TSTP Solution File: GRP696-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP696-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:15:09 EDT 2023
% Result : Unsatisfiable 159.99s 32.18s
% Output : Refutation 160.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 20
% Syntax : Number of formulae : 603 ( 205 unt; 8 typ; 0 def)
% Number of atoms : 1190 (1189 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 6093 ( 908 ~; 595 |; 0 &;4590 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 633 ( 0 ^; 633 !; 0 ?; 633 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_type,type,
mult: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(ld_type,type,
ld: $i > $i > $i ).
thf(rd_type,type,
rd: $i > $i > $i ).
thf(unit_type,type,
unit: $i ).
thf(i_type,type,
i: $i > $i ).
thf(11,axiom,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
thf(34,plain,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,plain,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
inference(lifteq,[status(thm)],[34]) ).
thf(6,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
thf(24,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( unit = B )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ B @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[35,25]) ).
thf(43,plain,
( ( i @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( unit )),bind(B,$thf( i @ unit ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( i @ ( mult @ B @ A ) ) )
= ( i @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( i @ ( mult @ B @ A ) ) )
= ( i @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( i @ ( mult @ B @ A ) ) )
= ( i @ B ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(903,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ C @ ( i @ A ) )
= ( i @ D ) )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,29]) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( i @ A ) )
= ( i @ ( rd @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[903:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( rd @ E @ F ))]]) ).
thf(960,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( i @ A ) )
= ( i @ ( rd @ A @ B ) ) ),
inference(simp,[status(thm)],[904]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[18]) ).
thf(514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ B @ unit )
= C )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,19]) ).
thf(515,plain,
! [A: $i] :
( ( ld @ ( i @ A ) @ unit )
= A ),
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( D )),bind(B,$thf( i @ D )),bind(C,$thf( D ))]]) ).
thf(520,plain,
! [A: $i] :
( ( ld @ ( i @ A ) @ unit )
= A ),
inference(simp,[status(thm)],[515]) ).
thf(12,axiom,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c11) ).
thf(36,plain,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(37,plain,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
inference(lifteq,[status(thm)],[36]) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ B @ unit )
= C )
| ( ( mult @ A @ ( i @ A ) )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[37,19]) ).
thf(517,plain,
! [A: $i] :
( ( ld @ A @ unit )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[516:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( i @ D ))]]) ).
thf(521,plain,
! [A: $i] :
( ( ld @ A @ unit )
= ( i @ A ) ),
inference(simp,[status(thm)],[517]) ).
thf(561,plain,
! [A: $i] :
( ( i @ ( i @ A ) )
= A ),
inference(rewrite,[status(thm)],[520,521]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[22]) ).
thf(876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( rd @ ( i @ B ) @ D )
= C )
| ( ( mult @ A @ ( i @ ( mult @ B @ A ) ) )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,23]) ).
thf(877,plain,
! [B: $i,A: $i] :
( ( rd @ ( i @ A ) @ ( i @ ( mult @ A @ B ) ) )
= B ),
inference(pattern_uni,[status(thm)],[876:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( i @ ( mult @ F @ G ) ))]]) ).
thf(1004,plain,
! [B: $i,A: $i] :
( ( rd @ ( i @ A ) @ ( i @ ( mult @ A @ B ) ) )
= B ),
inference(simp,[status(thm)],[877]) ).
thf(3992,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ ( i @ B ) @ ( i @ unit ) )
= C )
| ( ( mult @ A @ ( i @ A ) )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[37,1004]) ).
thf(3993,plain,
! [A: $i] :
( ( rd @ ( i @ A ) @ ( i @ unit ) )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[3992:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( i @ D ))]]) ).
thf(4075,plain,
! [A: $i] :
( ( rd @ ( i @ A ) @ ( i @ unit ) )
= ( i @ A ) ),
inference(simp,[status(thm)],[3993]) ).
thf(4218,plain,
! [A: $i] :
( ( rd @ ( i @ A ) @ unit )
= ( i @ A ) ),
inference(rewrite,[status(thm)],[4075,43]) ).
thf(625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ld @ C @ A )
= D )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[21,19]) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( ld @ ( rd @ A @ B ) @ A )
= B ),
inference(pattern_uni,[status(thm)],[625:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( rd @ E @ F )),bind(D,$thf( F ))]]) ).
thf(749,plain,
! [B: $i,A: $i] :
( ( ld @ ( rd @ A @ B ) @ A )
= B ),
inference(simp,[status(thm)],[626]) ).
thf(4237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ ( i @ A ) @ B )
= C )
| ( ( rd @ ( i @ A ) @ unit )
!= ( rd @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4218,749]) ).
thf(4238,plain,
! [A: $i] :
( ( ld @ ( i @ A ) @ ( i @ A ) )
= unit ),
inference(pattern_uni,[status(thm)],[4237:[bind(A,$thf( D )),bind(B,$thf( i @ D )),bind(C,$thf( unit ))]]) ).
thf(4281,plain,
! [A: $i] :
( ( ld @ ( i @ A ) @ ( i @ A ) )
= unit ),
inference(simp,[status(thm)],[4238]) ).
thf(913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ld @ C @ ( i @ B ) )
= D )
| ( ( mult @ A @ ( i @ ( mult @ B @ A ) ) )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,19]) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( ld @ B @ ( i @ A ) )
= ( i @ ( mult @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( i @ ( mult @ F @ G ) ))]]) ).
thf(963,plain,
! [B: $i,A: $i] :
( ( ld @ B @ ( i @ A ) )
= ( i @ ( mult @ A @ B ) ) ),
inference(simp,[status(thm)],[914]) ).
thf(4290,plain,
! [A: $i] :
( ( i @ ( mult @ A @ ( i @ A ) ) )
= unit ),
inference(rewrite,[status(thm)],[4281,963]) ).
thf(4315,plain,
! [B: $i,A: $i] :
( ( ( i @ ( mult @ B @ A ) )
= unit )
| ( ( i @ ( i @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[561,4290]) ).
thf(4316,plain,
! [A: $i] :
( ( i @ ( mult @ ( i @ A ) @ A ) )
= unit ),
inference(pattern_uni,[status(thm)],[4315:[bind(A,$thf( C )),bind(B,$thf( i @ C ))]]) ).
thf(4389,plain,
! [A: $i] :
( ( i @ ( mult @ ( i @ A ) @ A ) )
= unit ),
inference(simp,[status(thm)],[4316]) ).
thf(4959,plain,
! [C: $i,B: $i,A: $i] :
( ( ( i @ ( i @ ( rd @ A @ B ) ) )
= unit )
| ( ( mult @ B @ ( i @ A ) )
!= ( mult @ ( i @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[960,4389]) ).
thf(4960,plain,
! [A: $i] :
( ( i @ ( i @ ( rd @ A @ ( i @ ( i @ A ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[4959:[bind(A,$thf( E )),bind(B,$thf( i @ ( i @ E ) )),bind(C,$thf( i @ E ))]]) ).
thf(4993,plain,
! [A: $i] :
( ( i @ ( i @ ( rd @ A @ ( i @ ( i @ A ) ) ) ) )
= unit ),
inference(simp,[status(thm)],[4960]) ).
thf(6928,plain,
! [A: $i] :
( ( rd @ A @ ( i @ ( i @ A ) ) )
= unit ),
inference(rewrite,[status(thm)],[4993,561]) ).
thf(6963,plain,
! [A: $i] :
( ( ( rd @ A @ ( i @ unit ) )
= unit )
| ( ( i @ unit )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43,6928]) ).
