%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD043-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 07:10:26 AM UTC 2026
% Result : Unsatisfiable 148.01s 40.22s
% Output : Refutation 144.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 28
% Syntax : Number of formulae : 1101 ( 275 unt; 0 typ; 0 def)
% Number of atoms : 4068 ( 756 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 13042 (1761 ~;1699 |; 0 &;9582 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 1699 ( 0 ^;1699 !; 0 ?;1699 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(a_decl,type,
a: $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(defined_decl,type,
defined: $i > $o ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(22,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/sandbox/benchmark/theBenchmark.p',associativity_multiplication_1) ).
thf(68,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)],[22]) ).
thf(69,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)],[68]) ).
thf(20,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(65,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(cnf,[status(esa)],[36]) ).
thf(545,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[65,37]) ).
thf(546,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[545]) ).
thf(547,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(pattern_uni,[status(thm)],[546:[bind(A,$thf( A )),bind(B,$thf( additive_identity ))]]) ).
thf(3811,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[65,547]) ).
thf(3812,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3811]) ).
thf(3813,plain,
additive_identity @ ( additive_identity @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3812:[bind(A,$thf( additive_identity ))]]) ).
thf(23,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(70,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(71,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(7099,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[3813,71]) ).
thf(7100,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7099]) ).
thf(7101,plain,
additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ multiply ) @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7100:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(23426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ multiply ) @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7101,77]) ).
thf(23427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ multiply ) @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[23426]) ).
thf(23428,plain,
additive_identity @ ( additive_identity @ multiply ) @ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ product ) ),
inference(pattern_uni,[status(thm)],[23427:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(3,axiom,
multiplicative_identity @ defined,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(33,plain,
multiplicative_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(40,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[40]) ).
thf(119,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[33,41]) ).
thf(120,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
multiplicative_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(13,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(52,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(53,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(cnf,[status(esa)],[52]) ).
thf(136,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[121,53]) ).
thf(137,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(3787,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[121,547]) ).
thf(3788,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3787]) ).
thf(3789,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3788:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(4167,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3789,41]) ).
thf(4168,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4167]) ).
thf(4169,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4168:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) ))]]) ).
thf(19,axiom,
a @ defined,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
thf(64,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(131,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[64,41]) ).
thf(132,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
a @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( a ))]]) ).
thf(196,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[133,41]) ).
thf(197,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[196]) ).
thf(198,plain,
a @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(246,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[198,41]) ).
thf(247,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[246]) ).
thf(248,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(3796,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[248,547]) ).
thf(3797,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3796]) ).
thf(3798,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3797:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_multiplication) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',associativity_multiplication_2) ).
thf(54,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)],[14]) ).
thf(55,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)],[54]) ).
thf(1,negated_conjecture,
~ ( additive_identity @ ( a @ ( additive_identity @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_2) ).
thf(29,plain,
~ ( additive_identity @ ( a @ ( additive_identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(30,plain,
~ ( additive_identity @ ( a @ ( additive_identity @ product ) ) ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(4039,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ product ) ) ) )
| ~ $true
| ~ ( C @ ( F @ ( D @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( A @ ( E @ ( D @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,30]) ).
thf(4040,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ product ) ) ) )
| ~ ( C @ ( F @ ( D @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( A @ ( E @ ( D @ product ) ) ) ),
inference(simp,[status(thm)],[4039]) ).
thf(4041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( additive_identity @ ( C @ ( A @ product ) ) )
| ~ ( C @ ( a @ ( B @ product ) ) )
| ~ ( additive_identity @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[4040:[bind(A,$thf( additive_identity )),bind(B,$thf( a )),bind(C,$thf( additive_identity ))]]) ).
thf(4051,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( additive_identity @ ( C @ ( A @ product ) ) )
| ~ ( C @ ( a @ ( B @ product ) ) )
| ~ ( additive_identity @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[4041]) ).
thf(4295,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( a @ ( B @ product ) ) )
!= ( additive_identity @ ( B @ ( A @ product ) ) ) )
| ~ ( additive_identity @ ( C @ ( A @ product ) ) )
| ~ ( additive_identity @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4051]) ).
thf(4300,plain,
( ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) )
| ~ ( additive_identity @ ( a @ ( a @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[4295:[bind(A,$thf( a )),bind(B,$thf( a )),bind(C,$thf( additive_identity ))]]) ).
thf(4320,plain,
( ~ $true
| ( ( additive_identity @ ( a @ ( a @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4300]) ).
thf(4322,plain,
( ( additive_identity != additive_identity )
| ( a != additive_identity )
| ( a != a )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[4320]) ).
thf(4323,plain,
( ( a != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[4322]) ).
thf(5080,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) )
| ( a != additive_identity )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,4323]) ).
thf(5081,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) )
| ( a != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5080]) ).
thf(5405,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= additive_identity )
| ( B != additive_identity )
| ( A != a )
| ( a != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5081]) ).
thf(5424,plain,
( ( ( additive_identity @ ( a @ multiply ) )
!= additive_identity )
| ( a != additive_identity )
| ~ ( additive_identity @ defined )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[5405]) ).
thf(6282,plain,
( ( ( additive_identity @ ( a @ multiply ) )
!= additive_identity )
| ( a != additive_identity )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[5424,64,65]) ).
thf(6283,plain,
( ( ( additive_identity @ ( a @ multiply ) )
!= additive_identity )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[6282]) ).
thf(122,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[65,41]) ).
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(28,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(80,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(81,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(9978,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,81]) ).
thf(9979,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9978]) ).
thf(9980,plain,
additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9979:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(12627,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)],[9980,45]) ).
thf(12628,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12627]) ).
thf(12629,plain,
additive_identity @ additive_inverse @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[12628:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ additive_inverse ))]]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(56,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(57,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(4350,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,57]) ).
thf(4351,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4350]) ).
thf(4352,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4351:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(9220,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)],[4352,45]) ).
thf(9221,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[9220]) ).
thf(9222,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[9221:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(4164,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3789,547]) ).
thf(4165,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[4164]) ).
thf(4166,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[4165:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) ))]]) ).
thf(7164,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,71]) ).
thf(7165,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7164]) ).
thf(7166,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7165:[bind(A,$thf( additive_identity ))]]) ).
thf(9379,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)],[7166,77]) ).
thf(9380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[9379]) ).
thf(9381,plain,
additive_identity @ ( multiplicative_identity @ ( additive_identity @ product ) ),
inference(pattern_uni,[status(thm)],[9380:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(4296,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( additive_identity @ ( C @ ( A @ product ) ) )
!= ( additive_identity @ ( B @ ( A @ product ) ) ) )
| ~ ( C @ ( a @ ( B @ product ) ) )
| ~ ( additive_identity @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4051]) ).
thf(4301,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( a @ ( B @ product ) ) )
| ~ ( additive_identity @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[4296:[bind(A,$thf( A )),bind(B,$thf( C ))]]) ).
thf(4309,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( a @ ( B @ product ) ) )
| ~ ( additive_identity @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[4301]) ).
thf(9571,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ product ) ) )
!= ( additive_identity @ ( B @ ( A @ product ) ) ) )
| ~ ( B @ ( a @ ( B @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9381,4309]) ).
thf(9572,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ product ) ) )
!= ( additive_identity @ ( B @ ( A @ product ) ) ) )
| ~ ( B @ ( a @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[9571]) ).
thf(9573,plain,
~ ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ),
inference(pattern_uni,[status(thm)],[9572:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity ))]]) ).
thf(385,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[248,41]) ).
thf(386,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[385]) ).
thf(387,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[386:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(424,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)],[387,41]) ).
thf(425,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[424]) ).
thf(426,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[425:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(729,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)],[426,41]) ).
thf(730,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[729]) ).
thf(731,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[730:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(904,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)],[731,41]) ).
thf(905,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[904]) ).
thf(906,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[905:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1404,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[906,41]) ).
thf(1405,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1404]) ).
thf(1406,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1405:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(4361,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,57]) ).
thf(4362,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4361]) ).
thf(4363,plain,
additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4362:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(13473,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)],[4363,45]) ).
thf(13474,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[13473]) ).
thf(13475,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[13474:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( a @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(1494,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1406,41]) ).
thf(1495,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1494]) ).
thf(1496,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1495:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1782,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1496,41]) ).
thf(1783,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1782]) ).
thf(1784,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1783:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2246,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1784,41]) ).
thf(2247,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2246]) ).
thf(2248,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2247:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(139,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[121,41]) ).
thf(140,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(199,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[141,41]) ).
thf(200,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(3799,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[201,547]) ).
thf(3800,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3799]) ).
thf(3801,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3800:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( ( A @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ( B @ additive_inverse @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[41,41]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( ( A @ additive_inverse @ defined )
!= ( B @ defined ) )
| ( B @ additive_inverse @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[128]) ).
thf(130,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse @ defined )
| ~ ( A @ defined ) ),
inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( C )),bind(B,$thf( C @ additive_inverse ))]]) ).
thf(134,plain,
! [A: $i] :
( ( A @ additive_inverse @ additive_inverse @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[130]) ).
thf(8313,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3801,134]) ).
thf(8314,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8313]) ).
thf(8315,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8314:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_addition) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,35]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(269,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( multiplicative_identity @ additive_inverse @ ( A @ add ) @ ( multiplicative_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( A )),bind(B,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(3820,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[124,547]) ).
thf(3821,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3820]) ).
thf(3822,plain,
additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3821:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(4252,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3822,547]) ).
thf(4253,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[4252]) ).
thf(4254,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[4253:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) ))]]) ).
thf(9001,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4254,547]) ).
thf(9002,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[9001]) ).
thf(9003,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[9002:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(3856,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[64,547]) ).
thf(3857,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3856]) ).
thf(3858,plain,
additive_identity @ ( a @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3857:[bind(A,$thf( a ))]]) ).
thf(4121,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3858,547]) ).
thf(4122,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[4121]) ).
thf(4123,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[4122:[bind(A,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(6493,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4123,41]) ).
