ additive_inverse @ ( d @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[15420]) ).
thf(15422,plain,
d @ additive_inverse @ ( additive_identity @ ( d @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[15421:[bind(A,$thf( d @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( d @ additive_inverse ))]]) ).
thf(1654,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53,1600]) ).
thf(1655,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[1654]) ).
thf(1656,plain,
( ( ( c @ ( c @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( c @ ( d @ ( c @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[1655:[bind(A,$thf( c ))]]) ).
thf(518,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[252,45]) ).
thf(519,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[518]) ).
thf(520,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(680,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[520,45]) ).
thf(681,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[680]) ).
thf(682,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[681:[bind(A,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2626,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)],[242,63]) ).
thf(2627,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2626]) ).
thf(2628,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2627:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(12189,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2174,95]) ).
thf(12190,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12189]) ).
thf(12191,plain,
b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12190:[bind(A,$thf( b @ multiplicative_inverse ))]]) ).
thf(15720,plain,
( ( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12191,90]) ).
thf(15721,plain,
( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15720]) ).
thf(15730,plain,
( ( ( b @ multiplicative_inverse )
!= multiplicative_identity )
| ( ( b @ multiplicative_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[15721]) ).
thf(15756,plain,
( ( ( b @ multiplicative_inverse )
!= multiplicative_identity )
| ( ( b @ multiplicative_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[15730]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_multiplication) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(2607,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[138,63]) ).
thf(2608,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2607]) ).
thf(2609,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2608:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(3690,plain,
( ( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2660,40]) ).
thf(3691,plain,
( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[3690]) ).
thf(3708,plain,
( ( additive_identity != additive_identity )
| ( a != d )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3691]) ).
thf(3731,plain,
( ( a != d )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3708]) ).
thf(132,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[112,45]) ).
thf(133,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[132]) ).
thf(134,plain,
d @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( d @ additive_inverse ))]]) ).
thf(260,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[134,45]) ).
thf(261,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[260]) ).
thf(262,plain,
d @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( d @ additive_inverse @ additive_inverse ))]]) ).
thf(535,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[262,45]) ).
thf(536,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[535]) ).
thf(537,plain,
d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[536:[bind(A,$thf( d @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(716,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[537,45]) ).
thf(717,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[716]) ).
thf(718,plain,
d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1433,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[718,45]) ).
thf(1434,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1433]) ).
thf(1435,plain,
d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1434:[bind(A,$thf( d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1968,plain,
! [A: $i] :
( ( ( d @ 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)],[1435,45]) ).
thf(1969,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1968]) ).
thf(1970,plain,
d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1969:[bind(A,$thf( d @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(6317,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[118,80]) ).
thf(6318,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6317]) ).
thf(6319,plain,
c @ additive_inverse @ ( c @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6318:[bind(A,$thf( c @ additive_inverse ))]]) ).
thf(10150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ additive_inverse @ ( c @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6319,88]) ).
thf(10151,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ additive_inverse @ ( c @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10150]) ).
thf(10152,plain,
c @ additive_inverse @ ( multiplicative_identity @ ( c @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10151:[bind(A,$thf( c @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( c @ additive_inverse ))]]) ).
thf(2104,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1760,39]) ).
thf(2105,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2104]) ).
thf(2150,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != b )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2105]) ).
thf(2161,plain,
( ( multiplicative_identity != b )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2150]) ).
thf(3117,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != b ) ),
inference(paramod_ordered,[status(thm)],[2161,45]) ).
thf(3118,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != b ) ),
inference(simp,[status(thm)],[3117]) ).
thf(3119,plain,
( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ defined )
| ( multiplicative_identity != b ) ),
inference(pattern_uni,[status(thm)],[3118:[bind(A,$thf( multiplicative_identity @ multiplicative_inverse ))]]) ).
thf(6407,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[2174,80]) ).
thf(6408,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6407]) ).
thf(6409,plain,
b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6408:[bind(A,$thf( b @ multiplicative_inverse ))]]) ).
thf(10124,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6409,88]) ).
thf(10125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10124]) ).
thf(10126,plain,
b @ multiplicative_inverse @ ( multiplicative_identity @ ( b @ multiplicative_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10125:[bind(A,$thf( b @ multiplicative_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( b @ multiplicative_inverse ))]]) ).
thf(14781,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12083,52]) ).
thf(14782,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[14781]) ).
thf(14783,plain,
c @ additive_inverse @ ( additive_identity @ ( c @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[14782:[bind(A,$thf( c @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( c @ additive_inverse ))]]) ).
thf(6269,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,80]) ).
thf(6270,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6269]) ).
thf(6271,plain,
a @ ( a @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6270:[bind(A,$thf( a ))]]) ).
thf(10118,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)],[6271,88]) ).
thf(10119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10118]) ).
thf(10120,plain,
a @ ( multiplicative_identity @ ( a @ product ) ),
inference(pattern_uni,[status(thm)],[10119:[bind(A,$thf( a )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a ))]]) ).
thf(6302,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,80]) ).
thf(6303,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6302]) ).
thf(6304,plain,
d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6303:[bind(A,$thf( d @ additive_inverse @ additive_inverse ))]]) ).
thf(19865,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[46,192]) ).
thf(19866,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[19865]) ).
thf(19867,plain,
( ( multiplicative_identity @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( multiplicative_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[19866:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(12221,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[242,95]) ).
thf(12222,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12221]) ).
thf(12223,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12222:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(1642,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,1600]) ).
thf(1643,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[1642]) ).
thf(1644,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( a @ ( d @ ( a @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[1643:[bind(A,$thf( a ))]]) ).
thf(4786,plain,
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2612,40]) ).
thf(4787,plain,
( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4786]) ).
thf(4802,plain,
( ( additive_identity != additive_identity )
| ( ( a @ additive_inverse )
!= d )
| ( ( a @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4787]) ).
thf(4814,plain,
( ( ( a @ additive_inverse )
!= d )
| ( ( a @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4802]) ).
thf(6323,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[144,80]) ).
thf(6324,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6323]) ).
thf(6325,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6324:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(20357,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)],[6325,88]) ).
thf(20358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[20357]) ).
thf(20359,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[20358:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(12824,plain,
( ( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12023,90]) ).
thf(12825,plain,
( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12824]) ).
thf(12837,plain,
( ( multiplicative_identity != a )
| ( a != additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12825]) ).
thf(12859,plain,
( ( multiplicative_identity != a )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[12837]) ).
thf(4322,plain,
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3816,39]) ).
thf(4323,plain,
( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4322]) ).
thf(4365,plain,
( ( additive_identity != additive_identity )
| ( ( additive_identity @ additive_inverse )
!= b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[4323]) ).
thf(4384,plain,
( ( additive_identity @ additive_inverse )
!= b ),
inference(simp,[status(thm)],[4365]) ).
thf(14617,plain,
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11971,90]) ).
thf(14618,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[14617]) ).
thf(14630,plain,
( ( ( a @ additive_inverse )
!= multiplicative_identity )
| ( ( a @ additive_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[14618]) ).
thf(14655,plain,
( ( ( a @ additive_inverse )
!= multiplicative_identity )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[14630]) ).
thf(12349,plain,
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11986,90]) ).
thf(12350,plain,
( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12349]) ).
thf(12359,plain,
( ( multiplicative_identity != multiplicative_identity )
| ( multiplicative_identity != additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12350]) ).
thf(12378,plain,
multiplicative_identity != additive_identity,
inference(simp,[status(thm)],[12359]) ).