thf(6964,plain,
( ( rd @ unit @ ( i @ unit ) )
= unit ),
inference(pattern_uni,[status(thm)],[6963:[bind(A,$thf( unit ))]]) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ unit @ C )
= B )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,23]) ).
thf(784,plain,
! [A: $i] :
( ( rd @ unit @ A )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[783:[bind(A,$thf( D )),bind(B,$thf( i @ D )),bind(C,$thf( D ))]]) ).
thf(788,plain,
! [A: $i] :
( ( rd @ unit @ A )
= ( i @ A ) ),
inference(simp,[status(thm)],[784]) ).
thf(7024,plain,
( ( i @ ( i @ unit ) )
= unit ),
inference(rewrite,[status(thm)],[6964,788]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[16]) ).
thf(907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ C @ ( i @ B ) )
= ( i @ D ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,29]) ).
thf(908,plain,
! [B: $i,A: $i] :
( ( mult @ ( ld @ A @ B ) @ ( i @ B ) )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[907:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( ld @ E @ F )),bind(D,$thf( E ))]]) ).
thf(961,plain,
! [B: $i,A: $i] :
( ( mult @ ( ld @ A @ B ) @ ( i @ B ) )
= ( i @ A ) ),
inference(simp,[status(thm)],[908]) ).
thf(7075,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( ld @ A @ B ) @ unit )
= ( i @ A ) )
| ( ( i @ ( i @ unit ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7024,961]) ).
thf(7076,plain,
! [A: $i] :
( ( mult @ ( ld @ A @ ( i @ unit ) ) @ unit )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[7075:[bind(A,$thf( A )),bind(B,$thf( i @ unit ))]]) ).
thf(11895,plain,
! [A: $i] :
( ( ld @ A @ ( i @ unit ) )
= ( i @ A ) ),
inference(rewrite,[status(thm)],[7076,25]) ).
thf(11917,plain,
! [C: $i,B: $i,A: $i] :
( ( ( i @ A )
= C )
| ( ( ld @ A @ ( i @ unit ) )
!= ( ld @ ( rd @ B @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11895,749]) ).
thf(11918,plain,
! [A: $i] :
( ( i @ ( rd @ ( i @ unit ) @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[11917:[bind(A,$thf( rd @ ( i @ unit ) @ E )),bind(B,$thf( i @ unit )),bind(C,$thf( E ))]]) ).
thf(11951,plain,
! [A: $i] :
( ( i @ ( rd @ ( i @ unit ) @ A ) )
= A ),
inference(simp,[status(thm)],[11918]) ).
thf(12436,plain,
! [A: $i] :
( ( i @ ( rd @ unit @ A ) )
= A ),
inference(rewrite,[status(thm)],[11951,43]) ).
thf(12499,plain,
! [B: $i,A: $i] :
( ( ( rd @ B @ ( i @ A ) )
= unit )
| ( ( i @ ( rd @ unit @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12436,6928]) ).
thf(12500,plain,
! [A: $i] :
( ( rd @ ( rd @ unit @ A ) @ ( i @ A ) )
= unit ),
inference(pattern_uni,[status(thm)],[12499:[bind(A,$thf( D )),bind(B,$thf( rd @ unit @ D ))]]) ).
thf(12579,plain,
! [A: $i] :
( ( rd @ ( rd @ unit @ A ) @ ( i @ A ) )
= unit ),
inference(simp,[status(thm)],[12500]) ).
thf(13002,plain,
! [A: $i] :
( ( rd @ ( i @ A ) @ ( i @ A ) )
= unit ),
inference(rewrite,[status(thm)],[12579,788]) ).
thf(13061,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7024,13002]) ).
thf(13062,plain,
( ( rd @ unit @ ( i @ ( i @ unit ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[13061:[bind(A,$thf( i @ unit ))]]) ).
thf(13176,plain,
( ( i @ ( i @ ( i @ unit ) ) )
= unit ),
inference(rewrite,[status(thm)],[13062,788]) ).
thf(6933,plain,
! [B: $i,A: $i] :
( ( ( rd @ B @ ( i @ unit ) )
= unit )
| ( ( i @ ( mult @ ( i @ A ) @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4389,6928]) ).
thf(6934,plain,
! [A: $i] :
( ( rd @ ( mult @ ( i @ A ) @ A ) @ ( i @ unit ) )
= unit ),
inference(pattern_uni,[status(thm)],[6933:[bind(A,$thf( D )),bind(B,$thf( mult @ ( i @ D ) @ D ))]]) ).
thf(7012,plain,
! [A: $i] :
( ( rd @ ( mult @ ( i @ A ) @ A ) @ ( i @ unit ) )
= unit ),
inference(simp,[status(thm)],[6934]) ).
thf(9858,plain,
! [A: $i] :
( ( rd @ ( mult @ ( i @ A ) @ A ) @ unit )
= unit ),
inference(rewrite,[status(thm)],[7012,43]) ).
thf(9922,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ ( i @ ( rd @ A @ B ) ) @ unit )
= unit )
| ( ( mult @ B @ ( i @ A ) )
!= ( mult @ ( i @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[960,9858]) ).
thf(9923,plain,
! [A: $i] :
( ( rd @ ( i @ ( rd @ A @ ( i @ ( i @ A ) ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[9922:[bind(A,$thf( E )),bind(B,$thf( i @ ( i @ E ) )),bind(C,$thf( i @ E ))]]) ).
thf(9954,plain,
! [A: $i] :
( ( rd @ ( i @ ( rd @ A @ ( i @ ( i @ A ) ) ) ) @ unit )
= unit ),
inference(simp,[status(thm)],[9923]) ).
thf(45343,plain,
! [A: $i] :
( ( i @ ( rd @ A @ ( i @ ( i @ A ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[9954,4218]) ).
thf(45508,plain,
! [A: $i] :
( ( ( i @ ( rd @ A @ ( i @ unit ) ) )
= unit )
| ( ( i @ ( i @ ( i @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13176,45343]) ).
thf(45509,plain,
( ( i @ ( rd @ ( i @ ( i @ unit ) ) @ ( i @ unit ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[45508:[bind(A,$thf( i @ ( i @ unit ) ))]]) ).
thf(46173,plain,
( ( i @ ( rd @ unit @ unit ) )
= unit ),
inference(rewrite,[status(thm)],[45509,7024,43]) ).
thf(13048,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ unit @ B )
= C )
| ( ( rd @ ( i @ A ) @ ( i @ A ) )
!= ( rd @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13002,749]) ).
thf(13049,plain,
! [A: $i] :
( ( ld @ unit @ ( i @ A ) )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[13048:[bind(A,$thf( E )),bind(B,$thf( i @ E )),bind(C,$thf( i @ E ))]]) ).
thf(13120,plain,
! [A: $i] :
( ( ld @ unit @ ( i @ A ) )
= ( i @ A ) ),
inference(simp,[status(thm)],[13049]) ).
thf(22872,plain,
! [A: $i] :
( ( i @ ( mult @ A @ unit ) )
= ( i @ A ) ),
inference(rewrite,[status(thm)],[13120,963]) ).
thf(22934,plain,
! [B: $i,A: $i] :
( ( ( rd @ ( i @ B ) @ ( i @ A ) )
= unit )
| ( ( i @ ( mult @ A @ unit ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22872,13002]) ).
thf(22935,plain,
! [A: $i] :
( ( rd @ ( i @ ( mult @ A @ unit ) ) @ ( i @ A ) )
= unit ),
inference(pattern_uni,[status(thm)],[22934:[bind(A,$thf( C )),bind(B,$thf( mult @ C @ unit ))]]) ).