thf(6494,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6493]) ).
thf(6495,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6494:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) ))]]) ).
thf(3793,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[133,547]) ).
thf(3794,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3793]) ).
thf(3795,plain,
additive_identity @ ( a @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3794:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(4210,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3795,41]) ).
thf(4211,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4210]) ).
thf(4212,plain,
additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4211:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ multiply ) ))]]) ).
thf(6742,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4212,547]) ).
thf(6743,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6742]) ).
thf(6744,plain,
additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6743:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(3808,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[33,547]) ).
thf(3809,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3808]) ).
thf(3810,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3809:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(3996,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3810,134]) ).
thf(3997,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[3996]) ).
thf(3998,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[3997:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(6197,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3998,547]) ).
thf(6198,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6197]) ).
thf(6199,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6198:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(7218,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,71]) ).
thf(7219,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7218]) ).
thf(7220,plain,
a @ ( a @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7219:[bind(A,$thf( a ))]]) ).
thf(9322,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)],[7220,77]) ).
thf(9323,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[9322]) ).
thf(9324,plain,
a @ ( multiplicative_identity @ ( a @ product ) ),
inference(pattern_uni,[status(thm)],[9323:[bind(A,$thf( a )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a ))]]) ).
thf(4389,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,57]) ).
thf(4390,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4389]) ).
thf(4391,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4390:[bind(A,$thf( additive_identity ))]]) ).
thf(3910,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[426,547]) ).
thf(3911,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3910]) ).
thf(3912,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3911:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(3993,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3810,41]) ).
thf(3994,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[3993]) ).
thf(3995,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[3994:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(4639,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3995,547]) ).
thf(4640,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[4639]) ).
thf(4641,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[4640:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse ))]]) ).
thf(13670,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4641,547]) ).
thf(13671,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[13670]) ).
thf(13672,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[13671:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(4213,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3795,134]) ).
thf(4214,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4213]) ).
thf(4215,plain,
additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4214:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ multiply ) ))]]) ).
thf(4078,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3813,547]) ).
thf(4079,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[4078]) ).
thf(4080,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[4079:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(6253,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4080,41]) ).
thf(6254,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6253]) ).
thf(6255,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6254:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) ))]]) ).
thf(15502,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[6255,547]) ).
thf(15503,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[15502]) ).
thf(15504,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[15503:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse ))]]) ).
thf(9954,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,81]) ).
thf(9955,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9954]) ).
thf(9956,plain,
multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9955:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(7266,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[198,71]) ).
thf(7267,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7266]) ).
thf(7268,plain,
a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7267:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(25177,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)],[7268,77]) ).
thf(25178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[25177]) ).
thf(25179,plain,
a @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( a @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[25178:[bind(A,$thf( a @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(4124,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3858,41]) ).
thf(4125,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4124]) ).
thf(4126,plain,
additive_identity @ ( a @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4125:[bind(A,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(4737,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4126,134]) ).
thf(4738,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4737]) ).
thf(4739,plain,
additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4738:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse ))]]) ).
thf(4645,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3995,134]) ).
thf(4646,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4645]) ).
thf(4647,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4646:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse ))]]) ).
thf(252,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[201,41]) ).
thf(253,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[252]) ).
thf(254,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(398,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)],[254,41]) ).
thf(399,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[398]) ).
thf(400,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(3940,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[400,547]) ).
thf(3941,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3940]) ).
thf(3942,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3941:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,35]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(287,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ additive_inverse @ ( A @ add ) @ ( additive_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ additive_inverse ))]]) ).
thf(57176,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ additive_inverse @ ( A @ add ) @ ( additive_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,287]) ).
thf(57177,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ additive_inverse @ ( A @ add ) @ ( additive_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[57176]) ).
thf(57178,plain,
additive_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[57177:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(59018,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[57178,45]) ).
thf(59019,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[59018]) ).
thf(59020,plain,
additive_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( multiplicative_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[59019:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ additive_inverse @ ( multiplicative_identity @ add ) ))]]) ).
thf(50423,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( multiplicative_identity @ additive_inverse @ ( A @ add ) @ ( multiplicative_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,269]) ).
thf(50424,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( multiplicative_identity @ additive_inverse @ ( A @ add ) @ ( multiplicative_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[50423]) ).
thf(50425,plain,
multiplicative_identity @ additive_inverse @ ( a @ add ) @ ( multiplicative_identity @ additive_inverse @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[50424:[bind(A,$thf( a ))]]) ).
thf(51768,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( a @ add ) @ ( multiplicative_identity @ additive_inverse @ ( a @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[50425,45]) ).
thf(51769,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( a @ add ) @ ( multiplicative_identity @ additive_inverse @ ( a @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[51768]) ).
thf(51770,plain,
multiplicative_identity @ additive_inverse @ ( a @ add ) @ ( a @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[51769:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( a )),bind(C,$thf( multiplicative_identity @ additive_inverse @ ( a @ add ) ))]]) ).
thf(4127,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3858,134]) ).
thf(4128,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4127]) ).
thf(4129,plain,
additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4128:[bind(A,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(6549,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4129,134]) ).
thf(6550,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6549]) ).
thf(6551,plain,
additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6550:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(9886,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3813,81]) ).
thf(9887,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9886]) ).
thf(9888,plain,
additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9887:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(28116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[9888,45]) ).
thf(28117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[28116]) ).
thf(28118,plain,
additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ sum ) ),
inference(pattern_uni,[status(thm)],[28117:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(3817,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[141,547]) ).
thf(3818,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3817]) ).
thf(3819,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3818:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(6044,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3819,134]) ).
thf(6045,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6044]) ).
thf(6046,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6045:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(8428,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4166,41]) ).
thf(8429,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8428]) ).
thf(8430,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8429:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(13673,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4641,41]) ).
thf(13674,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[13673]) ).
thf(13675,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[13674:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(2,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/sandbox/benchmark/theBenchmark.p',associativity_addition_2) ).
thf(31,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)],[2]) ).
thf(32,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)],[31]) ).
thf(27,axiom,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
thf(78,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(79,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[78]) ).
thf(157,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,79]) ).
thf(158,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity ))]]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
!= ( C @ ( additive_identity @ ( B @ sum ) ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[186]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplicative_identity != C )
| ( C != additive_identity )
| ( A != B )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(241,plain,
! [A: $i] :
( ( multiplicative_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ ( A @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(456,plain,
! [A: $i] :
( ~ $true
| ( ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
!= ( additive_identity @ ( A @ ( A @ sum ) ) ) )
| ( multiplicative_identity != additive_identity )
| ~ ( additive_identity @ ( A @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[241]) ).
thf(458,plain,
( ( multiplicative_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( additive_identity ))]]) ).
thf(10282,plain,
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity != additive_identity )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9956,458]) ).
thf(10283,plain,
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity != additive_identity ) ),
inference(simp,[status(thm)],[10282]) ).
thf(10319,plain,
( ( multiplicative_identity != additive_identity )
| ( multiplicative_identity != additive_identity )
| ( additive_identity != additive_identity )
| ( multiplicative_identity != additive_identity ) ),
inference(simp,[status(thm)],[10283]) ).
thf(10341,plain,
multiplicative_identity != additive_identity,
inference(simp,[status(thm)],[10319]) ).
thf(154,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( D @ ( G @ ( E @ sum ) ) ) )
| ~ $true
| ~ ( G @ ( C @ ( F @ sum ) ) )
| ~ ( B @ ( F @ ( E @ sum ) ) )
| ( D @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,32]) ).
thf(155,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( D @ ( G @ ( E @ sum ) ) ) )
| ~ ( G @ ( C @ ( F @ sum ) ) )
| ~ ( B @ ( F @ ( E @ sum ) ) )
| ( D @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ sum ) ) )
| ~ ( B @ ( D @ ( additive_identity @ sum ) ) )
| ( additive_identity @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( additive_identity )),bind(E,$thf( additive_identity )),bind(F,$thf( F )),bind(G,$thf( A ))]]) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ sum ) ) )
| ~ ( B @ ( D @ ( additive_identity @ sum ) ) )
| ( additive_identity @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[156]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(42,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(6041,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3819,41]) ).
thf(6042,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6041]) ).
thf(6043,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6042:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(15316,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6043,134]) ).
thf(15317,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[15316]) ).
thf(15318,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[15317:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(689,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)],[400,41]) ).
thf(690,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[689]) ).
thf(691,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[690:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(749,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[691,41]) ).
thf(750,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[749]) ).
thf(751,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[750:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(924,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[751,41]) ).
thf(925,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[924]) ).
thf(926,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[925:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1434,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[926,41]) ).
thf(1435,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1434]) ).
thf(1436,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1435:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1722,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1436,41]) ).
thf(1723,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1722]) ).
thf(1724,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1723:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(10026,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,81]) ).
thf(10027,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[10026]) ).
thf(10028,plain,
a @ ( a @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[10027:[bind(A,$thf( a ))]]) ).
thf(11149,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)],[10028,45]) ).
thf(11150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( a @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[11149]) ).
thf(11151,plain,
a @ ( additive_identity @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[11150:[bind(A,$thf( a )),bind(B,$thf( additive_identity )),bind(C,$thf( a ))]]) ).
thf(5244,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) )
| ~ $true
| ~ ( additive_identity @ ( a @ ( a @ product ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,4300]) ).
thf(5245,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) )
| ~ ( additive_identity @ ( a @ ( a @ product ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5244]) ).
thf(5406,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= additive_identity )
| ( B != additive_identity )
| ( A != a )
| ~ ( additive_identity @ ( a @ ( a @ product ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5245]) ).
thf(5426,plain,
( ( ( additive_identity @ ( a @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( a @ ( a @ product ) ) )
| ~ ( additive_identity @ defined )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[5406]) ).
thf(7042,plain,
( ( ( additive_identity @ ( a @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( a @ ( a @ product ) ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[5426,64,65]) ).
thf(7043,plain,
( ( ( additive_identity @ ( a @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( a @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[7042]) ).