thf(14600,plain,
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11971,40]) ).
thf(14601,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[14600]) ).
thf(14624,plain,
( ( ( a @ additive_inverse )
!= additive_identity )
| ( ( a @ additive_inverse )
!= d )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[14601]) ).
thf(14649,plain,
( ( ( a @ additive_inverse )
!= additive_identity )
| ( ( a @ additive_inverse )
!= d ) ),
inference(simp,[status(thm)],[14624]) ).
thf(12057,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,95]) ).
thf(12058,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12057]) ).
thf(12059,plain,
d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12058:[bind(A,$thf( d @ additive_inverse @ additive_inverse ))]]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( ( a @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[70,48]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( ( a @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(162,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( A )),bind(B,$thf( a ))]]) ).
thf(16720,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[53,162]) ).
thf(16721,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[16720]) ).
thf(16722,plain,
( ( c @ ( a @ less_or_equal ) )
| ( a @ ( c @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[16721:[bind(A,$thf( c ))]]) ).
thf(6286,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,80]) ).
thf(6287,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6286]) ).
thf(6288,plain,
c @ ( c @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6287:[bind(A,$thf( c ))]]) ).
thf(10156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( c @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6288,88]) ).
thf(10157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( c @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10156]) ).
thf(10158,plain,
c @ ( multiplicative_identity @ ( c @ product ) ),
inference(pattern_uni,[status(thm)],[10157:[bind(A,$thf( c )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( c ))]]) ).
thf(12003,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[74,95]) ).
thf(12004,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12003]) ).
thf(12005,plain,
d @ ( d @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12004:[bind(A,$thf( d ))]]) ).
thf(12896,plain,
( ( ( c @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12047,39]) ).
thf(12897,plain,
( ( c @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12896]) ).
thf(12940,plain,
( ( c != additive_identity )
| ( c != b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12897]) ).
thf(12962,plain,
( ( c != additive_identity )
| ( c != b ) ),
inference(simp,[status(thm)],[12940]) ).
thf(6215,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[115,80]) ).
thf(6216,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6215]) ).
thf(6217,plain,
a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6216:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(10141,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)],[6217,88]) ).
thf(10142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10141]) ).
thf(10143,plain,
a @ additive_inverse @ ( multiplicative_identity @ ( a @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10142:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a @ additive_inverse ))]]) ).
thf(10067,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,88]) ).
thf(10068,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10067]) ).
thf(10069,plain,
d @ multiplicative_inverse @ ( c @ multiply ) @ ( a @ ( b @ multiplicative_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10068:[bind(A,$thf( b @ multiplicative_inverse )),bind(B,$thf( a )),bind(C,$thf( d @ multiplicative_inverse @ ( c @ multiply ) ))]]) ).
thf(349,plain,
( ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( a @ ( a @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(350,plain,
( ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( a @ ( a @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(895,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( a @ ( a @ ( a @ sum ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[55,350]) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( a @ ( a @ ( a @ sum ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[895]) ).
thf(986,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= a )
| ( B != a )
| ( A != a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[896]) ).
thf(1030,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( a @ defined )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[986]) ).
thf(1168,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[1030]) ).
thf(1169,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ $true ),
inference(rewrite,[status(thm)],[1168,70]) ).
thf(1170,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d ) ),
inference(simp,[status(thm)],[1169]) ).
thf(2747,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,63]) ).
thf(2748,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2747]) ).
thf(2749,plain,
additive_identity @ ( d @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2748:[bind(A,$thf( d @ additive_inverse ))]]) ).
thf(5207,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2749,52]) ).
thf(5208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5207]) ).
thf(5209,plain,
additive_identity @ ( d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5208:[bind(A,$thf( d @ additive_inverse )),bind(B,$thf( d @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(953,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[55,40]) ).
thf(954,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[953]) ).
thf(985,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= additive_identity )
| ( B != d )
| ( A != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[954]) ).
thf(1029,plain,
( ( ( d @ ( additive_identity @ add ) )
!= additive_identity )
| ~ ( d @ defined )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[985]) ).
thf(1166,plain,
( ( ( d @ ( additive_identity @ add ) )
!= additive_identity )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1029,71,74]) ).
thf(1167,plain,
( ( d @ ( additive_identity @ add ) )
!= additive_identity ),
inference(simp,[status(thm)],[1166]) ).
thf(29923,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)],[2628,52]) ).
thf(29924,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[29923]) ).
thf(29925,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[29924:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(22,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(72,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)],[22]) ).
thf(73,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)],[72]) ).
thf(43,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)],[42]) ).
thf(103,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)],[43,43]) ).
thf(104,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)],[103]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ less_or_equal ) )
| ( B @ ( D @ less_or_equal ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(15536,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)],[12188,52]) ).
thf(15537,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[15536]) ).
thf(15538,plain,
multiplicative_identity @ additive_inverse @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[15537:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(31613,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[242,233]) ).
thf(31614,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31613]) ).
thf(31615,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31614:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(19973,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[71,192]) ).
thf(19974,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[19973]) ).
thf(19975,plain,
( ( additive_identity @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( additive_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[19974:[bind(A,$thf( additive_identity ))]]) ).
thf(20140,plain,
additive_identity @ ( additive_identity @ less_or_equal ),
inference(simp,[status(thm)],[19975]) ).
thf(19528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6274,88]) ).
thf(19529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[19528]) ).
thf(19530,plain,
b @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( b @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[19529:[bind(A,$thf( b @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(31422,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[141,233]) ).
thf(31423,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31422]) ).
thf(31424,plain,
c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31423:[bind(A,$thf( c @ additive_inverse @ additive_inverse ))]]) ).
thf(17540,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[46,168]) ).
thf(17541,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[17540]) ).
thf(17542,plain,
( ( multiplicative_identity @ ( c @ less_or_equal ) )
| ( c @ ( multiplicative_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[17541:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(6375,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,80]) ).
thf(6376,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6375]) ).
thf(6377,plain,
d @ additive_inverse @ ( d @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6376:[bind(A,$thf( d @ additive_inverse ))]]) ).
thf(10153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ additive_inverse @ ( d @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6377,88]) ).
thf(10154,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ additive_inverse @ ( d @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10153]) ).
thf(10155,plain,
d @ additive_inverse @ ( multiplicative_identity @ ( d @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10154:[bind(A,$thf( d @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( d @ additive_inverse ))]]) ).
thf(12048,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,95]) ).
thf(12049,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12048]) ).
thf(12050,plain,
additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12049:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(14733,plain,
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12050,90]) ).
thf(14734,plain,
( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[14733]) ).
thf(14738,plain,
( ( ( additive_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( additive_identity @ additive_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[14734]) ).
thf(14760,plain,
( ( ( additive_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( additive_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[14738]) ).
thf(12229,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2177,95]) ).
thf(12230,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12229]) ).
thf(12231,plain,
b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12230:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(24230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12231,52]) ).
thf(24231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[24230]) ).
thf(24232,plain,
b @ multiplicative_inverse @ additive_inverse @ ( additive_identity @ ( b @ multiplicative_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[24231:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( b @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(6227,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,80]) ).
thf(6228,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6227]) ).
thf(6229,plain,
b @ ( b @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6228:[bind(A,$thf( b ))]]) ).
thf(202,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_or_equal ) )
!= ( D @ ( E @ less_or_equal ) ) )
| ~ $true
| ~ ( E @ ( C @ less_or_equal ) )
| ( D @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[48,43]) ).