thf(23139,plain,
! [A: $i] :
( ( rd @ ( i @ ( mult @ A @ unit ) ) @ ( i @ A ) )
= unit ),
inference(simp,[status(thm)],[22935]) ).
thf(39129,plain,
! [A: $i] :
( ( rd @ ( i @ A ) @ ( i @ A ) )
= unit ),
inference(rewrite,[status(thm)],[23139,22872]) ).
thf(46277,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( rd @ unit @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[46173,39129]) ).
thf(46278,plain,
( ( rd @ unit @ ( i @ ( rd @ unit @ unit ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[46277:[bind(A,$thf( rd @ unit @ unit ))]]) ).
thf(47054,plain,
( ( i @ ( i @ ( rd @ unit @ unit ) ) )
= unit ),
inference(rewrite,[status(thm)],[46278,788]) ).
thf(47170,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( rd @ unit @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47054,39129]) ).
thf(47171,plain,
( ( rd @ unit @ ( i @ ( i @ ( rd @ unit @ unit ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[47170:[bind(A,$thf( i @ ( rd @ unit @ unit ) ))]]) ).
thf(48836,plain,
( ( i @ ( i @ ( i @ ( rd @ unit @ unit ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[47171,788]) ).
thf(48967,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ ( rd @ unit @ unit ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[48836,39129]) ).
thf(48968,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ ( rd @ unit @ unit ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[48967:[bind(A,$thf( i @ ( i @ ( rd @ unit @ unit ) ) ))]]) ).
thf(51650,plain,
( ( i @ ( i @ ( i @ ( i @ ( rd @ unit @ unit ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[48968,788]) ).
thf(51963,plain,
! [B: $i,A: $i] :
( ( ( i @ ( i @ ( i @ ( mult @ B @ ( i @ A ) ) ) ) )
= unit )
| ( ( i @ ( rd @ A @ B ) )
!= ( i @ ( rd @ unit @ unit ) ) ) ),
inference(paramod_ordered,[status(thm)],[960,51650]) ).
thf(51964,plain,
( ( i @ ( i @ ( i @ ( mult @ unit @ ( i @ unit ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[51963:[bind(A,$thf( unit )),bind(B,$thf( unit ))]]) ).
thf(52190,plain,
( ( i @ ( mult @ unit @ ( i @ unit ) ) )
= unit ),
inference(rewrite,[status(thm)],[51964,561]) ).
thf(52318,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( mult @ unit @ ( i @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52190,39129]) ).
thf(52319,plain,
( ( rd @ unit @ ( i @ ( mult @ unit @ ( i @ unit ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[52318:[bind(A,$thf( mult @ unit @ ( i @ unit ) ))]]) ).
thf(53630,plain,
( ( i @ ( i @ ( mult @ unit @ ( i @ unit ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[52319,788]) ).
thf(53768,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( mult @ unit @ ( i @ unit ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[53630,39129]) ).
thf(53769,plain,
( ( rd @ unit @ ( i @ ( i @ ( mult @ unit @ ( i @ unit ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[53768:[bind(A,$thf( i @ ( mult @ unit @ ( i @ unit ) ) ))]]) ).
thf(57102,plain,
( ( i @ ( i @ ( i @ ( mult @ unit @ ( i @ unit ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[53769,788]) ).
thf(57397,plain,
( ( ( i @ ( i @ ( i @ ( mult @ unit @ unit ) ) ) )
= unit )
| ( ( i @ unit )
!= ( i @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[43,57102]) ).
thf(57398,plain,
( ( i @ ( i @ ( i @ ( mult @ unit @ unit ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[57397:[]]) ).
thf(58341,plain,
( ( i @ ( mult @ unit @ unit ) )
= unit ),
inference(rewrite,[status(thm)],[57398,561]) ).
thf(58546,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( mult @ unit @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58341,9858]) ).
thf(58547,plain,
( ( rd @ ( mult @ unit @ ( mult @ unit @ unit ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[58546:[bind(A,$thf( mult @ unit @ unit ))]]) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[21,25]) ).
thf(642,plain,
! [A: $i] :
( ( rd @ A @ unit )
= A ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( D )),bind(B,$thf( unit )),bind(C,$thf( rd @ D @ unit ))]]) ).
thf(700,plain,
! [A: $i] :
( ( rd @ A @ unit )
= A ),
inference(simp,[status(thm)],[642]) ).
thf(61535,plain,
( ( mult @ unit @ ( mult @ unit @ unit ) )
= unit ),
inference(rewrite,[status(thm)],[58547,700]) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
thf(26,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(lifteq,[status(thm)],[26]) ).
thf(1,negated_conjecture,
( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(13,plain,
( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,plain,
( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(63,plain,
! [A: $i] :
( ( ( mult @ A @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ a @ b ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(108,plain,
! [A: $i] :
( ( A != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( A != a ) ),
inference(simp,[status(thm)],[63]) ).
thf(174,plain,
( ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit ) ),
inference(simp,[status(thm)],[108]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[17,174]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( B != a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit )
| ( A
!= ( mult @ b @ a ) )
| ( ( ld @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[312]) ).
thf(365,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( ld @ ( mult @ b @ a ) @ a )
!= a ) ),
inference(simp,[status(thm)],[324]) ).
thf(189,plain,
! [A: $i] :
( ( ( mult @ A @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[27,174]) ).
thf(205,plain,
! [A: $i] :
( ( A != a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ b @ a )
!= unit )
| ( A != a ) ),
inference(simp,[status(thm)],[189]) ).
thf(239,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( mult @ b @ a )
!= unit ) ),
inference(simp,[status(thm)],[205]) ).
thf(265,plain,
! [A: $i] :
( ( ( mult @ b @ a )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[35,239]) ).
thf(272,plain,
! [A: $i] :
( ( ( mult @ b @ a )
!= unit )
| ( ( i @ A )
!= a )
| ( A != b ) ),
inference(simp,[status(thm)],[265]) ).
thf(283,plain,
( ( ( mult @ b @ a )
!= unit )
| ( ( i @ b )
!= a ) ),
inference(simp,[status(thm)],[272]) ).
thf(602,plain,
! [A: $i] :
( ( ( i @ b )
!= a )
| ( ( mult @ A @ ( i @ A ) )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[37,283]) ).
thf(606,plain,
! [A: $i] :
( ( ( i @ b )
!= a )
| ( A != b )
| ( ( i @ A )
!= a ) ),
inference(simp,[status(thm)],[602]) ).
thf(618,plain,
( ( i @ b )
!= a ),
inference(simp,[status(thm)],[606]) ).
thf(751,plain,
! [A: $i] :
( ( A != a )
| ( ( i @ ( i @ A ) )
!= ( i @ b ) ) ),
inference(paramod_ordered,[status(thm)],[561,618]) ).
thf(754,plain,
( ( i @ a )
!= b ),
inference(simp,[status(thm)],[751]) ).
thf(22981,plain,
! [A: $i] :
( ( ( i @ A )
!= b )
| ( ( i @ ( mult @ A @ unit ) )
!= ( i @ a ) ) ),
inference(paramod_ordered,[status(thm)],[22872,754]) ).
thf(23116,plain,
! [A: $i] :
( ( ( i @ A )
!= b )
| ( ( mult @ A @ unit )
!= a ) ),
inference(simp,[status(thm)],[22981]) ).
thf(30638,plain,
! [A: $i] :
( ( ( i @ A )
!= b )
| ( A != a ) ),
inference(rewrite,[status(thm)],[23116,25]) ).