thf(7176,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,71]) ).
thf(7177,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7176]) ).
thf(7178,plain,
additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7177:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(4384,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,57]) ).
thf(4385,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4384]) ).
thf(4386,plain,
additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4385:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(255,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[201,53]) ).
thf(256,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(151,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( G @ ( C @ ( F @ sum ) ) ) )
| ~ ( D @ ( G @ ( E @ sum ) ) )
| ~ $true
| ~ ( B @ ( F @ ( E @ sum ) ) )
| ( D @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,32]) ).
thf(152,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( G @ ( C @ ( F @ sum ) ) ) )
| ~ ( D @ ( G @ ( E @ sum ) ) )
| ~ ( B @ ( F @ ( E @ sum ) ) )
| ( D @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[151]) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( additive_identity @ ( D @ sum ) ) )
| ~ ( B @ ( additive_identity @ ( D @ sum ) ) )
| ( C @ ( A @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( additive_identity )),bind(G,$thf( additive_identity ))]]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( additive_identity @ ( D @ sum ) ) )
| ~ ( B @ ( additive_identity @ ( D @ sum ) ) )
| ( C @ ( A @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[153]) ).
thf(4332,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3813,57]) ).
thf(4333,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4332]) ).
thf(4334,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4333:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,35]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(281,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( additive_identity ))]]) ).
thf(54501,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,281]) ).
thf(54502,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[54501]) ).
thf(54503,plain,
additive_identity @ ( a @ additive_inverse @ add ) @ ( additive_identity @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[54502:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(190,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[124,41]) ).
thf(191,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
additive_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(205,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[192,41]) ).
thf(206,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(3922,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[207,547]) ).
thf(3923,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3922]) ).
thf(3924,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3923:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(8372,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3924,134]) ).
thf(8373,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8372]) ).
thf(8374,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8373:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(7096,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[3858,71]) ).
thf(7097,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7096]) ).
thf(7098,plain,
additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( a @ multiply ) @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7097:[bind(A,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(23256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( a @ multiply ) @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7098,77]) ).
thf(23257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( a @ multiply ) @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[23256]) ).
thf(23258,plain,
additive_identity @ ( a @ multiply ) @ ( multiplicative_identity @ ( additive_identity @ ( a @ multiply ) @ product ) ),
inference(pattern_uni,[status(thm)],[23257:[bind(A,$thf( additive_identity @ ( a @ multiply ) )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(9975,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[141,81]) ).
thf(9976,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9975]) ).
thf(9977,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9976:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(29909,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)],[9977,45]) ).
thf(29910,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[29909]) ).
thf(29911,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[29910:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',associativity_addition_1) ).
thf(46,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)],[10]) ).
thf(3990,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3810,547]) ).
thf(3991,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3990]) ).
thf(3992,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3991:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(6147,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3992,41]) ).
thf(6148,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6147]) ).
thf(6149,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6148:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) ))]]) ).
thf(5242,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( a @ ( a @ product ) ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,4300]) ).
thf(5243,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( a @ ( a @ product ) ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5242]) ).
thf(5408,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= additive_identity )
| ( B != a )
| ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5243]) ).
thf(5428,plain,
( ( ( a @ ( a @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) )
| ~ ( a @ defined )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[5408]) ).
thf(7058,plain,
( ( ( a @ ( a @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[5428]) ).
thf(7059,plain,
( ( ( a @ ( a @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7058,64]) ).
thf(7060,plain,
( ( ( a @ ( a @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[7059]) ).
thf(4381,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)],[192,57]) ).
thf(4382,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4381]) ).
thf(4383,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4382:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(4081,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3813,41]) ).
thf(4082,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4081]) ).
thf(4083,plain,
additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4082:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(4691,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4083,134]) ).
thf(4692,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4691]) ).
thf(4693,plain,
additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4692:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse ))]]) ).
thf(14268,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4693,547]) ).
thf(14269,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[14268]) ).
thf(14270,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[14269:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(9605,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ product ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9381,30]) ).
thf(9606,plain,
( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ product ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ product ) ) ) ),
inference(simp,[status(thm)],[9605]) ).
thf(9617,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != a )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[9606]) ).
thf(9636,plain,
multiplicative_identity != a,
inference(simp,[status(thm)],[9617]) ).
thf(4983,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( a @ ( B @ product ) ) )
!= ( additive_identity @ ( B @ ( A @ product ) ) ) )
| ~ ( additive_identity @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4309]) ).
thf(4985,plain,
! [B: $i,A: $i] :
( ( B != additive_identity )
| ( a != B )
| ( B != A )
| ~ ( additive_identity @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[4983]) ).
thf(4988,plain,
( ( a != additive_identity )
| ~ ( additive_identity @ ( a @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[4985]) ).
thf(171,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( F @ ( D @ sum ) ) )
!= ( F @ ( B @ ( E @ sum ) ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ sum ) ) )
| ~ ( A @ ( C @ ( C @ sum ) ) )
| ( B @ ( B @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( A )),bind(B,$thf( C )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( C ))]]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ sum ) ) )
| ~ ( A @ ( C @ ( C @ sum ) ) )
| ( B @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(7173,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[141,71]) ).
thf(7174,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7173]) ).
thf(7175,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7174:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(104,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[33,53]) ).
thf(105,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[104]) ).
thf(106,plain,
( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(1630,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)],[106,45]) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[1630]) ).
thf(1632,plain,
( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[1631:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(4731,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4126,547]) ).
thf(4732,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[4731]) ).
thf(4733,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[4732:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse ))]]) ).
thf(10269,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)],[9956,45]) ).
thf(10270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[10269]) ).
thf(10271,plain,
multiplicative_identity @ ( additive_identity @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[10270:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity ))]]) ).
thf(225,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( I @ ( G @ sum ) ) ) )
| ~ $true
| ~ ( I @ ( additive_identity @ ( H @ sum ) ) )
| ~ ( additive_identity @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,186]) ).
thf(226,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( multiplicative_identity @ ( I @ ( G @ sum ) ) ) )
| ~ ( I @ ( additive_identity @ ( H @ sum ) ) )
| ~ ( additive_identity @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(227,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( additive_identity @ ( F @ sum ) ) )
| ~ ( additive_identity @ ( F @ ( A @ sum ) ) )
| ~ ( multiplicative_identity @ ( E @ ( C @ sum ) ) )
| ~ ( E @ ( B @ ( D @ sum ) ) )
| ~ ( A @ ( D @ ( C @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( multiplicative_identity )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( A )),bind(H,$thf( H )),bind(I,$thf( B ))]]) ).
thf(238,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( additive_identity @ ( F @ sum ) ) )
| ~ ( additive_identity @ ( F @ ( A @ sum ) ) )
| ~ ( multiplicative_identity @ ( E @ ( C @ sum ) ) )
| ~ ( E @ ( B @ ( D @ sum ) ) )
| ~ ( A @ ( D @ ( C @ sum ) ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(7614,plain,
! [B: $i,A: $i] :
( ( ( a @ ( a @ ( multiplicative_identity @ product ) ) )
!= ( additive_identity @ ( B @ ( A @ product ) ) ) )
| ~ ( B @ ( a @ ( B @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7220,4309]) ).
thf(7615,plain,
! [B: $i,A: $i] :
( ( ( a @ ( a @ ( multiplicative_identity @ product ) ) )
!= ( additive_identity @ ( B @ ( A @ product ) ) ) )
| ~ ( B @ ( a @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[7614]) ).
thf(7658,plain,
! [B: $i,A: $i] :
( ( a != additive_identity )
| ( a != B )
| ( multiplicative_identity != A )
| ~ ( B @ ( a @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[7615]) ).
thf(7677,plain,
( ( a != additive_identity )
| ~ ( a @ ( a @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[7658]) ).
thf(54693,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,281]) ).
thf(54694,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[54693]) ).
thf(54695,plain,
additive_identity @ ( a @ add ) @ ( additive_identity @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[54694:[bind(A,$thf( a ))]]) ).
thf(56137,plain,
( ( ( additive_identity @ ( a @ add ) @ ( additive_identity @ ( a @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54695,79]) ).
thf(56138,plain,
( ( additive_identity @ ( a @ add ) @ ( additive_identity @ ( a @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[56137]) ).
thf(56183,plain,
( ( ( additive_identity @ ( a @ add ) )
!= multiplicative_identity )
| ( additive_identity != additive_identity )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[56138]) ).
thf(56272,plain,
( ( ( additive_identity @ ( a @ add ) )
!= multiplicative_identity )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[56183]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',distributivity_2) ).
thf(60,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)],[17]) ).
thf(61,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)],[60]) ).
thf(6496,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4123,134]) ).
thf(6497,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6496]) ).
thf(6498,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6497:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) ))]]) ).
thf(9912,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,81]) ).
thf(9913,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9912]) ).
thf(9914,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9913:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(12467,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)],[9914,79]) ).
thf(12468,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12467]) ).
thf(12490,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12468]) ).
thf(12499,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[12490]) ).
thf(7135,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,71]) ).
thf(7136,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7135]) ).
thf(7137,plain,
a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7136:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(9678,plain,
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7137,9573]) ).
thf(9679,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[9678]) ).
thf(9688,plain,
( ( ( a @ additive_inverse )
!= multiplicative_identity )
| ( ( a @ additive_inverse )
!= a )
| ( multiplicative_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[9679]) ).
thf(9700,plain,
( ( ( a @ additive_inverse )
!= multiplicative_identity )
| ( ( a @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[9688]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[207,35]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(312,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( A @ add ) @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(25,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ product ) ) )
| ~ ( A @ ( G @ ( D @ product ) ) )
| ~ ( C @ ( G @ ( F @ product ) ) )
| ~ ( F @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_1) ).
thf(74,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ product ) ) )
| ~ ( A @ ( G @ ( D @ product ) ) )
| ~ ( C @ ( G @ ( F @ product ) ) )
| ~ ( F @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9661,plain,
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7178,9573]) ).