thf(203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_or_equal ) )
!= ( D @ ( E @ less_or_equal ) ) )
| ~ ( E @ ( C @ less_or_equal ) )
| ( D @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ less_or_equal ) )
| ( B @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(2895,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2640,39]) ).
thf(2896,plain,
( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[2895]) ).
thf(2941,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != b )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[2896]) ).
thf(2959,plain,
( ( multiplicative_identity != b )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[2941]) ).
thf(19415,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)],[6214,88]) ).
thf(19416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[19415]) ).
thf(19417,plain,
a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( a @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[19416:[bind(A,$thf( a @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(14074,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1115,131]) ).
thf(14075,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14074]) ).
thf(14076,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14075:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(15703,plain,
( ( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12191,40]) ).
thf(15704,plain,
( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15703]) ).
thf(15737,plain,
( ( ( b @ multiplicative_inverse )
!= additive_identity )
| ( ( b @ multiplicative_inverse )
!= d )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[15704]) ).
thf(15765,plain,
( ( ( b @ multiplicative_inverse )
!= additive_identity )
| ( ( b @ multiplicative_inverse )
!= d ) ),
inference(simp,[status(thm)],[15737]) ).
thf(3666,plain,
( ( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2660,39]) ).
thf(3667,plain,
( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[3666]) ).
thf(3702,plain,
( ( additive_identity != additive_identity )
| ( a != b )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3667]) ).
thf(3726,plain,
( ( a != b )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3702]) ).
thf(16777,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[71,162]) ).
thf(16778,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[16777]) ).
thf(16779,plain,
( ( additive_identity @ ( a @ less_or_equal ) )
| ( a @ ( additive_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[16778:[bind(A,$thf( additive_identity ))]]) ).
thf(5050,plain,
( ( ( additive_identity @ ( b @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2726,40]) ).
thf(5051,plain,
( ( additive_identity @ ( b @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[5050]) ).
thf(5073,plain,
( ( additive_identity != additive_identity )
| ( ( b @ additive_inverse )
!= d )
| ( ( b @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[5051]) ).
thf(5086,plain,
( ( ( b @ additive_inverse )
!= d )
| ( ( b @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[5073]) ).
thf(11966,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[138,95]) ).
thf(11967,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11966]) ).
thf(11968,plain,
a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[11967:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(9,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(49,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( C @ defined )
| ~ $true
| ( B @ ( C @ less_or_equal ) )
| ( C @ ( B @ less_or_equal ) )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[45,48]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( C @ defined )
| ( B @ ( C @ less_or_equal ) )
| ( C @ ( B @ less_or_equal ) )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[175]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ~ ( A @ defined )
| ( B @ additive_inverse @ ( A @ less_or_equal ) )
| ( A @ ( B @ additive_inverse @ less_or_equal ) )
| ~ ( B @ defined ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( D )),bind(B,$thf( D @ additive_inverse ))]]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ~ ( A @ defined )
| ( B @ additive_inverse @ ( A @ less_or_equal ) )
| ( A @ ( B @ additive_inverse @ less_or_equal ) )
| ~ ( B @ defined ) ),
inference(simp,[status(thm)],[177]) ).
thf(6256,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[74,80]) ).
thf(6257,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6256]) ).
thf(6258,plain,
d @ ( d @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6257:[bind(A,$thf( d ))]]) ).
thf(6697,plain,
( ( ( d @ ( d @ ( multiplicative_identity @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6258,41]) ).
thf(6698,plain,
( ( d @ ( d @ ( multiplicative_identity @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[6697]) ).
thf(6740,plain,
( ( ( c @ ( b @ multiply ) )
!= d )
| ( d != d )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[6698]) ).
thf(6757,plain,
( ( ( c @ ( b @ multiply ) )
!= d )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[6740]) ).
thf(1636,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,1600]) ).
thf(1637,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[1636]) ).
thf(1638,plain,
( ( ( d @ ( d @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( d @ ( d @ ( d @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[1637:[bind(A,$thf( d ))]]) ).
thf(86,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)],[85]) ).
thf(14665,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)],[12050,52]) ).
thf(14666,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[14665]) ).
thf(14667,plain,
additive_identity @ additive_inverse @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[14666:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ additive_inverse ))]]) ).
thf(965,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[55,90]) ).
thf(966,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[965]) ).
thf(977,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= multiplicative_identity )
| ( B != additive_identity )
| ( A != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[966]) ).
thf(1020,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ ( additive_identity @ defined )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[977]) ).
thf(1137,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[1020]) ).
thf(1138,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ $true ),
inference(rewrite,[status(thm)],[1137,71]) ).
thf(1139,plain,
( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[1138]) ).
thf(12030,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[252,95]) ).
thf(12031,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12030]) ).
thf(12032,plain,
b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12031:[bind(A,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(31588,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[2174,233]) ).
thf(31589,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31588]) ).
thf(31590,plain,
b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31589:[bind(A,$thf( b @ multiplicative_inverse ))]]) ).
thf(15851,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[53,156]) ).
thf(15852,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[15851]) ).
thf(15853,plain,
( ( c @ ( d @ less_or_equal ) )
| ( d @ ( c @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[15852:[bind(A,$thf( c ))]]) ).
thf(1142,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[682,45]) ).
thf(1143,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1142]) ).
thf(1144,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1143:[bind(A,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1931,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1144,45]) ).
thf(1932,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1931]) ).
thf(1933,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1932:[bind(A,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(15652,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12191,52]) ).
thf(15653,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[15652]) ).
thf(15654,plain,
b @ multiplicative_inverse @ ( additive_identity @ ( b @ multiplicative_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[15653:[bind(A,$thf( b @ multiplicative_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( b @ multiplicative_inverse ))]]) ).
thf(1569,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)],[1115,45]) ).
thf(1570,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1569]) ).
thf(1571,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1570:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(27,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(81,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)],[27]) ).
thf(6134,plain,
( ( ( additive_identity @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( c @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1792,39]) ).
thf(6135,plain,
( ( ( additive_identity @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[6134]) ).
thf(6177,plain,
( ( additive_identity != additive_identity )
| ( c != b )
| ( additive_identity != additive_identity )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[6135]) ).
thf(6197,plain,
( ( c != b )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[6177]) ).
thf(19868,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[93,192]) ).
thf(19869,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[19868]) ).
thf(19870,plain,
( ( b @ ( additive_identity @ less_or_equal ) )
| ( additive_identity @ ( b @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[19869:[bind(A,$thf( b ))]]) ).
thf(31528,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[130,233]) ).
thf(31529,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31528]) ).
thf(31530,plain,
b @ additive_inverse @ ( b @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31529:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[112,48]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(198,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( d @ additive_inverse @ less_or_equal ) )
| ( d @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( A )),bind(B,$thf( d @ additive_inverse ))]]) ).
thf(100,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_or_equal ) )
!= ( F @ ( D @ less_or_equal ) ) )
| ~ ( E @ ( F @ less_or_equal ) )
| ~ $true
| ( E @ ( D @ less_or_equal ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[43,43]) ).
thf(101,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_or_equal ) )
!= ( F @ ( D @ less_or_equal ) ) )
| ~ ( E @ ( F @ less_or_equal ) )
| ( E @ ( D @ less_or_equal ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ less_or_equal ) )
| ( D @ ( A @ less_or_equal ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( E )),bind(F,$thf( B ))]]) ).
thf(108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ less_or_equal ) )
| ( D @ ( A @ less_or_equal ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(23882,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12089,52]) ).
thf(23883,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[23882]) ).