thf(13208,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13176,13002]) ).
thf(13209,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ unit ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[13208:[bind(A,$thf( i @ ( i @ unit ) ))]]) ).
thf(13861,plain,
( ( i @ ( i @ ( i @ ( i @ unit ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[13209,788]) ).
thf(13896,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ unit ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13861,13002]) ).
thf(13897,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[13896:[bind(A,$thf( i @ ( i @ ( i @ unit ) ) ))]]) ).
thf(15345,plain,
( ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[13897,788]) ).
thf(15387,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15345,13002]) ).
thf(15388,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[15387:[bind(A,$thf( i @ ( i @ ( i @ ( i @ unit ) ) ) ))]]) ).
thf(17894,plain,
( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[15388,788]) ).
thf(17952,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17894,13002]) ).
thf(17953,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[17952:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ))]]) ).
thf(19924,plain,
( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[17953,788]) ).
thf(20003,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19924,13002]) ).
thf(20004,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[20003:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ))]]) ).
thf(23175,plain,
( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[20004,788]) ).
thf(23276,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[23175,13002]) ).
thf(23277,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[23276:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ))]]) ).
thf(26651,plain,
( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[23277,788]) ).
thf(26862,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26651,9858]) ).
thf(26863,plain,
( ( rd @ ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[26862:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ))]]) ).
thf(42102,plain,
( ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[26863,700]) ).
thf(193,plain,
! [A: $i] :
( ( ( mult @ unit @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[35,174]) ).
thf(215,plain,
! [A: $i] :
( ( unit != a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(249,plain,
! [A: $i] :
( ( unit != a )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(66,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ A )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ a @ c ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(104,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ A )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( unit != a )
| ( A != c ) ),
inference(simp,[status(thm)],[66]) ).
thf(170,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ c )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( unit != a ) ),
inference(simp,[status(thm)],[104]) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( mult @ B @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[17,15]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( mult @ B @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( A != a )
| ( ( ld @ A @ B )
!= b ) ),
inference(simp,[status(thm)],[304]) ).
thf(379,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( ld @ a @ A )
!= b ) ),
inference(simp,[status(thm)],[342]) ).
thf(4940,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ ( mult @ ( i @ A ) @ A ) )
!= ( i @ a ) ) ),
inference(paramod_ordered,[status(thm)],[4389,754]) ).
thf(4973,plain,
! [A: $i] :
( ( unit != b )
| ( ( mult @ ( i @ A ) @ A )
!= a ) ),
inference(simp,[status(thm)],[4940]) ).
thf(78,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ unit ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(120,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ a @ c )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(188,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ unit @ A )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[27,174]) ).
thf(213,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( unit != b )
| ( A != a ) ),
inference(simp,[status(thm)],[188]) ).
thf(247,plain,
( ( ( mult @ ( mult @ a @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( unit != b ) ),
inference(simp,[status(thm)],[213]) ).
thf(5643,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( B != a )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( i @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,4973]) ).
thf(5662,plain,
! [B: $i,A: $i] :
( ( unit != b )
| ( A
!= ( i @ B ) )
| ( ( ld @ A @ a )
!= B ) ),
inference(simp,[status(thm)],[5643]) ).
thf(5681,plain,
! [A: $i] :
( ( unit != b )
| ( ( ld @ ( i @ A ) @ a )
!= A ) ),
inference(simp,[status(thm)],[5662]) ).
thf(13129,plain,
! [B: $i,A: $i] :
( ( unit != b )
| ( ( ld @ A @ a )
!= B )
| ( ( i @ ( i @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[561,5681]) ).
thf(13130,plain,
! [A: $i] :
( ( unit != b )
| ( ( ld @ A @ a )
!= ( i @ A ) ) ),
inference(pattern_uni,[status(thm)],[13129:[bind(A,$thf( C )),bind(B,$thf( i @ C ))]]) ).
thf(13165,plain,
! [A: $i] :
( ( unit != b )
| ( ( ld @ A @ a )
!= ( i @ A ) ) ),
inference(simp,[status(thm)],[13130]) ).
thf(22208,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( B
!= ( i @ C ) )
| ( ( ld @ ( rd @ A @ B ) @ A )
!= ( ld @ C @ a ) ) ),
inference(paramod_ordered,[status(thm)],[749,13165]) ).
thf(22209,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ ( rd @ a @ A ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[22208:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( rd @ a @ E ))]]) ).
thf(22223,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ ( rd @ a @ A ) )
!= A ) ),
inference(simp,[status(thm)],[22209]) ).
thf(28413,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( ( mult @ B @ ( i @ A ) )
!= C )
| ( ( i @ ( rd @ A @ B ) )
!= ( i @ ( rd @ a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[960,22223]) ).
thf(28414,plain,
! [A: $i] :
( ( unit != b )
| ( ( mult @ A @ ( i @ a ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[28413:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(28471,plain,
! [A: $i] :
( ( unit != b )
| ( ( mult @ A @ ( i @ a ) )
!= A ) ),
inference(simp,[status(thm)],[28414]) ).
thf(38701,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( A != C )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ ( i @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,28471]) ).
thf(38702,plain,
! [A: $i] :
( ( unit != b )
| ( ( rd @ A @ ( i @ a ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[38701:[bind(A,$thf( D )),bind(B,$thf( i @ a )),bind(C,$thf( rd @ D @ ( i @ a ) ))]]) ).
thf(38784,plain,
! [A: $i] :
( ( unit != b )
| ( ( rd @ A @ ( i @ a ) )
!= A ) ),
inference(simp,[status(thm)],[38702]) ).
thf(71,plain,
! [A: $i] :
( ( ( mult @ unit @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ a @ b ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(130,plain,
! [A: $i] :
( ( ( mult @ unit @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( i @ A )
!= ( mult @ a @ b ) )
| ( A != a ) ),
inference(simp,[status(thm)],[71]) ).
thf(144,plain,
( ( ( mult @ unit @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ a @ b )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(11962,plain,
( ( ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= ( i @ a ) ) ),
inference(rewrite,[status(thm)],[144,27]) ).
thf(196,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ unit )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[25,174]) ).
thf(200,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ unit )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(234,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ unit )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(39606,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( ( mult @ a @ b )
!= unit )
| ( A
!= ( mult @ b @ a ) ) ),
inference(rewrite,[status(thm)],[234,25]) ).
thf(62,plain,
! [A: $i] :
( ( ( mult @ a @ A )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(142,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( A
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ ( mult @ b @ a ) @ a ) )
| ( unit != c ) ),
inference(simp,[status(thm)],[62]) ).
thf(153,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= ( mult @ a @ c ) )
| ( unit != c ) ),
inference(simp,[status(thm)],[142]) ).
thf(894,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ B @ ( i @ unit ) )
= ( i @ C ) )
| ( ( mult @ A @ ( i @ A ) )
!= ( mult @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[37,29]) ).
thf(895,plain,
! [A: $i] :
( ( mult @ ( i @ A ) @ ( i @ unit ) )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[894:[bind(A,$thf( D )),bind(B,$thf( i @ D )),bind(C,$thf( D ))]]) ).
thf(1005,plain,
! [A: $i] :
( ( mult @ ( i @ A ) @ ( i @ unit ) )
= ( i @ A ) ),
inference(simp,[status(thm)],[895]) ).
thf(1196,plain,
! [A: $i] :
( ( mult @ ( i @ A ) @ unit )
= ( i @ A ) ),
inference(rewrite,[status(thm)],[1005,43]) ).