thf(9662,plain,
( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[9661]) ).
thf(9691,plain,
( ( ( additive_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( additive_identity @ additive_inverse )
!= a )
| ( multiplicative_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[9662]) ).
thf(9703,plain,
( ( ( additive_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( additive_identity @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[9691]) ).
thf(4170,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3789,134]) ).
thf(4171,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4170]) ).
thf(4172,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4171:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) ))]]) ).
thf(193,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[133,53]) ).
thf(194,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[193]) ).
thf(195,plain,
( ( additive_identity @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(3677,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) )
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[195,45]) ).
thf(3678,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) )
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[3677]) ).
thf(3679,plain,
( ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ sum ) ) )
| ( a @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[3678:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(8484,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4172,547]) ).
thf(8485,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[8484]) ).
thf(8486,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[8485:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(98,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( B @ ( F @ ( E @ sum ) ) ) )
| ~ ( D @ ( H @ ( G @ sum ) ) )
| ~ ( H @ ( C @ ( F @ product ) ) )
| ~ ( G @ ( C @ ( E @ product ) ) )
| ~ $true
| ( D @ ( C @ ( B @ product ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,61]) ).
thf(99,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( B @ ( F @ ( E @ sum ) ) ) )
| ~ ( D @ ( H @ ( G @ sum ) ) )
| ~ ( H @ ( C @ ( F @ product ) ) )
| ~ ( G @ ( C @ ( E @ product ) ) )
| ( D @ ( C @ ( B @ product ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ sum ) ) )
| ~ ( E @ ( B @ ( A @ product ) ) )
| ~ ( D @ ( B @ ( additive_identity @ product ) ) )
| ( C @ ( B @ ( additive_identity @ product ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( A )),bind(B,$thf( additive_identity )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( additive_identity )),bind(F,$thf( A ))]]) ).
thf(117,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ sum ) ) )
| ~ ( E @ ( B @ ( A @ product ) ) )
| ~ ( D @ ( B @ ( additive_identity @ product ) ) )
| ( C @ ( B @ ( additive_identity @ product ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[100]) ).
thf(313,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)],[35,79]) ).
thf(314,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)],[313]) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ add ) )
!= multiplicative_identity )
| ( B != additive_identity )
| ( A != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[314]) ).
thf(379,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ ( additive_identity @ defined )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[360]) ).
thf(437,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[379]) ).
thf(438,plain,
( ( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ~ $true ),
inference(rewrite,[status(thm)],[437,65]) ).
thf(439,plain,
( ( additive_identity @ ( additive_identity @ add ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[438]) ).
thf(9007,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4254,134]) ).
thf(9008,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[9007]) ).
thf(9009,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[9008:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(7126,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,71]) ).
thf(7127,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7126]) ).
thf(7128,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7127:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(9668,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7128,9573]) ).
thf(9669,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[9668]) ).
thf(9693,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= a )
| ( multiplicative_identity != multiplicative_identity ) ),
inference(simp,[status(thm)],[9669]) ).
thf(9705,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[9693]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(38,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)],[6]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[201,35]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( A @ add ) @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( A )),bind(B,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(258,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[207,41]) ).
thf(259,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(4207,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3795,547]) ).
thf(4208,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[4207]) ).
thf(4209,plain,
additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[4208:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ multiply ) ))]]) ).
thf(8886,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4209,41]) ).
thf(8887,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8886]) ).
thf(8888,plain,
additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8887:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(3946,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[254,547]) ).
thf(3947,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3946]) ).
thf(3948,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3947:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(3805,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[192,547]) ).
thf(3806,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3805]) ).
thf(3807,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3806:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(5935,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3807,547]) ).
thf(5936,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[5935]) ).
thf(5937,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[5936:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(91,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( G @ ( F @ sum ) ) )
!= ( A @ ( E @ ( D @ sum ) ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( D @ product ) ) )
| ~ ( C @ ( A @ ( C @ product ) ) )
| ~ ( B @ ( D @ ( C @ sum ) ) )
| ( B @ ( A @ ( B @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( D @ product ) ) )
| ~ ( C @ ( A @ ( C @ product ) ) )
| ~ ( B @ ( D @ ( C @ sum ) ) )
| ( B @ ( A @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(3892,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[387,547]) ).
thf(3893,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3892]) ).
thf(3894,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3893:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(9883,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3858,81]) ).
thf(9884,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9883]) ).
thf(9885,plain,
additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9884:[bind(A,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(4685,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4083,547]) ).
thf(4686,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[4685]) ).
thf(4687,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[4686:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse ))]]) ).
thf(14215,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4687,134]) ).
thf(14216,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14215]) ).
thf(14217,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14216:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(8369,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3924,41]) ).
thf(8370,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8369]) ).
thf(8371,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8370:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(4084,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3813,134]) ).
thf(4085,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4084]) ).
thf(4086,plain,
additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4085:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(6443,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4086,134]) ).
thf(6444,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6443]) ).
thf(6445,plain,
additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6444:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(4400,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,57]) ).
thf(4401,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4400]) ).
thf(4402,plain,
additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4401:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(3898,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[198,547]) ).
thf(3899,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3898]) ).
thf(3900,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3899:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(6094,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3900,41]) ).
thf(6095,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6094]) ).
thf(6096,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6095:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(5333,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ product ) ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,30]) ).
thf(5334,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ product ) ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5333]) ).
thf(5404,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= additive_identity )
| ( B != a )
| ( A != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5334]) ).
thf(5423,plain,
( ( ( a @ ( additive_identity @ multiply ) )
!= additive_identity )
| ~ ( a @ defined )
| ~ ( additive_identity @ defined ) ),
inference(simp,[status(thm)],[5404]) ).
thf(5977,plain,
( ( ( a @ ( additive_identity @ multiply ) )
!= additive_identity )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[5423,64,65]) ).
thf(5978,plain,
( ( a @ ( additive_identity @ multiply ) )
!= additive_identity ),
inference(simp,[status(thm)],[5977]) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( D @ ( additive_identity @ ( C @ sum ) ) ) )
| ~ ( multiplicative_identity @ ( D @ ( B @ sum ) ) )
| ~ $true
| ~ ( additive_identity @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,186]) ).
thf(215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( D @ ( additive_identity @ ( C @ sum ) ) ) )
| ~ ( multiplicative_identity @ ( D @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[214]) ).
thf(216,plain,
! [A: $i] :
( ~ ( multiplicative_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ defined )
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( additive_identity )),bind(B,$thf( B )),bind(C,$thf( additive_identity )),bind(D,$thf( additive_identity ))]]) ).
thf(240,plain,
! [A: $i] :
( ~ ( multiplicative_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ defined )
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[216]) ).
thf(44249,plain,
! [A: $i] :
( ~ ( multiplicative_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ $true
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[240,65]) ).
thf(44250,plain,
! [A: $i] :
( ~ ( multiplicative_identity @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) )
| ( additive_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[44249]) ).
thf(14274,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4693,134]) ).
thf(14275,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14274]) ).
thf(14276,plain,
additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14275:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(25000,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)],[7175,77]) ).
thf(25001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[25000]) ).
thf(25002,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[25001:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(15310,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[6043,547]) ).
thf(15311,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[15310]) ).
thf(15312,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[15311:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(5938,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3807,41]) ).
thf(5939,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[5938]) ).
thf(5940,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[5939:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(14471,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[5940,547]) ).
thf(14472,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[14471]) ).
thf(14473,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[14472:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(9665,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) )
| ~ $true
| ~ ( C @ ( A @ ( B @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,9573]) ).
thf(9666,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) )
| ~ ( C @ ( A @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[9665]) ).
thf(9667,plain,
~ ( multiplicative_identity @ ( multiplicative_identity @ ( a @ product ) ) ),
inference(pattern_uni,[status(thm)],[9666:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( a )),bind(C,$thf( multiplicative_identity ))]]) ).
thf(15508,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6255,134]) ).
thf(15509,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[15508]) ).
thf(15510,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[15509:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse ))]]) ).
thf(90,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( G @ ( B @ ( E @ product ) ) )
!= ( F @ ( B @ ( D @ product ) ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(92,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( E @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( D @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E )),bind(E,$thf( E )),bind(F,$thf( G ))]]) ).
thf(96,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( E @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( D @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(8889,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4209,134]) ).
thf(8890,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8889]) ).
thf(8891,plain,
additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8890:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(7167,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[3810,71]) ).
thf(7168,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7167]) ).
thf(7169,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7168:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(4480,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[198,57]) ).
thf(4481,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4480]) ).
thf(4482,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4481:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(13729,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4647,547]) ).
thf(13730,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[13729]) ).
thf(13731,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[13730:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(6150,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3992,134]) ).
thf(6151,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6150]) ).
thf(6152,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6151:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) ))]]) ).
thf(1625,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[138,45]) ).
thf(1626,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[1625]) ).
thf(1627,plain,
( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[1626:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(4258,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3822,134]) ).
thf(4259,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4258]) ).
thf(4260,plain,
additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4259:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) ))]]) ).
thf(9066,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4260,134]) ).
thf(9067,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[9066]) ).
thf(9068,plain,
additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[9067:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(72,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(73,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(222,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( I @ ( additive_identity @ ( H @ sum ) ) ) )
| ~ ( multiplicative_identity @ ( I @ ( G @ sum ) ) )
| ~ $true
| ~ ( additive_identity @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,186]) ).
thf(223,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( I @ ( additive_identity @ ( H @ sum ) ) ) )
| ~ ( multiplicative_identity @ ( I @ ( G @ sum ) ) )
| ~ ( additive_identity @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(224,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( B @ ( F @ sum ) ) )
| ~ ( additive_identity @ ( A @ ( F @ sum ) ) )
| ~ ( B @ ( E @ ( C @ sum ) ) )
| ~ ( E @ ( additive_identity @ ( D @ sum ) ) )
| ~ ( A @ ( D @ ( C @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( A )),bind(B,$thf( additive_identity )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( A )),bind(I,$thf( C ))]]) ).