thf(23884,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[23883:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(17648,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[71,168]) ).
thf(17649,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[17648]) ).
thf(17650,plain,
( ( additive_identity @ ( c @ less_or_equal ) )
| ( c @ ( additive_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[17649:[bind(A,$thf( additive_identity ))]]) ).
thf(12042,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[141,95]) ).
thf(12043,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12042]) ).
thf(12044,plain,
c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12043:[bind(A,$thf( c @ additive_inverse @ additive_inverse ))]]) ).
thf(5173,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)],[76,90]) ).
thf(5174,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[5173]) ).
thf(5175,plain,
( ~ ( additive_identity @ ( multiplicative_identity @ less_or_equal ) )
| ~ ( multiplicative_identity @ ( additive_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[5174:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity ))]]) ).
thf(12753,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)],[12023,52]) ).
thf(12754,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12753]) ).
thf(12755,plain,
a @ ( additive_identity @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[12754:[bind(A,$thf( a )),bind(B,$thf( additive_identity )),bind(C,$thf( a ))]]) ).
thf(6427,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[2177,80]) ).
thf(6428,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6427]) ).
thf(6429,plain,
b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6428:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(24114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12223,52]) ).
thf(24115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[24114]) ).
thf(24116,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[24115:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(2128,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1760,40]) ).
thf(2129,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2128]) ).
thf(2151,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != d )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2129]) ).
thf(2162,plain,
( ( multiplicative_identity != d )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[2151]) ).
thf(3157,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != d ) ),
inference(paramod_ordered,[status(thm)],[2162,45]) ).
thf(3158,plain,
! [A: $i] :
( ( ( multiplicative_identity @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( multiplicative_identity != d ) ),
inference(simp,[status(thm)],[3157]) ).
thf(3159,plain,
( ( multiplicative_identity @ multiplicative_inverse @ additive_inverse @ defined )
| ( multiplicative_identity != d ) ),
inference(pattern_uni,[status(thm)],[3158:[bind(A,$thf( multiplicative_identity @ multiplicative_inverse ))]]) ).
thf(14578,plain,
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11971,39]) ).
thf(14579,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[14578]) ).
thf(14634,plain,
( ( ( a @ additive_inverse )
!= additive_identity )
| ( ( a @ additive_inverse )
!= b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[14579]) ).
thf(14660,plain,
( ( ( a @ additive_inverse )
!= additive_identity )
| ( ( a @ additive_inverse )
!= b ) ),
inference(simp,[status(thm)],[14634]) ).
thf(96,plain,
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37,41]) ).
thf(97,plain,
( ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( ( b @ multiplicative_inverse )
!= d )
| ( a != a ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( ( b @ multiplicative_inverse )
!= d ) ),
inference(simp,[status(thm)],[98]) ).
thf(135,plain,
( ( ( d @ multiplicative_inverse )
!= c )
| ( c != b )
| ( ( b @ multiplicative_inverse )
!= d ) ),
inference(simp,[status(thm)],[99]) ).
thf(961,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( a @ ( a @ ( a @ sum ) ) ) )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[55,346]) ).
thf(962,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( a @ ( a @ ( a @ sum ) ) ) )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[961]) ).
thf(974,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= a )
| ( B != a )
| ( A != a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[962]) ).
thf(1016,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
| ~ ( a @ defined )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[974]) ).
thf(1560,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[1016]) ).
thf(1561,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1560,70]) ).
thf(1562,plain,
( ( ( a @ ( a @ add ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ~ ( c @ ( b @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( d @ multiplicative_inverse @ ( c @ multiply ) @ sum ) ) ) ),
inference(simp,[status(thm)],[1561]) ).
thf(14832,plain,
( ( ( c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12083,40]) ).
thf(14833,plain,
( ( c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[14832]) ).
thf(14856,plain,
( ( ( c @ additive_inverse )
!= additive_identity )
| ( ( c @ additive_inverse )
!= d )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[14833]) ).
thf(14876,plain,
( ( ( c @ additive_inverse )
!= additive_identity )
| ( ( c @ additive_inverse )
!= d ) ),
inference(simp,[status(thm)],[14856]) ).
thf(1526,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)],[1091,45]) ).
thf(1527,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1526]) ).
thf(1528,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1527:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(31343,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[138,233]) ).
thf(31344,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31343]) ).
thf(31345,plain,
a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31344:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(6402,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[127,80]) ).
thf(6403,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6402]) ).
thf(6404,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6403:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(10206,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)],[6404,88]) ).
thf(10207,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10206]) ).
thf(10208,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10207:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(15827,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[70,156]) ).
thf(15828,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[15827]) ).
thf(15829,plain,
( ( a @ ( d @ less_or_equal ) )
| ( d @ ( a @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[15828:[bind(A,$thf( a ))]]) ).
thf(2670,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,63]) ).
thf(2671,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2670]) ).
thf(2672,plain,
additive_identity @ ( c @ ( c @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2671:[bind(A,$thf( c ))]]) ).
thf(3738,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( c @ ( c @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2672,52]) ).
thf(3739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( c @ ( c @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[3738]) ).
thf(3740,plain,
additive_identity @ ( c @ additive_inverse @ ( c @ sum ) ),
inference(pattern_uni,[status(thm)],[3739:[bind(A,$thf( c )),bind(B,$thf( c @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(4246,plain,
( ( ( additive_identity @ ( c @ additive_inverse @ ( c @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3740,39]) ).
thf(4247,plain,
( ( additive_identity @ ( c @ additive_inverse @ ( c @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4246]) ).
thf(4278,plain,
( ( additive_identity != additive_identity )
| ( ( c @ additive_inverse )
!= b )
| ( c != additive_identity ) ),
inference(simp,[status(thm)],[4247]) ).
thf(4304,plain,
( ( ( c @ additive_inverse )
!= b )
| ( c != additive_identity ) ),
inference(simp,[status(thm)],[4278]) ).
thf(199,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_or_equal ) )
!= ( E @ ( C @ less_or_equal ) ) )
| ~ ( D @ ( E @ less_or_equal ) )
| ~ $true
| ( D @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[48,43]) ).
thf(200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ less_or_equal ) )
!= ( E @ ( C @ less_or_equal ) ) )
| ~ ( D @ ( E @ less_or_equal ) )
| ( D @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ less_or_equal ) )
| ( C @ ( A @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ less_or_equal ) )
| ( C @ ( A @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(2965,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ ( b @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2643,52]) ).
thf(2966,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ ( b @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[2965]) ).
thf(2967,plain,
additive_identity @ ( b @ additive_inverse @ ( b @ sum ) ),
inference(pattern_uni,[status(thm)],[2966:[bind(A,$thf( b )),bind(B,$thf( b @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(1624,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1600]) ).
thf(1625,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[1624]) ).
thf(1626,plain,
( ( ( multiplicative_identity @ ( multiplicative_identity @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( multiplicative_identity @ ( d @ ( multiplicative_identity @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[1625:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(14188,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1144,131]) ).
thf(14189,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14188]) ).
thf(14190,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14189:[bind(A,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ) )
!= ( A @ ( d @ ( A @ product ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( B @ ( d @ ( B @ product ) ) )
| ~ $true
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,323]) ).
thf(573,plain,
! [B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) @ ( b @ multiplicative_inverse @ ( a @ product ) ) )
!= ( A @ ( d @ ( A @ product ) ) ) )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( B @ ( d @ ( B @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(584,plain,
! [B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= A )
| ( ( b @ multiplicative_inverse )
!= d )
| ( a != A )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( B @ ( d @ ( B @ product ) ) )
| ~ ( a @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[573]) ).