thf(216,plain,
! [A: $i] :
( ( ( mult @ unit @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( i @ A )
!= ( mult @ b @ a ) )
| ( A != a ) ),
inference(simp,[status(thm)],[193]) ).
thf(250,plain,
( ( ( mult @ unit @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ b @ a )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(44834,plain,
( ( ( mult @ a @ c )
!= c )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ b @ a )
!= ( i @ a ) ) ),
inference(rewrite,[status(thm)],[250,27]) ).
thf(195,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[35,174]) ).
thf(231,plain,
! [A: $i] :
( ( ( mult @ ( mult @ b @ a ) @ a )
!= a )
| ( c != c )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(257,plain,
! [A: $i] :
( ( ( mult @ ( mult @ b @ a ) @ a )
!= a )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(1775,plain,
! [C: $i,B: $i,A: $i] :
( ( ( i @ ( rd @ A @ B ) )
= unit )
| ( ( mult @ B @ ( i @ A ) )
!= ( mult @ C @ ( i @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[960,37]) ).
thf(1776,plain,
! [A: $i] :
( ( i @ ( rd @ A @ A ) )
= unit ),
inference(pattern_uni,[status(thm)],[1775:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1966,plain,
! [A: $i] :
( ( unit != a )
| ( ( i @ ( rd @ A @ A ) )
!= ( i @ b ) ) ),
inference(paramod_ordered,[status(thm)],[1776,618]) ).
thf(1985,plain,
! [A: $i] :
( ( unit != a )
| ( ( rd @ A @ A )
!= b ) ),
inference(simp,[status(thm)],[1966]) ).
thf(3986,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ ( i @ B ) @ ( i @ A ) )
= C )
| ( ( mult @ unit @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,1004]) ).
thf(3987,plain,
! [A: $i] :
( ( rd @ ( i @ unit ) @ ( i @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[3986:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(4089,plain,
! [A: $i] :
( ( rd @ unit @ ( i @ A ) )
= A ),
inference(rewrite,[status(thm)],[3987,43]) ).
thf(4090,plain,
! [B: $i,A: $i] :
( ( unit != a )
| ( A != b )
| ( ( rd @ unit @ ( i @ A ) )
!= ( rd @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4089,1985]) ).
thf(4130,plain,
! [A: $i] :
( ( unit != a )
| ( unit != A )
| ( ( i @ b )
!= A ) ),
inference(simp,[status(thm)],[4090]) ).
thf(4151,plain,
( ( unit != a )
| ( ( i @ b )
!= unit ) ),
inference(simp,[status(thm)],[4130]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( B
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[17,174]) ).
thf(333,plain,
! [A: $i] :
( ( ( mult @ a @ b )
!= unit )
| ( A
!= ( mult @ ( mult @ b @ a ) @ a ) )
| ( ( ld @ A @ ( mult @ a @ c ) )
!= c ) ),
inference(simp,[status(thm)],[313]) ).
thf(372,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( ld @ ( mult @ ( mult @ b @ a ) @ a ) @ ( mult @ a @ c ) )
!= c ) ),
inference(simp,[status(thm)],[333]) ).
thf(12488,plain,
! [B: $i,A: $i] :
( ( ( rd @ ( mult @ A @ B ) @ unit )
= unit )
| ( ( i @ ( rd @ unit @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12436,9858]) ).
thf(12489,plain,
! [A: $i] :
( ( rd @ ( mult @ A @ ( rd @ unit @ A ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[12488:[bind(A,$thf( D )),bind(B,$thf( rd @ unit @ D ))]]) ).
thf(12577,plain,
! [A: $i] :
( ( rd @ ( mult @ A @ ( rd @ unit @ A ) ) @ unit )
= unit ),
inference(simp,[status(thm)],[12489]) ).
thf(37087,plain,
! [A: $i] :
( ( mult @ A @ ( rd @ unit @ A ) )
= unit ),
inference(rewrite,[status(thm)],[12577,700]) ).
thf(141,plain,
! [A: $i] :
( ( ( mult @ a @ A )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( A
!= ( mult @ ( mult @ b @ a ) @ a ) )
| ( unit != c ) ),
inference(simp,[status(thm)],[62]) ).
thf(152,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ b @ a ) @ a ) ) )
| ( unit != c ) ),
inference(simp,[status(thm)],[141]) ).
thf(77,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ unit @ c ) ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(94,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ unit @ c )
!= ( mult @ a @ c ) )
| ( ( i @ A )
!= ( mult @ b @ a ) )
| ( A != a ) ),
inference(simp,[status(thm)],[77]) ).
thf(162,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ unit @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ b @ a )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(20716,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ a @ c )
!= c )
| ( ( mult @ b @ a )
!= ( i @ a ) ) ),
inference(rewrite,[status(thm)],[162,27]) ).
thf(64,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(97,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( unit != a )
| ( A != b ) ),
inference(simp,[status(thm)],[64]) ).
thf(164,plain,
( ( ( mult @ ( mult @ b @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( unit != a ) ),
inference(simp,[status(thm)],[97]) ).
thf(7086,plain,
! [B: $i,A: $i] :
( ( ( rd @ unit @ ( i @ ( mult @ A @ B ) ) )
= B )
| ( ( i @ ( i @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7024,1004]) ).
thf(7087,plain,
! [A: $i] :
( ( rd @ unit @ ( i @ ( mult @ ( i @ unit ) @ A ) ) )
= A ),
inference(pattern_uni,[status(thm)],[7086:[bind(A,$thf( i @ unit )),bind(B,$thf( B ))]]) ).
thf(7105,plain,
! [A: $i] :
( ( rd @ unit @ ( i @ ( mult @ ( i @ unit ) @ A ) ) )
= A ),
inference(simp,[status(thm)],[7087]) ).
thf(30695,plain,
! [A: $i] :
( ( mult @ ( i @ unit ) @ A )
= A ),
inference(rewrite,[status(thm)],[7105,4089]) ).
thf(31005,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( i @ ( rd @ B @ C ) ) )
| ( ( mult @ ( i @ unit ) @ A )
!= ( mult @ C @ ( i @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[30695,960]) ).
thf(31006,plain,
! [A: $i] :
( ( i @ ( rd @ A @ ( i @ unit ) ) )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[31005:[bind(A,$thf( i @ E )),bind(B,$thf( E )),bind(C,$thf( i @ unit ))]]) ).
thf(31654,plain,
! [A: $i] :
( ( i @ ( rd @ A @ ( i @ unit ) ) )
= ( i @ A ) ),
inference(simp,[status(thm)],[31006]) ).
thf(34045,plain,
! [A: $i] :
( ( i @ ( rd @ A @ unit ) )
= ( i @ A ) ),
inference(rewrite,[status(thm)],[31654,43]) ).
thf(26895,plain,
! [A: $i] :
( ( ( rd @ A @ ( i @ unit ) )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26651,6928]) ).
thf(26896,plain,
( ( rd @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) @ ( i @ unit ) )
= unit ),
inference(pattern_uni,[status(thm)],[26895:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ))]]) ).
thf(38574,plain,
( ( rd @ unit @ unit )
= unit ),
inference(rewrite,[status(thm)],[26896,23175,43]) ).
thf(4933,plain,
! [A: $i] :
( ( unit != a )
| ( ( i @ ( mult @ ( i @ A ) @ A ) )
!= ( i @ b ) ) ),
inference(paramod_ordered,[status(thm)],[4389,618]) ).
thf(4981,plain,
! [A: $i] :
( ( unit != a )
| ( ( mult @ ( i @ A ) @ A )
!= b ) ),
inference(simp,[status(thm)],[4933]) ).