thf(237,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( B @ ( F @ sum ) ) )
| ~ ( additive_identity @ ( A @ ( F @ sum ) ) )
| ~ ( B @ ( E @ ( C @ sum ) ) )
| ~ ( E @ ( additive_identity @ ( D @ sum ) ) )
| ~ ( A @ ( D @ ( C @ sum ) ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(219,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( H @ ( G @ sum ) ) ) )
| ~ ( multiplicative_identity @ ( I @ ( G @ sum ) ) )
| ~ ( I @ ( additive_identity @ ( H @ sum ) ) )
| ~ $true
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,186]) ).
thf(220,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( additive_identity @ ( H @ ( G @ sum ) ) ) )
| ~ ( multiplicative_identity @ ( I @ ( G @ sum ) ) )
| ~ ( I @ ( additive_identity @ ( H @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(221,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( F @ ( A @ sum ) ) )
| ~ ( F @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( E @ ( C @ sum ) ) )
| ~ ( E @ ( B @ ( D @ sum ) ) )
| ~ ( A @ ( D @ ( C @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( additive_identity )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( A )),bind(H,$thf( B ))]]) ).
thf(244,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( F @ ( A @ sum ) ) )
| ~ ( F @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( E @ ( C @ sum ) ) )
| ~ ( E @ ( B @ ( D @ sum ) ) )
| ~ ( A @ ( D @ ( C @ sum ) ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(1812,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1724,41]) ).
thf(1813,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1812]) ).
thf(1814,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1813:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(411,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)],[260,41]) ).
thf(412,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[411]) ).
thf(413,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[412:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(709,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)],[413,41]) ).
thf(710,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[709]) ).
thf(711,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[710:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(884,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)],[711,41]) ).
thf(885,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[884]) ).
thf(886,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[885:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(944,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[886,41]) ).
thf(945,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[944]) ).
thf(946,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[945:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1464,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[946,41]) ).
thf(1465,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1464]) ).
thf(1466,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1465:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(7939,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,73]) ).
thf(7940,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(simp,[status(thm)],[7939]) ).
thf(7941,plain,
( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ multiplicative_inverse @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[7940:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(4255,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3822,41]) ).
thf(4256,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[4255]) ).
thf(4257,plain,
additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[4256:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) ))]]) ).
thf(6948,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4257,547]) ).
thf(6949,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6948]) ).
thf(6950,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6949:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(14333,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4733,134]) ).
thf(14334,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14333]) ).
thf(14335,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14334:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(9962,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,81]) ).
thf(9963,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9962]) ).
thf(9964,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9963:[bind(A,$thf( additive_identity ))]]) ).
thf(9350,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)],[7128,77]) ).
thf(9351,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[9350]) ).
thf(9352,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[9351:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(57206,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ additive_inverse @ ( A @ add ) @ ( additive_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,287]) ).
thf(57207,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ additive_inverse @ ( A @ add ) @ ( additive_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[57206]) ).
thf(57208,plain,
additive_identity @ additive_inverse @ ( additive_identity @ add ) @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[57207:[bind(A,$thf( additive_identity ))]]) ).
thf(10070,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[198,81]) ).
thf(10071,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[10070]) ).
thf(10072,plain,
a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[10071:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(30141,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)],[10072,45]) ).
thf(30142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[30141]) ).
thf(30143,plain,
a @ additive_inverse @ additive_inverse @ ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[30142:[bind(A,$thf( a @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(6490,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4123,547]) ).
thf(6491,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6490]) ).
thf(6492,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6491:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ multiply ) @ multiply ) ))]]) ).
thf(6596,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4169,547]) ).
thf(6597,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6596]) ).
thf(6598,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6597:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(7158,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,71]) ).
thf(7159,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7158]) ).
thf(7160,plain,
multiplicative_identity @ ( multiplicative_identity @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7159:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(27892,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[9885,45]) ).
thf(27893,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[27892]) ).
thf(27894,plain,
additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ sum ) ),
inference(pattern_uni,[status(thm)],[27893:[bind(A,$thf( additive_identity @ ( a @ multiply ) )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(14386,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4739,547]) ).
thf(14387,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[14386]) ).
thf(14388,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[14387:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1752,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1466,41]) ).
thf(1753,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1752]) ).
thf(1754,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1753:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(9672,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,9573]) ).
thf(9673,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( multiplicative_identity @ ( a @ ( multiplicative_identity @ product ) ) ) )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[9672]) ).
thf(9692,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= multiplicative_identity )
| ( B != a )
| ( A != multiplicative_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[9673]) ).
thf(9704,plain,
( ( ( a @ ( multiplicative_identity @ multiply ) )
!= multiplicative_identity )
| ~ ( a @ defined )
| ~ ( multiplicative_identity @ defined ) ),
inference(simp,[status(thm)],[9692]) ).
thf(64157,plain,
( ( ( a @ ( multiplicative_identity @ multiply ) )
!= multiplicative_identity )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[9704,64,33]) ).
thf(64158,plain,
( ( a @ ( multiplicative_identity @ multiply ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[64157]) ).
thf(54561,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,281]) ).
thf(54562,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[54561]) ).
thf(54563,plain,
additive_identity @ ( additive_identity @ add ) @ ( additive_identity @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[54562:[bind(A,$thf( additive_identity ))]]) ).
thf(50293,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( multiplicative_identity @ additive_inverse @ ( A @ add ) @ ( multiplicative_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,269]) ).
thf(50294,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( multiplicative_identity @ additive_inverse @ ( A @ add ) @ ( multiplicative_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[50293]) ).
thf(50295,plain,
multiplicative_identity @ additive_inverse @ ( additive_identity @ add ) @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[50294:[bind(A,$thf( additive_identity ))]]) ).
thf(51405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( additive_identity @ add ) @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[50295,45]) ).
thf(51406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( additive_identity @ add ) @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[51405]) ).
thf(51407,plain,
multiplicative_identity @ additive_inverse @ ( additive_identity @ add ) @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[51406:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse @ ( additive_identity @ add ) ))]]) ).
thf(163,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( L @ ( H @ ( K @ sum ) ) ) )
| ~ ( I @ ( L @ ( J @ sum ) ) )
| ~ $true
| ~ ( G @ ( K @ ( J @ sum ) ) )
| ( I @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,32]) ).
thf(164,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( L @ ( H @ ( K @ sum ) ) ) )
| ~ ( I @ ( L @ ( J @ sum ) ) )
| ~ ( G @ ( K @ ( J @ sum ) ) )
| ( I @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( C @ ( I @ sum ) ) )
| ~ ( G @ ( A @ ( I @ sum ) ) )
| ( H @ ( B @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( B )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( A )),bind(L,$thf( C ))]]) ).
thf(176,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( C @ ( I @ sum ) ) )
| ~ ( G @ ( A @ ( I @ sum ) ) )
| ( H @ ( B @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(9060,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4260,547]) ).
thf(9061,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[9060]) ).
thf(9062,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[9061:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(14392,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4739,134]) ).
thf(14393,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14392]) ).
thf(14394,plain,
additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14393:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(50263,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( multiplicative_identity @ additive_inverse @ ( A @ add ) @ ( multiplicative_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,269]) ).
thf(50264,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( multiplicative_identity @ additive_inverse @ ( A @ add ) @ ( multiplicative_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[50263]) ).
thf(50265,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[50264:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(51040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[50265,45]) ).
thf(51041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[51040]) ).
thf(51042,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[51041:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) ))]]) ).
thf(58321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ add ) @ ( additive_identity @ ( a @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[54503,45]) ).
thf(58322,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ add ) @ ( additive_identity @ ( a @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[58321]) ).
thf(58323,plain,
additive_identity @ ( a @ additive_inverse @ add ) @ ( a @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[58322:[bind(A,$thf( additive_identity )),bind(B,$thf( a @ additive_inverse )),bind(C,$thf( additive_identity @ ( a @ additive_inverse @ add ) ))]]) ).
thf(101,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( D @ ( H @ ( G @ sum ) ) ) )
| ~ $true
| ~ ( H @ ( C @ ( F @ product ) ) )
| ~ ( G @ ( C @ ( E @ product ) ) )
| ~ ( B @ ( F @ ( E @ sum ) ) )
| ( D @ ( C @ ( B @ product ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,61]) ).
thf(102,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( D @ ( H @ ( G @ sum ) ) ) )
| ~ ( H @ ( C @ ( F @ product ) ) )
| ~ ( G @ ( C @ ( E @ product ) ) )
| ~ ( B @ ( F @ ( E @ sum ) ) )
| ( D @ ( C @ ( B @ product ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ product ) ) )
| ~ ( additive_identity @ ( C @ ( D @ product ) ) )
| ~ ( B @ ( E @ ( D @ sum ) ) )
| ( additive_identity @ ( C @ ( B @ product ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( additive_identity )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( additive_identity )),bind(H,$thf( A ))]]) ).
thf(118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ product ) ) )
| ~ ( additive_identity @ ( C @ ( D @ product ) ) )
| ~ ( B @ ( E @ ( D @ sum ) ) )
| ( additive_identity @ ( C @ ( B @ product ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[103]) ).
thf(202,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[141,53]) ).
thf(203,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[202]) ).
thf(204,plain,
( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(2216,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1754,41]) ).
thf(2217,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2216]) ).
thf(2218,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2217:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2306,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2218,41]) ).
thf(2307,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2306]) ).
thf(2308,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2307:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(cnf,[status(esa)],[48]) ).
thf(54489,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,281]) ).
thf(54490,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[54489]) ).
thf(54491,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ add ) @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[54490:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(9965,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3810,81]) ).
thf(9966,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9965]) ).
thf(9967,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9966:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(9951,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[192,81]) ).
thf(9952,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9951]) ).
thf(9953,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9952:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(28340,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)],[9953,45]) ).
thf(28341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[28340]) ).
thf(28342,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[28341:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(8490,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4172,134]) ).
thf(8491,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8490]) ).