thf(589,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ ( c @ multiply ) )
!= a )
| ( ( b @ multiplicative_inverse )
!= d )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ ( a @ ( A @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[584]) ).
thf(6328,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,80]) ).
thf(6329,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6328]) ).
thf(6330,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6329:[bind(A,$thf( additive_identity ))]]) ).
thf(10189,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)],[6330,88]) ).
thf(10190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10189]) ).
thf(10191,plain,
additive_identity @ ( multiplicative_identity @ ( additive_identity @ product ) ),
inference(pattern_uni,[status(thm)],[10190:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(2782,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2532,63]) ).
thf(2783,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2782]) ).
thf(2784,plain,
additive_identity @ ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2783:[bind(A,$thf( d @ multiplicative_inverse ))]]) ).
thf(24465,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( multiplicative_identity @ less_or_equal ) )
| ( multiplicative_identity @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[93,216]) ).
thf(24466,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( multiplicative_identity @ less_or_equal ) )
| ( multiplicative_identity @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[24465]) ).
thf(24467,plain,
( ( b @ ( multiplicative_identity @ less_or_equal ) )
| ( multiplicative_identity @ ( b @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[24466:[bind(A,$thf( b ))]]) ).
thf(2650,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[74,63]) ).
thf(2651,plain,
! [A: $i] :
( ( ( d @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2650]) ).
thf(2652,plain,
additive_identity @ ( d @ ( d @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2651:[bind(A,$thf( d ))]]) ).
thf(2469,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)],[1528,45]) ).
thf(2470,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2469]) ).
thf(2471,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2470:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(16672,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[93,162]) ).
thf(16673,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[16672]) ).
thf(16674,plain,
( ( b @ ( a @ less_or_equal ) )
| ( a @ ( b @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[16673:[bind(A,$thf( b ))]]) ).
thf(12281,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)],[11986,52]) ).
thf(12282,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12281]) ).
thf(12283,plain,
multiplicative_identity @ ( additive_identity @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[12282:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity ))]]) ).
thf(12807,plain,
( ( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12023,40]) ).
thf(12808,plain,
( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12807]) ).
thf(12832,plain,
( ( a != additive_identity )
| ( a != d )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12808]) ).
thf(12854,plain,
( ( a != additive_identity )
| ( a != d ) ),
inference(simp,[status(thm)],[12832]) ).
thf(8888,plain,
! [A: $i] :
( ( ( c @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( c != d ) ),
inference(paramod_ordered,[status(thm)],[6200,45]) ).
thf(8889,plain,
! [A: $i] :
( ( ( c @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( c != d ) ),
inference(simp,[status(thm)],[8888]) ).
thf(8890,plain,
( ( c @ multiplicative_inverse @ additive_inverse @ defined )
| ( c != d ) ),
inference(pattern_uni,[status(thm)],[8889:[bind(A,$thf( c @ multiplicative_inverse ))]]) ).
thf(11987,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,95]) ).
thf(11988,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11987]) ).
thf(11989,plain,
b @ ( b @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[11988:[bind(A,$thf( b ))]]) ).
thf(20883,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( d @ additive_inverse @ less_or_equal ) )
| ( d @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[112,198]) ).
thf(20884,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( d @ additive_inverse @ less_or_equal ) )
| ( d @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[20883]) ).
thf(20885,plain,
( ( d @ additive_inverse @ ( d @ additive_inverse @ less_or_equal ) )
| ( d @ additive_inverse @ ( d @ additive_inverse @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[20884:[bind(A,$thf( d @ additive_inverse ))]]) ).
thf(20983,plain,
d @ additive_inverse @ ( d @ additive_inverse @ less_or_equal ),
inference(simp,[status(thm)],[20885]) ).
thf(22547,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12044,52]) ).
thf(22548,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[22547]) ).
thf(22549,plain,
c @ additive_inverse @ additive_inverse @ ( additive_identity @ ( c @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[22548:[bind(A,$thf( c @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( c @ additive_inverse @ additive_inverse ))]]) ).
thf(12935,plain,
( ( ( c @ ( c @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12047,90]) ).
thf(12936,plain,
( ( c @ ( c @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12935]) ).
thf(12941,plain,
( ( multiplicative_identity != c )
| ( c != additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12936]) ).
thf(12963,plain,
( ( multiplicative_identity != c )
| ( c != additive_identity ) ),
inference(simp,[status(thm)],[12941]) ).
thf(2737,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2535,63]) ).
thf(2738,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2737]) ).
thf(2739,plain,
additive_identity @ ( d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2738:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(30571,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2739,52]) ).
thf(30572,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[30571]) ).
thf(30573,plain,
additive_identity @ ( d @ multiplicative_inverse @ additive_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[30572:[bind(A,$thf( d @ multiplicative_inverse @ additive_inverse )),bind(B,$thf( d @ multiplicative_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(12517,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ ( d @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12005,52]) ).
thf(12518,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ ( d @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12517]) ).
thf(12519,plain,
d @ ( additive_identity @ ( d @ sum ) ),
inference(pattern_uni,[status(thm)],[12518:[bind(A,$thf( d )),bind(B,$thf( additive_identity )),bind(C,$thf( d ))]]) ).
thf(4346,plain,
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3816,40]) ).
thf(4347,plain,
( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4346]) ).
thf(4358,plain,
( ( additive_identity != additive_identity )
| ( ( additive_identity @ additive_inverse )
!= d )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[4347]) ).
thf(4377,plain,
( ( additive_identity @ additive_inverse )
!= d ),
inference(simp,[status(thm)],[4358]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(cnf,[status(esa)],[49]) ).
thf(10121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) )
| ~ $true
| ~ ( C @ ( A @ ( B @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[88,41]) ).
thf(10122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) )
| ~ ( C @ ( A @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[10121]) ).
thf(10123,plain,
~ ( c @ ( b @ multiply ) @ ( a @ ( d @ product ) ) ),
inference(pattern_uni,[status(thm)],[10122:[bind(A,$thf( a )),bind(B,$thf( d )),bind(C,$thf( c @ ( b @ multiply ) ))]]) ).
thf(12192,plain,
! [A: $i] :
( ( ( A @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[95,40]) ).
thf(12193,plain,
! [A: $i] :
( ( ( A @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[12192]) ).
thf(12236,plain,
! [A: $i] :
( ( A != additive_identity )
| ( A != d )
| ( additive_identity != additive_identity )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[12193]) ).
thf(12264,plain,
( ( d != additive_identity )
| ~ ( d @ defined ) ),
inference(simp,[status(thm)],[12236]) ).
thf(12513,plain,
( ( d != additive_identity )
| ~ $true ),
inference(rewrite,[status(thm)],[12264,74]) ).
thf(12514,plain,
d != additive_identity,
inference(simp,[status(thm)],[12513]) ).
thf(4167,plain,
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3661,39]) ).
thf(4168,plain,
( ( additive_identity @ ( a @ additive_inverse @ ( a @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4167]) ).
thf(4207,plain,
( ( additive_identity != additive_identity )
| ( ( a @ additive_inverse )
!= b )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[4168]) ).
thf(4222,plain,
( ( ( a @ additive_inverse )
!= b )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[4207]) ).
thf(6350,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[130,80]) ).
thf(6351,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6350]) ).