thf(8251,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( B != b )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( i @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,4981]) ).
thf(8273,plain,
! [B: $i,A: $i] :
( ( unit != a )
| ( A
!= ( i @ B ) )
| ( ( ld @ A @ b )
!= B ) ),
inference(simp,[status(thm)],[8251]) ).
thf(8289,plain,
! [A: $i] :
( ( unit != a )
| ( ( ld @ ( i @ A ) @ b )
!= A ) ),
inference(simp,[status(thm)],[8273]) ).
thf(18173,plain,
! [B: $i,A: $i] :
( ( unit != a )
| ( ( ld @ A @ b )
!= B )
| ( ( i @ ( i @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[561,8289]) ).
thf(18174,plain,
! [A: $i] :
( ( unit != a )
| ( ( ld @ A @ b )
!= ( i @ A ) ) ),
inference(pattern_uni,[status(thm)],[18173:[bind(A,$thf( C )),bind(B,$thf( i @ C ))]]) ).
thf(18219,plain,
! [A: $i] :
( ( unit != a )
| ( ( ld @ A @ b )
!= ( i @ A ) ) ),
inference(simp,[status(thm)],[18174]) ).
thf(27415,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( B
!= ( i @ C ) )
| ( ( ld @ ( rd @ A @ B ) @ A )
!= ( ld @ C @ b ) ) ),
inference(paramod_ordered,[status(thm)],[749,18219]) ).
thf(27416,plain,
! [A: $i] :
( ( unit != a )
| ( ( i @ ( rd @ b @ A ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[27415:[bind(A,$thf( b )),bind(B,$thf( E )),bind(C,$thf( rd @ b @ E ))]]) ).
thf(27436,plain,
! [A: $i] :
( ( unit != a )
| ( ( i @ ( rd @ b @ A ) )
!= A ) ),
inference(simp,[status(thm)],[27416]) ).
thf(33477,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( ( mult @ B @ ( i @ A ) )
!= C )
| ( ( i @ ( rd @ A @ B ) )
!= ( i @ ( rd @ b @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[960,27436]) ).
thf(33478,plain,
! [A: $i] :
( ( unit != a )
| ( ( mult @ A @ ( i @ b ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[33477:[bind(A,$thf( b )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(33531,plain,
! [A: $i] :
( ( unit != a )
| ( ( mult @ A @ ( i @ b ) )
!= A ) ),
inference(simp,[status(thm)],[33478]) ).
thf(41996,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( B != C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ C @ ( i @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,33531]) ).
thf(42030,plain,
! [B: $i,A: $i] :
( ( unit != a )
| ( A != B )
| ( ( ld @ A @ B )
!= ( i @ b ) ) ),
inference(simp,[status(thm)],[41996]) ).
thf(42081,plain,
! [A: $i] :
( ( unit != a )
| ( ( ld @ A @ A )
!= ( i @ b ) ) ),
inference(simp,[status(thm)],[42030]) ).
thf(58459,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( mult @ unit @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58341,39129]) ).
thf(58460,plain,
( ( rd @ unit @ ( i @ ( mult @ unit @ unit ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[58459:[bind(A,$thf( mult @ unit @ unit ))]]) ).
thf(60001,plain,
( ( i @ ( i @ ( mult @ unit @ unit ) ) )
= unit ),
inference(rewrite,[status(thm)],[58460,788]) ).
thf(781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( rd @ B @ D )
= C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[17,23]) ).
thf(782,plain,
! [B: $i,A: $i] :
( ( rd @ B @ ( ld @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( ld @ E @ F ))]]) ).
thf(794,plain,
! [B: $i,A: $i] :
( ( rd @ B @ ( ld @ A @ B ) )
= A ),
inference(simp,[status(thm)],[782]) ).
thf(1971,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ ( rd @ A @ A ) )
!= ( i @ a ) ) ),
inference(paramod_ordered,[status(thm)],[1776,754]) ).
thf(1981,plain,
! [A: $i] :
( ( unit != b )
| ( ( rd @ A @ A )
!= a ) ),
inference(simp,[status(thm)],[1971]) ).
thf(2377,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( A != a )
| ( ( rd @ B @ ( ld @ A @ B ) )
!= ( rd @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[794,1981]) ).
thf(2388,plain,
! [B: $i,A: $i] :
( ( unit != b )
| ( A != B )
| ( ( ld @ a @ A )
!= B ) ),
inference(simp,[status(thm)],[2377]) ).
thf(2392,plain,
! [A: $i] :
( ( unit != b )
| ( ( ld @ a @ A )
!= A ) ),
inference(simp,[status(thm)],[2388]) ).
thf(9885,plain,
! [B: $i,A: $i] :
( ( ( rd @ ( mult @ unit @ B ) @ unit )
= unit )
| ( ( i @ ( rd @ A @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1776,9858]) ).
thf(9886,plain,
! [A: $i] :
( ( rd @ ( mult @ unit @ ( rd @ A @ A ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[9885:[bind(A,$thf( D )),bind(B,$thf( rd @ D @ D ))]]) ).
thf(9979,plain,
! [A: $i] :
( ( rd @ ( mult @ unit @ ( rd @ A @ A ) ) @ unit )
= unit ),
inference(simp,[status(thm)],[9886]) ).
thf(35133,plain,
! [A: $i] :
( ( mult @ unit @ ( rd @ A @ A ) )
= unit ),
inference(rewrite,[status(thm)],[9979,700]) ).
thf(35179,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ B @ ( i @ unit ) )
= ( i @ C ) )
| ( ( mult @ unit @ ( rd @ A @ A ) )
!= ( mult @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35133,29]) ).
thf(35180,plain,
! [A: $i] :
( ( mult @ ( rd @ A @ A ) @ ( i @ unit ) )
= ( i @ unit ) ),
inference(pattern_uni,[status(thm)],[35179:[bind(A,$thf( E )),bind(B,$thf( rd @ E @ E )),bind(C,$thf( unit ))]]) ).
thf(36123,plain,
! [A: $i] :
( ( mult @ ( rd @ A @ A ) @ ( i @ unit ) )
= ( i @ unit ) ),
inference(simp,[status(thm)],[35180]) ).
thf(40655,plain,
! [A: $i] :
( ( mult @ ( rd @ A @ A ) @ unit )
= unit ),
inference(rewrite,[status(thm)],[36123,43]) ).
thf(41015,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ ( i @ B ) @ ( i @ unit ) )
= C )
| ( ( mult @ ( rd @ A @ A ) @ unit )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[40655,1004]) ).
thf(41016,plain,
! [A: $i] :
( ( rd @ ( i @ ( rd @ A @ A ) ) @ ( i @ unit ) )
= unit ),
inference(pattern_uni,[status(thm)],[41015:[bind(A,$thf( E )),bind(B,$thf( rd @ E @ E )),bind(C,$thf( unit ))]]) ).
thf(41645,plain,
! [A: $i] :
( ( rd @ ( i @ ( rd @ A @ A ) ) @ ( i @ unit ) )
= unit ),
inference(simp,[status(thm)],[41016]) ).
thf(44638,plain,
! [A: $i] :
( ( rd @ ( i @ ( rd @ A @ A ) ) @ unit )
= unit ),
inference(rewrite,[status(thm)],[41645,43]) ).
thf(6930,plain,
! [B: $i,A: $i] :
( ( ( rd @ B @ ( i @ unit ) )
= unit )
| ( ( i @ ( mult @ A @ ( i @ A ) ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4290,6928]) ).