thf(8492,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8491:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(142,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( G @ ( K @ ( J @ sum ) ) ) )
| ~ ( I @ ( M @ ( L @ sum ) ) )
| ~ ( M @ ( H @ ( K @ product ) ) )
| ~ ( L @ ( H @ ( J @ product ) ) )
| ~ $true
| ( I @ ( H @ ( G @ product ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,61]) ).
thf(143,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( G @ ( K @ ( J @ sum ) ) ) )
| ~ ( I @ ( M @ ( L @ sum ) ) )
| ~ ( M @ ( H @ ( K @ product ) ) )
| ~ ( L @ ( H @ ( J @ product ) ) )
| ( I @ ( H @ ( G @ product ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( J @ ( I @ sum ) ) )
| ~ ( J @ ( G @ ( B @ product ) ) )
| ~ ( I @ ( G @ ( A @ product ) ) )
| ( H @ ( G @ ( C @ product ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( C )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( A )),bind(K,$thf( B ))]]) ).
thf(181,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( J @ ( I @ sum ) ) )
| ~ ( J @ ( G @ ( B @ product ) ) )
| ~ ( I @ ( G @ ( A @ product ) ) )
| ( H @ ( G @ ( C @ product ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(7004,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3798,547]) ).
thf(7005,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[7004]) ).
thf(7006,plain,
additive_identity @ ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[7005:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(57351,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ additive_inverse @ ( A @ add ) @ ( additive_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,287]) ).
thf(57352,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ additive_inverse @ ( A @ add ) @ ( additive_identity @ additive_inverse @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[57351]) ).
thf(57353,plain,
additive_identity @ additive_inverse @ ( a @ add ) @ ( additive_identity @ additive_inverse @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[57352:[bind(A,$thf( a ))]]) ).
thf(60619,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( a @ add ) @ ( additive_identity @ additive_inverse @ ( a @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[57353,45]) ).
thf(60620,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( a @ add ) @ ( additive_identity @ additive_inverse @ ( a @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[60619]) ).
thf(60621,plain,
additive_identity @ additive_inverse @ ( a @ add ) @ ( a @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[60620:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( a )),bind(C,$thf( additive_identity @ additive_inverse @ ( a @ add ) ))]]) ).
thf(9373,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)],[7137,77]) ).
thf(9374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[9373]) ).
thf(9375,plain,
a @ additive_inverse @ ( multiplicative_identity @ ( a @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[9374:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( a @ additive_inverse ))]]) ).
thf(4439,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,57]) ).
thf(4440,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4439]) ).
thf(4441,plain,
additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4440:[bind(A,$thf( a ))]]) ).
thf(5518,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)],[4441,45]) ).
thf(5519,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ ( a @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5518]) ).
thf(5520,plain,
additive_identity @ ( a @ additive_inverse @ ( a @ sum ) ),
inference(pattern_uni,[status(thm)],[5519:[bind(A,$thf( a )),bind(B,$thf( a @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(39,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)],[38]) ).
thf(6602,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4169,134]) ).
thf(6603,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6602]) ).
thf(6604,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6603:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(59383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[57208,45]) ).
thf(59384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[59383]) ).
thf(59385,plain,
additive_identity @ additive_inverse @ ( additive_identity @ add ) @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[59384:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ additive_inverse @ ( additive_identity @ add ) ))]]) ).
thf(15436,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[6149,547]) ).
thf(15437,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[15436]) ).
thf(15438,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[15437:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse ))]]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(66,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)],[21]) ).
thf(2276,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1814,41]) ).
thf(2277,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2276]) ).
thf(2278,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2277:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(6954,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4257,134]) ).
thf(6955,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6954]) ).
thf(6956,plain,
additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6955:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(249,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[198,53]) ).
thf(250,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[249]) ).
thf(251,plain,
( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( a @ additive_inverse @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(6374,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)],[67,79]) ).
thf(6375,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) ) ),
inference(simp,[status(thm)],[6374]) ).
thf(6376,plain,
( ~ ( additive_identity @ ( multiplicative_identity @ less_or_equal ) )
| ~ ( multiplicative_identity @ ( additive_identity @ less_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[6375:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity ))]]) ).
thf(14327,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4733,547]) ).
thf(14328,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[14327]) ).
thf(14329,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[14328:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(9924,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,81]) ).
thf(9925,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[9924]) ).
thf(9926,plain,
a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[9925:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(12532,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)],[9926,45]) ).
thf(12533,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12532]) ).
thf(12534,plain,
a @ additive_inverse @ ( additive_identity @ ( a @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[12533:[bind(A,$thf( a @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( a @ additive_inverse ))]]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( ( A @ additive_inverse @ defined )
!= ( B @ defined ) )
| ( additive_identity @ ( B @ ( additive_identity @ sum ) ) )
| ~ $true
| ( B @ multiplicative_inverse @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[41,53]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( ( A @ additive_inverse @ defined )
!= ( B @ defined ) )
| ( additive_identity @ ( B @ ( additive_identity @ sum ) ) )
| ( B @ multiplicative_inverse @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[125]) ).
thf(127,plain,
! [A: $i] :
( ( additive_identity @ ( A @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( A @ additive_inverse @ multiplicative_inverse @ defined )
| ~ ( A @ defined ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( C )),bind(B,$thf( C @ additive_inverse ))]]) ).
thf(135,plain,
! [A: $i] :
( ( additive_identity @ ( A @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( A @ additive_inverse @ multiplicative_inverse @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[127]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ $true
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[198,35]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( B @ defined ) )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( a @ additive_inverse @ additive_inverse @ ( A @ add ) @ ( a @ additive_inverse @ additive_inverse @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( A )),bind(B,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(4888,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)],[4391,45]) ).
thf(4889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[4888]) ).
thf(4890,plain,
additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[4889:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(13735,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4647,134]) ).
thf(13736,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[13735]) ).
thf(13737,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[13736:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(3874,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[413,547]) ).
thf(3875,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3874]) ).
thf(3876,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3875:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(4329,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3858,57]) ).
thf(4330,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4329]) ).
thf(4331,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4330:[bind(A,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(110,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[64,53]) ).
thf(111,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
| ( a @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( a ))]]) ).
thf(14209,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4687,547]) ).
thf(14210,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[14209]) ).
thf(14211,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[14210:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(4392,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3810,57]) ).
thf(4393,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4392]) ).
thf(4394,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4393:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(8883,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4209,547]) ).
thf(8884,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[8883]) ).
thf(8885,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[8884:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(8310,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3801,41]) ).
thf(8311,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8310]) ).
thf(8312,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8311:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(15373,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[6096,547]) ).
thf(15374,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[15373]) ).
thf(15375,plain,
additive_identity @ ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[15374:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(85,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( N @ ( I @ ( L @ product ) ) ) )
| ~ ( J @ ( N @ ( M @ sum ) ) )
| ~ $true
| ~ ( M @ ( I @ ( K @ product ) ) )
| ~ ( H @ ( L @ ( K @ sum ) ) )
| ( J @ ( I @ ( H @ product ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,61]) ).
thf(86,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( N @ ( I @ ( L @ product ) ) ) )
| ~ ( J @ ( N @ ( M @ sum ) ) )
| ~ ( M @ ( I @ ( K @ product ) ) )
| ~ ( H @ ( L @ ( K @ sum ) ) )
| ( J @ ( I @ ( H @ product ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(87,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( C @ ( K @ sum ) ) )
| ~ ( K @ ( B @ ( J @ product ) ) )
| ~ ( H @ ( A @ ( J @ sum ) ) )
| ( I @ ( B @ ( H @ product ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( B )),bind(J,$thf( J )),bind(K,$thf( K )),bind(L,$thf( A )),bind(M,$thf( M )),bind(N,$thf( C ))]]) ).
thf(95,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( C @ ( K @ sum ) ) )
| ~ ( K @ ( B @ ( J @ product ) ) )
| ~ ( H @ ( A @ ( J @ sum ) ) )
| ( I @ ( B @ ( H @ product ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(54531,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,281]) ).
thf(54532,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[54531]) ).
thf(54533,plain,
additive_identity @ ( multiplicative_identity @ add ) @ ( additive_identity @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[54532:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(55314,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ add ) @ ( additive_identity @ ( multiplicative_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[54533,45]) ).
thf(55315,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ add ) @ ( additive_identity @ ( multiplicative_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[55314]) ).
thf(55316,plain,
additive_identity @ ( multiplicative_identity @ add ) @ ( multiplicative_identity @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[55315:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ ( multiplicative_identity @ add ) ))]]) ).
thf(261,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[207,53]) ).
thf(262,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[261]) ).
thf(263,plain,
( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(6144,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3992,547]) ).
thf(6145,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6144]) ).
thf(6146,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6145:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) ))]]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(62,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)],[18]) ).
thf(63,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)],[62]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(50,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)],[12]) ).
thf(6091,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3900,547]) ).
thf(6092,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6091]) ).
thf(6093,plain,
additive_identity @ ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6092:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(57970,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ add ) @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[54491,45]) ).
thf(57971,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ add ) @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[57970]) ).
thf(57972,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ add ) @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[57971:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity @ additive_inverse )),bind(C,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ add ) ))]]) ).
thf(7007,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[3798,41]) ).
thf(7008,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[7007]) ).
thf(7009,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[7008:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(166,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( I @ ( L @ ( J @ sum ) ) ) )
| ~ $true
| ~ ( L @ ( H @ ( K @ sum ) ) )
| ~ ( G @ ( K @ ( J @ sum ) ) )
| ( I @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,32]) ).
thf(167,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( I @ ( L @ ( J @ sum ) ) ) )
| ~ ( L @ ( H @ ( K @ sum ) ) )
| ~ ( G @ ( K @ ( J @ sum ) ) )
| ( I @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(168,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( H @ ( I @ sum ) ) )
| ~ ( G @ ( I @ ( A @ sum ) ) )
| ( C @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( C )),bind(J,$thf( A )),bind(K,$thf( K )),bind(L,$thf( B ))]]) ).