thf(6352,plain,
b @ additive_inverse @ ( b @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6351:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(2042,plain,
! [A: $i] :
( ( ( c @ 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)],[1497,45]) ).
thf(2043,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2042]) ).
thf(2044,plain,
c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2043:[bind(A,$thf( c @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(31407,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[252,233]) ).
thf(31408,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31407]) ).
thf(31409,plain,
b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31408:[bind(A,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(15681,plain,
( ( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12191,39]) ).
thf(15682,plain,
( ( b @ multiplicative_inverse @ ( b @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15681]) ).
thf(15728,plain,
( ( ( b @ multiplicative_inverse )
!= additive_identity )
| ( ( b @ multiplicative_inverse )
!= b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[15682]) ).
thf(15753,plain,
( ( ( b @ multiplicative_inverse )
!= additive_identity )
| ( ( b @ multiplicative_inverse )
!= b ) ),
inference(simp,[status(thm)],[15728]) ).
thf(10127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( b @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6229,88]) ).
thf(10128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( b @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10127]) ).
thf(10129,plain,
b @ ( multiplicative_identity @ ( b @ product ) ),
inference(pattern_uni,[status(thm)],[10128:[bind(A,$thf( b )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( b ))]]) ).
thf(12397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( b @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[11989,52]) ).
thf(12398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( b @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12397]) ).
thf(12399,plain,
b @ ( additive_identity @ ( b @ sum ) ),
inference(pattern_uni,[status(thm)],[12398:[bind(A,$thf( b )),bind(B,$thf( additive_identity )),bind(C,$thf( b ))]]) ).
thf(819,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[55,39]) ).
thf(820,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[819]) ).
thf(979,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= additive_identity )
| ( B != b )
| ( A != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[820]) ).
thf(1022,plain,
( ( ( b @ ( additive_identity @ add ) )
!= additive_identity )
| ~ ( b @ defined )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[979]) ).
thf(1140,plain,
( ( ( b @ ( additive_identity @ add ) )
!= additive_identity )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1022,71,93]) ).
thf(1141,plain,
( ( b @ ( additive_identity @ add ) )
!= additive_identity ),
inference(simp,[status(thm)],[1140]) ).
thf(22663,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12059,52]) ).
thf(22664,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[22663]) ).
thf(22665,plain,
d @ additive_inverse @ additive_inverse @ ( additive_identity @ ( d @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[22664:[bind(A,$thf( d @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( d @ additive_inverse @ additive_inverse ))]]) ).
thf(4746,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)],[2612,52]) ).
thf(4747,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[4746]) ).
thf(4748,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4747:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( a @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(4762,plain,
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2612,39]) ).
thf(4763,plain,
( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4762]) ).
thf(4811,plain,
( ( additive_identity != additive_identity )
| ( ( a @ additive_inverse )
!= b )
| ( ( a @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4763]) ).
thf(4819,plain,
( ( ( a @ additive_inverse )
!= b )
| ( ( a @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4811]) ).
thf(10266,plain,
( ( ( a @ ( multiplicative_identity @ ( a @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10120,41]) ).
thf(10267,plain,
( ( a @ ( multiplicative_identity @ ( a @ product ) ) )
!= ( c @ ( b @ multiply ) @ ( d @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[10266]) ).
thf(10313,plain,
( ( ( c @ ( b @ multiply ) )
!= a )
| ( multiplicative_identity != d )
| ( a != a ) ),
inference(simp,[status(thm)],[10267]) ).
thf(10332,plain,
( ( ( c @ ( b @ multiply ) )
!= a )
| ( multiplicative_identity != d ) ),
inference(simp,[status(thm)],[10313]) ).
thf(15803,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[93,156]) ).
thf(15804,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[15803]) ).
thf(15805,plain,
( ( b @ ( d @ less_or_equal ) )
| ( d @ ( b @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[15804:[bind(A,$thf( b ))]]) ).
thf(6410,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[2532,80]) ).
thf(6411,plain,
! [A: $i] :
( ( ( d @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6410]) ).
thf(6412,plain,
d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6411:[bind(A,$thf( d @ multiplicative_inverse ))]]) ).
thf(10197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6412,88]) ).
thf(10198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10197]) ).
thf(10199,plain,
d @ multiplicative_inverse @ ( multiplicative_identity @ ( d @ multiplicative_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10198:[bind(A,$thf( d @ multiplicative_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( d @ multiplicative_inverse ))]]) ).
thf(15908,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[71,156]) ).
thf(15909,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( d @ less_or_equal ) )
| ( d @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[15908]) ).
thf(15910,plain,
( ( additive_identity @ ( d @ less_or_equal ) )
| ( d @ ( additive_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[15909:[bind(A,$thf( additive_identity ))]]) ).
thf(2685,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,63]) ).
thf(2686,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2685]) ).
thf(2687,plain,
additive_identity @ ( d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2686:[bind(A,$thf( d @ additive_inverse @ additive_inverse ))]]) ).
thf(30259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2687,52]) ).
thf(30260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[30259]) ).
thf(30261,plain,
additive_identity @ ( d @ additive_inverse @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[30260:[bind(A,$thf( d @ additive_inverse @ additive_inverse )),bind(B,$thf( d @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(10186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ additive_inverse @ ( b @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6352,88]) ).
thf(10187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ additive_inverse @ ( b @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10186]) ).
thf(10188,plain,
b @ additive_inverse @ ( multiplicative_identity @ ( b @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10187:[bind(A,$thf( b @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( b @ additive_inverse ))]]) ).
thf(4270,plain,
( ( ( additive_identity @ ( c @ additive_inverse @ ( c @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3740,40]) ).
thf(4271,plain,
( ( additive_identity @ ( c @ additive_inverse @ ( c @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4270]) ).
thf(4285,plain,
( ( additive_identity != additive_identity )
| ( ( c @ additive_inverse )
!= d )
| ( c != additive_identity ) ),
inference(simp,[status(thm)],[4271]) ).
thf(4310,plain,
( ( ( c @ additive_inverse )
!= d )
| ( c != additive_identity ) ),
inference(simp,[status(thm)],[4285]) ).
thf(3745,plain,
( ( ( additive_identity @ ( c @ ( c @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2672,39]) ).
thf(3746,plain,
( ( additive_identity @ ( c @ ( c @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[3745]) ).
thf(3778,plain,
( ( additive_identity != additive_identity )
| ( c != b )
| ( ( c @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3746]) ).
thf(3797,plain,
( ( c != b )
| ( ( c @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3778]) ).
thf(22431,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[12032,52]) ).
thf(22432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[22431]) ).
thf(22433,plain,
b @ additive_inverse @ additive_inverse @ ( additive_identity @ ( b @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[22432:[bind(A,$thf( b @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(17591,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[53,168]) ).
thf(17592,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( A @ ( c @ less_or_equal ) )
| ( c @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[17591]) ).
thf(17593,plain,
( ( c @ ( c @ less_or_equal ) )
| ( c @ ( c @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[17592:[bind(A,$thf( c ))]]) ).
thf(17842,plain,
c @ ( c @ less_or_equal ),
inference(simp,[status(thm)],[17593]) ).
thf(30035,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2663,52]) ).
thf(30036,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[30035]) ).
thf(30037,plain,
additive_identity @ ( b @ additive_inverse @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[30036:[bind(A,$thf( b @ additive_inverse @ additive_inverse )),bind(B,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(24462,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( multiplicative_identity @ less_or_equal ) )
| ( multiplicative_identity @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[46,216]) ).
thf(24463,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( multiplicative_identity @ less_or_equal ) )
| ( multiplicative_identity @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[24462]) ).