thf(6931,plain,
! [A: $i] :
( ( rd @ ( mult @ A @ ( i @ A ) ) @ ( i @ unit ) )
= unit ),
inference(pattern_uni,[status(thm)],[6930:[bind(A,$thf( E )),bind(B,$thf( mult @ E @ ( i @ E ) ))]]) ).
thf(7010,plain,
! [A: $i] :
( ( rd @ ( mult @ A @ ( i @ A ) ) @ ( i @ unit ) )
= unit ),
inference(simp,[status(thm)],[6931]) ).
thf(8817,plain,
( ( rd @ unit @ unit )
= unit ),
inference(rewrite,[status(thm)],[7010,37,43]) ).
thf(28385,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ unit )
!= A )
| ( ( rd @ unit @ unit )
!= ( rd @ a @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8817,22223]) ).
thf(28462,plain,
( ( unit != b )
| ( ( rd @ unit @ unit )
!= ( rd @ a @ ( i @ unit ) ) ) ),
inference(simp,[status(thm)],[28385]) ).
thf(35088,plain,
( ( unit != b )
| ( ( rd @ a @ unit )
!= unit ) ),
inference(rewrite,[status(thm)],[28462,8817,43]) ).
thf(44719,plain,
! [A: $i] :
( ( unit != b )
| ( ( rd @ ( i @ ( rd @ A @ A ) ) @ unit )
!= ( rd @ a @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[44638,35088]) ).
thf(44745,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ ( rd @ A @ A ) )
!= a )
| ( unit != unit ) ),
inference(simp,[status(thm)],[44719]) ).
thf(44799,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ ( rd @ A @ A ) )
!= a ) ),
inference(simp,[status(thm)],[44745]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A != a )
| ( ( ld @ A @ B )
!= b ) ),
inference(simp,[status(thm)],[304]) ).
thf(380,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( ld @ a @ A )
!= b ) ),
inference(simp,[status(thm)],[343]) ).
thf(72,plain,
! [A: $i] :
( ( ( mult @ ( mult @ unit @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(112,plain,
! [A: $i] :
( ( ( mult @ unit @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(6295,plain,
! [A: $i] :
( ( a != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(rewrite,[status(thm)],[112,27]) ).
thf(6296,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ b ) ) ),
inference(simp,[status(thm)],[6295]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ B @ a ) @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[17,15]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ B @ a ) @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( A != b )
| ( ( ld @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[307]) ).
thf(366,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ A @ a ) @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( ld @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[326]) ).
thf(20067,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19924,9858]) ).
thf(20068,plain,
( ( rd @ ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[20067:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ))]]) ).
thf(24426,plain,
( ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[20068,700]) ).
thf(269,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( mult @ b @ a )
!= ( mult @ a @ b ) )
| ( unit != unit ) ),
inference(eqfactor_ordered,[status(thm)],[239]) ).
thf(270,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( mult @ b @ a )
!= ( mult @ a @ b ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(92,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ unit @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(5017,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ a @ c )
!= c )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(rewrite,[status(thm)],[92,27]) ).
thf(18010,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17894,9858]) ).
thf(18011,plain,
( ( rd @ ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[18010:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ))]]) ).
thf(20931,plain,
( ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[18011,700]) ).
thf(187,plain,
( ( ( mult @ ( mult @ b @ a ) @ a )
!= a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit ) ),
inference(simp,[status(thm)],[174]) ).
thf(260,plain,
( ( ( mult @ ( mult @ b @ a ) @ a )
!= a )
| ( ( mult @ a @ b )
!= unit ) ),
inference(simp,[status(thm)],[187]) ).
thf(70,plain,
! [A: $i] :
( ( ( mult @ a @ A )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(89,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( A
!= ( mult @ a @ c ) )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= unit )
| ( A != c ) ),
inference(simp,[status(thm)],[70]) ).
thf(160,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= unit )
| ( ( mult @ a @ c )
!= c ) ),
inference(simp,[status(thm)],[89]) ).
thf(294,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ unit @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,27]) ).
thf(295,plain,
! [A: $i] :
( ( ld @ unit @ A )
= A ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( unit )),bind(B,$thf( E )),bind(C,$thf( ld @ unit @ E ))]]) ).
thf(392,plain,
! [A: $i] :
( ( ld @ unit @ A )
= A ),
inference(simp,[status(thm)],[295]) ).
thf(56,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(82,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ A @ unit )
!= ( mult @ a @ b ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(3134,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ a @ b ) ) ),
inference(rewrite,[status(thm)],[82,25]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ C )
= ( mult @ ( mult @ A @ C ) @ ( ld @ C @ ( mult @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(46349,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( rd @ unit @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[46173,9858]) ).
thf(46350,plain,
( ( rd @ ( mult @ unit @ ( rd @ unit @ unit ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[46349:[bind(A,$thf( rd @ unit @ unit ))]]) ).
thf(47501,plain,
( ( mult @ unit @ ( rd @ unit @ unit ) )
= unit ),
inference(rewrite,[status(thm)],[46350,700]) ).
thf(22962,plain,
! [A: $i] :
( ( ( i @ A )
!= a )
| ( ( i @ ( mult @ A @ unit ) )
!= ( i @ b ) ) ),
inference(paramod_ordered,[status(thm)],[22872,618]) ).
thf(23052,plain,
! [A: $i] :
( ( ( i @ A )
!= a )
| ( ( mult @ A @ unit )
!= b ) ),
inference(simp,[status(thm)],[22962]) ).
thf(30584,plain,
! [A: $i] :
( ( ( i @ A )
!= a )
| ( A != b ) ),
inference(rewrite,[status(thm)],[23052,25]) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ B @ A )
= C )
| ( ( mult @ A @ unit )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25,19]) ).
thf(519,plain,
! [A: $i] :
( ( ld @ A @ A )
= unit ),
inference(pattern_uni,[status(thm)],[518:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).
thf(83,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( A != a )
| ( unit != b ) ),
inference(simp,[status(thm)],[56]) ).
thf(156,plain,
( ( ( mult @ ( mult @ a @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( unit != b ) ),
inference(simp,[status(thm)],[83]) ).
thf(52405,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( mult @ unit @ ( i @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52190,9858]) ).
thf(52406,plain,
( ( rd @ ( mult @ unit @ ( mult @ unit @ ( i @ unit ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[52405:[bind(A,$thf( mult @ unit @ ( i @ unit ) ))]]) ).
thf(55572,plain,
( ( mult @ unit @ ( mult @ unit @ ( i @ unit ) ) )
= unit ),
inference(rewrite,[status(thm)],[52406,700]) ).
thf(38703,plain,
! [B: $i,A: $i] :
( ( unit != b )
| ( unit != B )
| ( ( mult @ unit @ ( rd @ A @ A ) )
!= ( mult @ B @ ( i @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[35133,28471]) ).
thf(38776,plain,
! [A: $i] :
( ( unit != b )
| ( unit != unit )
| ( ( rd @ A @ A )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[38703]) ).
thf(38798,plain,
! [A: $i] :
( ( unit != b )
| ( ( rd @ A @ A )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[38776]) ).
thf(192,plain,
! [A: $i] :
( ( ( mult @ ( mult @ unit @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[35,174]) ).
thf(206,plain,
! [A: $i] :
( ( ( mult @ unit @ a )
!= a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(240,plain,
! [A: $i] :
( ( ( mult @ unit @ a )
!= a )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(40341,plain,
! [A: $i] :
( ( a != a )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(rewrite,[status(thm)],[240,27]) ).