thf(177,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( H @ ( I @ sum ) ) )
| ~ ( G @ ( I @ ( A @ sum ) ) )
| ( C @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(6543,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4129,547]) ).
thf(6544,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6543]) ).
thf(6545,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6544:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(145,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( I @ ( M @ ( L @ sum ) ) ) )
| ~ $true
| ~ ( M @ ( H @ ( K @ product ) ) )
| ~ ( L @ ( H @ ( J @ product ) ) )
| ~ ( G @ ( K @ ( J @ sum ) ) )
| ( I @ ( H @ ( G @ product ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,61]) ).
thf(146,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( I @ ( M @ ( L @ sum ) ) ) )
| ~ ( M @ ( H @ ( K @ product ) ) )
| ~ ( L @ ( H @ ( J @ product ) ) )
| ~ ( G @ ( K @ ( J @ sum ) ) )
| ( I @ ( H @ ( G @ product ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( H @ ( J @ product ) ) )
| ~ ( A @ ( H @ ( I @ product ) ) )
| ~ ( G @ ( J @ ( I @ sum ) ) )
| ( C @ ( H @ ( G @ product ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( C )),bind(J,$thf( J )),bind(K,$thf( K )),bind(L,$thf( A )),bind(M,$thf( B ))]]) ).
thf(182,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( H @ ( J @ product ) ) )
| ~ ( A @ ( H @ ( I @ product ) ) )
| ~ ( G @ ( J @ ( I @ sum ) ) )
| ( C @ ( H @ ( G @ product ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(7155,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[192,71]) ).
thf(7156,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[7155]) ).
thf(7157,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ),
inference(pattern_uni,[status(thm)],[7156:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(23595,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)],[7157,77]) ).
thf(23596,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[23595]) ).
thf(23597,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[23596:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(12437,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)],[9914,45]) ).
thf(12438,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12437]) ).
thf(12439,plain,
multiplicative_identity @ additive_inverse @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[12438:[bind(A,$thf( multiplicative_identity @ additive_inverse )),bind(B,$thf( additive_identity )),bind(C,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(160,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( G @ ( K @ ( J @ sum ) ) ) )
| ~ ( I @ ( L @ ( J @ sum ) ) )
| ~ ( L @ ( H @ ( K @ sum ) ) )
| ~ $true
| ( I @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,32]) ).
thf(161,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ sum ) ) )
!= ( G @ ( K @ ( J @ sum ) ) ) )
| ~ ( I @ ( L @ ( J @ sum ) ) )
| ~ ( L @ ( H @ ( K @ sum ) ) )
| ( I @ ( H @ ( G @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(162,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( I @ ( A @ sum ) ) )
| ~ ( I @ ( G @ ( B @ sum ) ) )
| ( H @ ( G @ ( C @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( C )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( A )),bind(K,$thf( B ))]]) ).
thf(175,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( I @ ( A @ sum ) ) )
| ~ ( I @ ( G @ ( B @ sum ) ) )
| ( H @ ( G @ ( C @ sum ) ) )
| ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(8431,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4166,134]) ).
thf(8432,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8431]) ).
thf(8433,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8432:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(14477,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5940,134]) ).
thf(14478,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14477]) ).
thf(14479,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14478:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(8942,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4215,547]) ).
thf(8943,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[8942]) ).
thf(8944,plain,
additive_identity @ ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[8943:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(12657,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)],[9980,79]) ).
thf(12658,plain,
( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12657]) ).
thf(12681,plain,
( ( ( additive_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( additive_identity @ additive_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12658]) ).
thf(12690,plain,
( ( ( additive_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( additive_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[12681]) ).
thf(54595,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,281]) ).
thf(54596,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ add ) @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[54595]) ).
thf(54597,plain,
additive_identity @ ( additive_identity @ additive_inverse @ add ) @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[54596:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(5969,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( a @ ( a @ product ) ) ) )
| ( a != additive_identity )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[59,4988]) ).
thf(5970,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( a @ ( a @ product ) ) ) )
| ( a != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5969]) ).
thf(5974,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= additive_identity )
| ( B != a )
| ( A != a )
| ( a != additive_identity )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[5970]) ).
thf(5976,plain,
( ( ( a @ ( a @ multiply ) )
!= additive_identity )
| ( a != additive_identity )
| ~ ( a @ defined )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[5974]) ).
thf(6284,plain,
( ( ( a @ ( a @ multiply ) )
!= additive_identity )
| ( a != additive_identity )
| ~ ( a @ defined ) ),
inference(simp,[status(thm)],[5976]) ).
thf(6285,plain,
( ( ( a @ ( a @ multiply ) )
!= additive_identity )
| ( a != additive_identity )
| ~ $true ),
inference(rewrite,[status(thm)],[6284,64]) ).
thf(6286,plain,
( ( ( a @ ( a @ multiply ) )
!= additive_identity )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[6285]) ).
thf(2922,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2248,41]) ).
thf(2923,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2922]) ).
thf(2924,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2923:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(8009,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[64,73]) ).
thf(8010,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(simp,[status(thm)],[8009]) ).
thf(8011,plain,
( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( a @ ( a @ multiplicative_inverse @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[8010:[bind(A,$thf( a ))]]) ).
thf(7010,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3798,134]) ).
thf(7011,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[7010]) ).
thf(7012,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[7011:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(75,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ product ) ) )
| ~ ( A @ ( G @ ( D @ product ) ) )
| ~ ( C @ ( G @ ( F @ product ) ) )
| ~ ( F @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
!= ( additive_identity @ ( B @ ( A @ sum ) ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[186]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
!= ( additive_identity @ ( B @ ( A @ sum ) ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(4321,plain,
( ( ( additive_identity @ ( a @ ( a @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[4320]) ).
thf(6250,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4080,547]) ).
thf(6251,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6250]) ).
thf(6252,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6251:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) ))]]) ).
thf(1676,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) )
| ( a @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[112,45]) ).
thf(1677,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) )
| ( a @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[1676]) ).
thf(1678,plain,
( ( additive_identity @ ( additive_identity @ ( a @ sum ) ) )
| ( a @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[1677:[bind(A,$thf( a )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity ))]]) ).
thf(6437,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4086,547]) ).
thf(6438,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6437]) ).
thf(6439,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6438:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(51,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)],[50]) ).
thf(14330,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4733,41]) ).
thf(14331,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14330]) ).
thf(14332,plain,
additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14331:[bind(A,$thf( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(13575,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)],[4402,45]) ).
thf(13576,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[13575]) ).
thf(13577,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[13576:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( additive_identity @ additive_inverse @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(148,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( B @ ( F @ ( E @ sum ) ) ) )
| ~ ( D @ ( G @ ( E @ sum ) ) )
| ~ ( G @ ( C @ ( F @ sum ) ) )
| ~ $true
| ( D @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,32]) ).
thf(149,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( B @ ( F @ ( E @ sum ) ) ) )
| ~ ( D @ ( G @ ( E @ sum ) ) )
| ~ ( G @ ( C @ ( F @ sum ) ) )
| ( D @ ( C @ ( B @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( additive_identity @ sum ) ) )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ( C @ ( B @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( A )),bind(B,$thf( additive_identity )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( additive_identity )),bind(F,$thf( A ))]]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( additive_identity @ sum ) ) )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ( C @ ( B @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[150]) ).
thf(28564,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[9967,45]) ).
thf(28565,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[28564]) ).
thf(28566,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ sum ) ),
inference(pattern_uni,[status(thm)],[28565:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(8366,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3924,547]) ).
thf(8367,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[8366]) ).
thf(8368,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[8367:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(4397,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)],[141,57]) ).
thf(4398,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[4397]) ).
thf(4399,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ),
inference(pattern_uni,[status(thm)],[4398:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(8307,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3801,547]) ).
thf(8308,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[8307]) ).
thf(8309,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[8308:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(9327,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)],[7178,77]) ).
thf(9328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[9327]) ).
thf(9329,plain,
additive_identity @ additive_inverse @ ( multiplicative_identity @ ( additive_identity @ additive_inverse @ product ) ),
inference(pattern_uni,[status(thm)],[9328:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ additive_inverse ))]]) ).
thf(211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( C @ ( B @ sum ) ) ) )
| ~ ( multiplicative_identity @ ( D @ ( B @ sum ) ) )
| ~ ( D @ ( additive_identity @ ( C @ sum ) ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[53,186]) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( C @ ( B @ sum ) ) ) )
| ~ ( multiplicative_identity @ ( D @ ( B @ sum ) ) )
| ~ ( D @ ( additive_identity @ ( C @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[211]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( B @ ( additive_identity @ sum ) ) )
| ~ ( B @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( A )),bind(B,$thf( additive_identity )),bind(C,$thf( A ))]]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ~ ( multiplicative_identity @ ( B @ ( additive_identity @ sum ) ) )
| ~ ( B @ ( additive_identity @ ( A @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[213]) ).
thf(12562,plain,
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9926,79]) ).
thf(12563,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12562]) ).
thf(12588,plain,
( ( ( a @ additive_inverse )
!= multiplicative_identity )
| ( ( a @ additive_inverse )
!= additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[12563]) ).
thf(12605,plain,
( ( ( a @ additive_inverse )
!= multiplicative_identity )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[12588]) ).
thf(6038,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[3819,547]) ).
thf(6039,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[6038]) ).
thf(6040,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[6039:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(58672,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ add ) @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[54597,45]) ).
thf(58673,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ add ) @ ( additive_identity @ ( additive_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[58672]) ).
thf(58674,plain,
additive_identity @ ( additive_identity @ additive_inverse @ add ) @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[58673:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity @ additive_inverse )),bind(C,$thf( additive_identity @ ( additive_identity @ additive_inverse @ add ) ))]]) ).
thf(208,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[192,53]) ).
thf(209,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[208]) ).
thf(210,plain,
( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) )
| ( additive_identity @ additive_inverse @ additive_inverse @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(3802,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[260,547]) ).