thf(24464,plain,
( ( multiplicative_identity @ ( multiplicative_identity @ less_or_equal ) )
| ( multiplicative_identity @ ( multiplicative_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[24463:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(24769,plain,
multiplicative_identity @ ( multiplicative_identity @ less_or_equal ),
inference(simp,[status(thm)],[24464]) ).
thf(22315,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[11968,52]) ).
thf(22316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[22315]) ).
thf(22317,plain,
a @ additive_inverse @ additive_inverse @ ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[22316:[bind(A,$thf( a @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(10070,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)],[6291,88]) ).
thf(10071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10070]) ).
thf(10072,plain,
additive_identity @ additive_inverse @ ( multiplicative_identity @ ( additive_identity @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[10071:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ additive_inverse ))]]) ).
thf(16225,plain,
( ( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12196,40]) ).
thf(16226,plain,
( ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[16225]) ).
thf(16259,plain,
( ( ( d @ multiplicative_inverse )
!= additive_identity )
| ( ( d @ multiplicative_inverse )
!= d )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[16226]) ).
thf(16267,plain,
( ( ( d @ multiplicative_inverse )
!= additive_identity )
| ( ( d @ multiplicative_inverse )
!= d ) ),
inference(simp,[status(thm)],[16259]) ).
thf(1627,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,1600]) ).
thf(1628,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( ( A @ ( A @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( A @ ( d @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[1627]) ).
thf(1629,plain,
( ( ( b @ ( b @ add ) )
!= a )
| ( ( c @ ( b @ multiply ) )
!= a )
| ~ ( b @ ( d @ ( b @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[1628:[bind(A,$thf( b ))]]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[118,48]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(186,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( c @ additive_inverse @ less_or_equal ) )
| ( c @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( A )),bind(B,$thf( c @ additive_inverse ))]]) ).
thf(8835,plain,
! [A: $i] :
( ( ( c @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined )
| ( c != b ) ),
inference(paramod_ordered,[status(thm)],[6197,45]) ).
thf(8836,plain,
! [A: $i] :
( ( ( c @ multiplicative_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined )
| ( c != b ) ),
inference(simp,[status(thm)],[8835]) ).
thf(8837,plain,
( ( c @ multiplicative_inverse @ additive_inverse @ defined )
| ( c != b ) ),
inference(pattern_uni,[status(thm)],[8836:[bind(A,$thf( c @ multiplicative_inverse ))]]) ).
thf(5117,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[76,39]) ).
thf(5118,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[5117]) ).
thf(5119,plain,
( ~ ( b @ ( additive_identity @ less_or_equal ) )
| ~ ( additive_identity @ ( b @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[5118:[bind(A,$thf( b )),bind(B,$thf( additive_identity ))]]) ).
thf(82,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)],[81]) ).
thf(31482,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[2214,233]) ).
thf(31483,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31482]) ).
thf(31484,plain,
b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31483:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(21187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6429,88]) ).
thf(21188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[21187]) ).
thf(21189,plain,
b @ multiplicative_inverse @ additive_inverse @ ( multiplicative_identity @ ( b @ multiplicative_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[21188:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( b @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(12918,plain,
( ( ( c @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12047,40]) ).
thf(12919,plain,
( ( c @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12918]) ).
thf(12949,plain,
( ( c != additive_identity )
| ( c != d )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12919]) ).
thf(12972,plain,
( ( c != additive_identity )
| ( c != d ) ),
inference(simp,[status(thm)],[12949]) ).
thf(14549,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)],[11971,52]) ).
thf(14550,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[14549]) ).
thf(14551,plain,
a @ additive_inverse @ ( additive_identity @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[14550:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( a @ additive_inverse ))]]) ).
thf(5026,plain,
( ( ( additive_identity @ ( b @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2726,39]) ).
thf(5027,plain,
( ( additive_identity @ ( b @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[5026]) ).
thf(5059,plain,
( ( additive_identity != additive_identity )
| ( ( b @ additive_inverse )
!= b )
| ( ( b @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[5027]) ).
thf(5078,plain,
( ( ( b @ additive_inverse )
!= b )
| ( ( b @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[5059]) ).
thf(19126,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( c @ additive_inverse @ less_or_equal ) )
| ( c @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[118,186]) ).
thf(19127,plain,
! [A: $i] :
( ( ( c @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( c @ additive_inverse @ less_or_equal ) )
| ( c @ additive_inverse @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[19126]) ).
thf(19128,plain,
( ( c @ additive_inverse @ ( c @ additive_inverse @ less_or_equal ) )
| ( c @ additive_inverse @ ( c @ additive_inverse @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[19127:[bind(A,$thf( c @ additive_inverse ))]]) ).
thf(19339,plain,
c @ additive_inverse @ ( c @ additive_inverse @ less_or_equal ),
inference(simp,[status(thm)],[19128]) ).
thf(6224,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,80]) ).
thf(6225,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[6224]) ).
thf(6226,plain,
multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[6225:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(10203,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ ( d @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6258,88]) ).
thf(10204,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ ( d @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[10203]) ).
thf(10205,plain,
d @ ( multiplicative_identity @ ( d @ product ) ),
inference(pattern_uni,[status(thm)],[10204:[bind(A,$thf( d )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( d ))]]) ).
thf(4938,plain,
( ( ( additive_identity @ ( c @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2696,39]) ).
thf(4939,plain,
( ( additive_identity @ ( c @ additive_inverse @ ( c @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4938]) ).
thf(4987,plain,
( ( additive_identity != additive_identity )
| ( ( c @ additive_inverse )
!= b )
| ( ( c @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4939]) ).
thf(5004,plain,
( ( ( c @ additive_inverse )
!= b )
| ( ( c @ additive_inverse @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4987]) ).
thf(29811,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)],[2609,52]) ).
thf(29812,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[29811]) ).
thf(29813,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[29812:[bind(A,$thf( a @ additive_inverse @ additive_inverse )),bind(B,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ less_or_equal ) )
!= ( D @ ( E @ less_or_equal ) ) )
| ~ $true
| ~ ( E @ ( C @ less_or_equal ) )
| ( D @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[48,43]) ).
thf(209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ less_or_equal ) )
!= ( D @ ( E @ less_or_equal ) ) )
| ~ ( E @ ( C @ less_or_equal ) )
| ( D @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_or_equal ) )
| ( A @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(14849,plain,
( ( ( c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12083,90]) ).
thf(14850,plain,
( ( c @ additive_inverse @ ( c @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[14849]) ).
thf(14865,plain,
( ( ( c @ additive_inverse )
!= multiplicative_identity )
| ( ( c @ additive_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[14850]) ).
thf(14888,plain,
( ( ( c @ additive_inverse )
!= multiplicative_identity )
| ( ( c @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[14865]) ).
thf(3769,plain,
( ( ( additive_identity @ ( c @ ( c @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2672,40]) ).
thf(3770,plain,
( ( additive_identity @ ( c @ ( c @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[3769]) ).
thf(3789,plain,
( ( additive_identity != additive_identity )
| ( c != d )
| ( ( c @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3770]) ).
thf(3804,plain,
( ( c != d )
| ( ( c @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[3789]) ).
thf(12426,plain,
( ( ( b @ ( b @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11989,39]) ).
thf(12427,plain,
( ( b @ ( b @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12426]) ).
thf(12472,plain,
( ( b != additive_identity )
| ( b != b )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12427]) ).