thf(3803,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[3802]) ).
thf(3804,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[3803:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(14212,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4687,41]) ).
thf(14213,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[14212]) ).
thf(14214,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[14213:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(6256,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4080,134]) ).
thf(6257,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6256]) ).
thf(6258,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6257:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ multiply ) ))]]) ).
thf(2959,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2278,41]) ).
thf(2960,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2959]) ).
thf(2961,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2960:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(82,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( M @ ( I @ ( K @ product ) ) ) )
| ~ ( J @ ( N @ ( M @ sum ) ) )
| ~ ( N @ ( I @ ( L @ product ) ) )
| ~ $true
| ~ ( H @ ( L @ ( K @ sum ) ) )
| ( J @ ( I @ ( H @ product ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,61]) ).
thf(83,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( M @ ( I @ ( K @ product ) ) ) )
| ~ ( J @ ( N @ ( M @ sum ) ) )
| ~ ( N @ ( I @ ( L @ product ) ) )
| ~ ( H @ ( L @ ( K @ sum ) ) )
| ( J @ ( I @ ( H @ product ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( K @ ( C @ sum ) ) )
| ~ ( K @ ( B @ ( J @ product ) ) )
| ~ ( H @ ( J @ ( A @ sum ) ) )
| ( I @ ( B @ ( H @ product ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( B )),bind(J,$thf( J )),bind(K,$thf( A )),bind(L,$thf( L )),bind(M,$thf( C ))]]) ).
thf(94,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( K @ ( C @ sum ) ) )
| ~ ( K @ ( B @ ( J @ product ) ) )
| ~ ( H @ ( J @ ( A @ sum ) ) )
| ( I @ ( B @ ( H @ product ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(24823,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[7169,77]) ).
thf(24824,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ ( multiplicative_identity @ product ) ) )
!= ( C @ ( A @ ( B @ product ) ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[24823]) ).
thf(24825,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ ( multiplicative_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ product ) ),
inference(pattern_uni,[status(thm)],[24824:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) )),bind(B,$thf( multiplicative_identity )),bind(C,$thf( additive_identity @ ( multiplicative_identity @ multiply ) ))]]) ).
thf(6203,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3998,134]) ).
thf(6204,plain,
! [A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6203]) ).
thf(6205,plain,
additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6204:[bind(A,$thf( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(15442,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6149,134]) ).
thf(15443,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[15442]) ).
thf(15444,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[15443:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ multiply ) @ additive_inverse ))]]) ).
thf(47,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)],[46]) ).
thf(56016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ add ) @ ( additive_identity @ ( a @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ~ $true
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[54695,45]) ).
thf(56017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( a @ add ) @ ( additive_identity @ ( a @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[56016]) ).
thf(56018,plain,
additive_identity @ ( a @ add ) @ ( a @ ( additive_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[56017:[bind(A,$thf( additive_identity )),bind(B,$thf( a )),bind(C,$thf( additive_identity @ ( a @ add ) ))]]) ).
thf(170,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( F @ ( D @ sum ) ) )
!= ( A @ ( E @ ( D @ sum ) ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( D @ sum ) ) )
| ~ ( B @ ( D @ ( C @ sum ) ) )
| ( B @ ( A @ ( B @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( D @ sum ) ) )
| ~ ( B @ ( D @ ( C @ sum ) ) )
| ( B @ ( A @ ( B @ sum ) ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(8425,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(paramod_ordered,[status(thm)],[4166,547]) ).
thf(8426,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ multiply ) @ defined ) ),
inference(simp,[status(thm)],[8425]) ).
thf(8427,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) @ multiply ) @ defined,
inference(pattern_uni,[status(thm)],[8426:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(6748,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4212,134]) ).
thf(6749,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6748]) ).
thf(6750,plain,
additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6749:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(6097,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3900,134]) ).
thf(6098,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[6097]) ).
thf(6099,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[6098:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(13676,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4641,134]) ).
thf(13677,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[13676]) ).
thf(13678,plain,
additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[13677:[bind(A,$thf( additive_identity @ ( additive_identity @ ( multiplicative_identity @ multiply ) @ additive_inverse @ multiply ) ))]]) ).
thf(8948,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4215,134]) ).
thf(8949,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[8948]) ).
thf(8950,plain,
additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[8949:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(5941,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3807,134]) ).
thf(5942,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[5941]) ).
thf(5943,plain,
additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[5942:[bind(A,$thf( additive_identity @ ( additive_identity @ additive_inverse @ additive_inverse @ multiply ) ))]]) ).
thf(9004,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[4254,41]) ).
thf(9005,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[9004]) ).
thf(9006,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[9005:[bind(A,$thf( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ multiply ) @ multiply ) ))]]) ).
thf(4782,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)],[4386,45]) ).
thf(4783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ ( multiplicative_identity @ additive_inverse @ sum ) ) )
!= ( C @ ( A @ ( B @ sum ) ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[4782]) ).
thf(4784,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ sum ) ),
inference(pattern_uni,[status(thm)],[4783:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( multiplicative_identity @ additive_inverse )),bind(C,$thf( additive_identity ))]]) ).
thf(15379,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6096,134]) ).
thf(15380,plain,
! [A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[15379]) ).
thf(15381,plain,
additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[15380:[bind(A,$thf( additive_identity @ ( a @ additive_inverse @ additive_inverse @ multiply ) @ additive_inverse ))]]) ).
thf(2996,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2308,41]) ).
thf(2997,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2996]) ).
thf(2998,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2997:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplicative_identity @ ( C @ ( A @ sum ) ) )
!= ( C @ ( additive_identity @ ( B @ sum ) ) ) )
| ~ ( C @ ( additive_identity @ ( B @ sum ) ) )
| ~ ( additive_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(3033,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[2924,41]) ).
thf(3034,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[3033]) ).
thf(3035,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[3034:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(78878,plain,
$false,
inference(e,[status(thm)],[69,23428,138,4169,3798,6283,12629,9222,4166,9573,1406,13475,2248,8315,269,9003,6495,3858,3813,6744,6199,9324,4391,3912,13672,4215,15504,9956,56,25179,4739,4647,3942,59020,51770,6551,28118,6046,8430,13675,10341,7220,185,42,15318,1724,37,11151,7043,7178,4386,257,52,50425,184,4334,54503,751,8374,3998,23258,29911,46,78,29,6149,7060,4383,57,14270,9636,4988,7268,179,7175,1632,4733,10271,106,238,7677,121,56272,61,6498,133,12499,9700,9914,312,74,9703,201,4172,3795,3679,8486,248,60,117,439,4323,3995,9009,9705,38,70,192,275,33,260,8888,3948,5937,97,3894,9885,4080,14217,3810,65,8371,6043,6445,4402,6096,4123,4693,54695,5978,44250,141,14276,9977,53,7101,25002,15312,124,14473,547,9667,77,15510,96,8891,7169,4482,3819,13731,4086,41,6152,1627,9068,134,73,237,244,4352,1814,1466,7941,6950,14335,9964,4212,926,3807,9352,7128,57208,45,30143,6492,6598,7160,27894,906,14388,1754,32,34,64,64158,54563,51407,176,9062,1784,14394,4309,5940,711,3900,413,44,51042,58323,59,118,281,204,71,54,2308,50265,49,54491,9967,28342,8492,181,7006,60621,9375,5520,81,57353,76,39,6604,4300,59385,387,15438,9888,66,2278,198,6956,251,7098,6376,50295,6255,14329,12534,9381,135,299,1496,4890,80,13737,3876,4209,35,4331,426,4260,112,14211,4394,4441,7137,8885,48,9926,8312,15375,95,9953,4641,55316,263,6146,63,7166,50,67,9980,6093,57972,3801,7009,31,177,6545,182,23597,12439,10028,72,175,8433,43,4257,14479,8944,12690,54533,54597,6286,2924,10072,3789,40,8011,946,7012,4126,186,55,731,75,58,235,4321,207,7157,6252,287,3992,2218,57178,1678,6439,36,4254,30,51,14332,13577,183,28566,8368,4399,4687,8309,9329,3822,239,4051,12605,195,6040,58674,886,1436,210,79,3804,14214,4083,6258,2961,400,94,24825,4129,6205,15444,47,56018,68,178,691,8427,4363,6750,6099,62,13678,254,8950,5943,9006,3924,4784,15381,2998,232,3035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD043-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.22/0.48 % Computer : n011.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sun Sep 27 02:27:29 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.97/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.14 % [INFO] Parsing done (178ms).
% 1.61/1.15 % [INFO] Running in sequential loop mode.
% 2.07/1.48 % [INFO] eprover registered as external prover.
% 2.07/1.49 % [INFO] Scanning for conjecture ...
% 2.35/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 27 axioms. Running axiom selection ...
% 2.54/1.64 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 2.54/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.78/1.70 % [INFO] Type checking passed.
% 2.78/1.70 % [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 ...
% 148.01/40.21 % External prover 'e' found a proof!
% 148.01/40.21 % [INFO] Killing All external provers ...
% 148.01/40.22 % Time passed: 39593ms (effective reasoning time: 39060ms)
% 148.01/40.22 % Axioms used in derivation (27): associativity_addition_1, existence_of_identity_multiplication, transitivity_of_order_relation, totality_of_multiplication, well_definedness_of_additive_identity, compatibility_of_order_relation_and_multiplication, a_is_defined, well_definedness_of_multiplication, existence_of_identity_addition, associativity_multiplication_1, antisymmetry_of_order_relation, totality_of_order_relation, totality_of_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_order_relation_and_addition, distributivity_2, existence_of_inverse_multiplication, well_definedness_of_multiplicative_identity, well_definedness_of_additive_inverse, distributivity_1, associativity_addition_2, commutativity_addition, associativity_multiplication_2, different_identities, well_definedness_of_multiplicative_inverse
% 148.01/40.22 % No. of inferences in proof: 1101
% 148.01/40.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 39593 ms resp. 39060 ms w/o parsing
% 143.61/40.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 144.09/40.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------