thf(12503,plain,
b != additive_identity,
inference(simp,[status(thm)],[12472]) ).
thf(16669,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[46,162]) ).
thf(16670,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[16669]) ).
thf(16671,plain,
( ( multiplicative_identity @ ( a @ less_or_equal ) )
| ( a @ ( multiplicative_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[16670:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(31437,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[134,233]) ).
thf(31438,plain,
! [A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31437]) ).
thf(31439,plain,
d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31438:[bind(A,$thf( d @ additive_inverse @ additive_inverse ))]]) ).
thf(2697,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)],[144,63]) ).
thf(2698,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[2697]) ).
thf(2699,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[2698:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(5471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2784,52]) ).
thf(5472,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ multiplicative_inverse @ ( d @ multiplicative_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5471]) ).
thf(5473,plain,
additive_identity @ ( d @ multiplicative_inverse @ additive_inverse @ ( d @ multiplicative_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[5472:[bind(A,$thf( d @ multiplicative_inverse )),bind(B,$thf( d @ multiplicative_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ less_or_equal ) )
!= ( E @ ( C @ less_or_equal ) ) )
| ~ ( D @ ( E @ less_or_equal ) )
| ~ $true
| ( D @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[48,43]) ).
thf(206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ less_or_equal ) )
!= ( E @ ( C @ less_or_equal ) ) )
| ~ ( D @ ( E @ less_or_equal ) )
| ( D @ ( C @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ less_or_equal ) )
| ( C @ ( B @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ less_or_equal ) )
| ( C @ ( B @ less_or_equal ) )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(31628,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[2177,233]) ).
thf(31629,plain,
! [A: $i] :
( ( ( b @ multiplicative_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[31628]) ).
thf(31630,plain,
b @ multiplicative_inverse @ additive_inverse @ ( b @ multiplicative_inverse @ additive_inverse @ less_or_equal ),
inference(pattern_uni,[status(thm)],[31629:[bind(A,$thf( b @ multiplicative_inverse @ additive_inverse ))]]) ).
thf(3045,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ ( d @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2652,52]) ).
thf(3046,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( d @ ( d @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[3045]) ).
thf(3047,plain,
additive_identity @ ( d @ additive_inverse @ ( d @ sum ) ),
inference(pattern_uni,[status(thm)],[3046:[bind(A,$thf( d )),bind(B,$thf( d @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(20244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[6304,88]) ).
thf(20245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( d @ additive_inverse @ additive_inverse @ ( d @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[20244]) ).
thf(20246,plain,
d @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( d @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[20245:[bind(A,$thf( d @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( d @ additive_inverse @ additive_inverse ))]]) ).
thf(30371,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)],[2699,52]) ).
thf(30372,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[30371]) ).
thf(30373,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[30372:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(21074,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)],[6423,88]) ).
thf(21075,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[21074]) ).
thf(21076,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[21075:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(16696,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(paramod_ordered,[status(thm)],[70,162]) ).
thf(16697,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( a @ less_or_equal ) )
| ( a @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[16696]) ).
thf(16698,plain,
( ( a @ ( a @ less_or_equal ) )
| ( a @ ( a @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[16697:[bind(A,$thf( a ))]]) ).
thf(16960,plain,
a @ ( a @ less_or_equal ),
inference(simp,[status(thm)],[16698]) ).
thf(51872,plain,
$false,
inference(e,[status(thm)],[69,5385,15628,2612,138,3661,6285,88,16092,115,5168,5820,3040,2099,14241,6214,12089,2953,5297,1497,31578,56,15632,4220,2434,2360,174,7944,42,31436,30149,37,6291,52,3029,1792,1760,6274,31593,6423,12869,20472,31542,16176,11986,15633,15306,17545,18624,46,1115,12864,57,78,31475,93,2007,216,19643,15802,12023,24000,348,84,11971,61,14874,2799,1600,74,14160,89,4924,233,85,30685,12132,1067,2660,4999,16279,248,5012,60,12100,6200,1091,15206,598,16264,192,3816,25212,7994,38,70,12083,2890,4836,92,252,2663,665,15422,1656,682,2628,15756,65,2609,12196,3731,1970,10152,3119,141,156,10126,14783,2726,53,10120,77,537,6304,19867,124,12223,1644,4814,20359,6271,12859,4384,14655,12378,14649,12059,16722,41,503,10158,12191,12005,12962,10143,10069,1170,1466,5209,1167,134,29925,2749,6409,73,105,15538,718,31615,20140,19530,31424,45,64,17542,4393,10155,14760,44,12231,24232,6229,204,2959,59,118,2161,19417,14076,54,15765,3726,16779,144,5086,11968,49,236,6757,1638,350,5634,86,71,14667,1139,12032,31590,2214,15853,5631,1933,76,1144,15654,1571,2774,6217,81,6197,19870,39,1043,631,6319,31530,198,108,23884,17650,12044,5175,323,12755,91,520,66,6429,24116,130,6377,3159,14660,135,1435,299,6325,80,35,1562,14876,1528,6288,31345,10208,15829,2535,4304,226,2967,1626,14190,589,162,10191,2784,24467,648,112,2652,2471,16674,2846,12283,12854,48,2397,150,95,8890,327,6367,11989,2678,1780,557,20983,63,22549,12963,30573,12519,4377,50,10123,67,331,12514,4222,127,6352,2044,6330,31409,12160,15753,2675,10129,12399,1141,22665,4748,72,43,4819,10332,99,15805,10199,15910,30261,10188,4310,3797,2696,87,2643,22433,17842,2174,40,30037,2532,24769,55,12050,22317,588,10072,16267,1629,186,75,58,8837,6412,2162,272,12152,5119,346,2739,82,31484,21189,2779,36,12972,14551,5078,19339,6226,10205,262,5004,168,51,29813,210,242,2572,2704,6258,14888,94,79,3804,12503,16671,31439,12188,68,2699,5473,131,47,2687,62,3740,227,83,6404,31630,222,3047,20246,90,30373,486,2672,2640,21076,16960,12047,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD049-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n026.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 02:32:26 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.20 % [INFO] Parsing done (206ms).
% 1.36/1.21 % [INFO] Running in sequential loop mode.
% 2.05/1.61 % [INFO] eprover registered as external prover.
% 2.05/1.62 % [INFO] Scanning for conjecture ...
% 2.21/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 2.21/1.79 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.42/1.83 % [INFO] Problem is propositional (TPTP CNF).
% 2.42/1.84 % [INFO] Type checking passed.
% 2.42/1.84 % [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 ...
% 91.21/23.73 % External prover 'e' found a proof!
% 91.21/23.73 % [INFO] Killing All external provers ...
% 91.21/23.73 % Time passed: 23187ms (effective reasoning time: 22514ms)
% 91.21/23.74 % Axioms used in derivation (30): associativity_addition_1, existence_of_identity_multiplication, transitivity_of_order_relation, totality_of_multiplication, c_is_defined, 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, totality_of_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_order_relation_and_addition, distributivity_2, d_is_defined, antisymmetry_of_order_relation, b_is_defined, totality_of_order_relation, existence_of_inverse_multiplication, well_definedness_of_multiplicative_identity, well_definedness_of_additive_inverse, distributivity_1, associativity_addition_2, commutativity_addition, associativity_multiplication_2, different_identities, well_definedness_of_multiplicative_inverse
% 91.21/23.74 % No. of inferences in proof: 1197
% 91.21/23.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23187 ms resp. 22514 ms w/o parsing
% 87.02/23.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 87.02/24.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------