thf(40342,plain,
! [A: $i] :
( ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[40341]) ).
thf(49056,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( i @ ( rd @ unit @ unit ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[48836,9858]) ).
thf(49057,plain,
( ( rd @ ( mult @ unit @ ( i @ ( i @ ( rd @ unit @ unit ) ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[49056:[bind(A,$thf( i @ ( i @ ( rd @ unit @ unit ) ) ))]]) ).
thf(70282,plain,
( ( mult @ unit @ ( i @ ( i @ ( rd @ unit @ unit ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[49057,700]) ).
thf(13935,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ unit ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13861,9858]) ).
thf(13936,plain,
( ( rd @ ( mult @ unit @ ( i @ ( i @ ( i @ unit ) ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[13935:[bind(A,$thf( i @ ( i @ ( i @ unit ) ) ))]]) ).
thf(16468,plain,
( ( mult @ unit @ ( i @ ( i @ ( i @ unit ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[13936,700]) ).
thf(60131,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( mult @ unit @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60001,39129]) ).
thf(60132,plain,
( ( rd @ unit @ ( i @ ( i @ ( mult @ unit @ unit ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[60131:[bind(A,$thf( i @ ( mult @ unit @ unit ) ))]]) ).
thf(63818,plain,
( ( i @ ( i @ ( i @ ( mult @ unit @ unit ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[60132,788]) ).
thf(107,plain,
! [A: $i] :
( ( ( mult @ A @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ a @ b )
!= unit )
| ( A != a ) ),
inference(simp,[status(thm)],[63]) ).
thf(173,plain,
( ( ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
!= ( mult @ a @ ( mult @ a @ c ) ) )
| ( ( mult @ a @ b )
!= unit ) ),
inference(simp,[status(thm)],[107]) ).
thf(129,plain,
! [A: $i] :
( ( unit != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ a @ b ) @ a ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(6937,plain,
! [B: $i,A: $i] :
( ( ( rd @ B @ ( i @ unit ) )
= unit )
| ( ( i @ ( rd @ A @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1776,6928]) ).
thf(6938,plain,
! [A: $i] :
( ( rd @ ( rd @ A @ A ) @ ( i @ unit ) )
= unit ),
inference(pattern_uni,[status(thm)],[6937:[bind(A,$thf( D )),bind(B,$thf( rd @ D @ D ))]]) ).
thf(7013,plain,
! [A: $i] :
( ( rd @ ( rd @ A @ A ) @ ( i @ unit ) )
= unit ),
inference(simp,[status(thm)],[6938]) ).
thf(8142,plain,
! [A: $i] :
( ( rd @ ( rd @ A @ A ) @ unit )
= unit ),
inference(rewrite,[status(thm)],[7013,43]) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( B = unit )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( i @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,35]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( B = unit )
| ( A
!= ( i @ C ) )
| ( ( ld @ A @ B )
!= C ) ),
inference(simp,[status(thm)],[298]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( A = unit )
| ( ( ld @ ( i @ B ) @ A )
!= B ) ),
inference(simp,[status(thm)],[331]) ).
thf(9910,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7024,9858]) ).
thf(9911,plain,
( ( rd @ ( mult @ unit @ ( i @ unit ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[9910:[bind(A,$thf( i @ unit ))]]) ).
thf(10851,plain,
( ( mult @ unit @ ( i @ unit ) )
= unit ),
inference(rewrite,[status(thm)],[9911,700]) ).
thf(55,plain,
! [A: $i] :
( ( ( mult @ A @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ ( mult @ a @ b ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(116,plain,
! [A: $i] :
( ( ( mult @ A @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( A
!= ( mult @ a @ b ) )
| ( unit != a ) ),
inference(simp,[status(thm)],[55]) ).
thf(180,plain,
( ( ( mult @ ( mult @ a @ b ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( unit != a ) ),
inference(simp,[status(thm)],[116]) ).
thf(58,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ A )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ a @ c ) ) ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(136,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ A )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( A != a )
| ( unit != c ) ),
inference(simp,[status(thm)],[58]) ).
thf(149,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ a )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( unit != c ) ),
inference(simp,[status(thm)],[136]) ).
thf(3124,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( A != b )
| ( ( rd @ ( mult @ A @ B ) @ B )
!= ( rd @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,1985]) ).
thf(3126,plain,
! [B: $i,A: $i] :
( ( unit != a )
| ( ( mult @ b @ A )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[3124]) ).
thf(3130,plain,
! [A: $i] :
( ( unit != a )
| ( ( mult @ b @ A )
!= A ) ),
inference(simp,[status(thm)],[3126]) ).
thf(59,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ A @ a ) @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(100,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ A @ a ) @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( A != b )
| ( unit != a ) ),
inference(simp,[status(thm)],[59]) ).
thf(166,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ b @ a ) @ c ) ) )
| ( unit != a ) ),
inference(simp,[status(thm)],[100]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( mult @ a @ b ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[17,15]) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( B != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ a @ b ) )
| ( ( ld @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[303]) ).
thf(375,plain,
( ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( ld @ ( mult @ a @ b ) @ a )
!= a ) ),
inference(simp,[status(thm)],[336]) ).
thf(67,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ A @ a ) @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(111,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( unit != b )
| ( A != a ) ),
inference(simp,[status(thm)],[67]) ).
thf(176,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ a @ a ) @ c )
!= ( mult @ a @ c ) )
| ( unit != b ) ),
inference(simp,[status(thm)],[111]) ).
thf(74,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ unit )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ c ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(127,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ unit )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( i @ A )
!= a )
| ( A != c ) ),
inference(simp,[status(thm)],[74]) ).
thf(186,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ unit )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( i @ c )
!= a ) ),
inference(simp,[status(thm)],[127]) ).
thf(36409,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( i @ c )
!= a ) ),
inference(rewrite,[status(thm)],[186,25]) ).
thf(54,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(8248,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( A != b )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ ( i @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,4981]) ).
thf(8270,plain,
! [B: $i,A: $i] :
( ( unit != a )
| ( ( rd @ b @ A )
!= ( i @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[8248]) ).
thf(8286,plain,
! [A: $i] :
( ( unit != a )
| ( ( rd @ b @ A )
!= ( i @ A ) ) ),
inference(simp,[status(thm)],[8270]) ).
thf(117,plain,
! [A: $i] :
( ( A != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ a @ b ) )
| ( unit != a ) ),
inference(simp,[status(thm)],[55]) ).
thf(181,plain,
( ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= a )
| ( unit != a ) ),
inference(simp,[status(thm)],[117]) ).
thf(58360,plain,
! [A: $i] :
( ( unit != b )
| ( ( mult @ unit @ A )
!= a )
| ( ( i @ ( mult @ unit @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58341,4973]) ).
thf(58361,plain,
( ( unit != b )
| ( ( mult @ unit @ ( mult @ unit @ unit ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[58360:[bind(A,$thf( mult @ unit @ unit ))]]) ).
thf(58993,plain,
( ( unit != b )
| ( ( mult @ unit @ unit )
!= a ) ),
inference(rewrite,[status(thm)],[58361,27]) ).
thf(60,plain,
! [A: $i] :
( ( A
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(86,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= unit ) ),
inference(simp,[status(thm)],[60]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ B @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[307]) ).
thf(50714,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ b @ a ) ) ),
inference(rewrite,[status(thm)],[325,17]) ).
thf(88,plain,
! [A: $i] :
( ( ( mult @ a @ A )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= unit )
| ( A != c ) ),
inference(simp,[status(thm)],[70]) ).
thf(159,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ c ) )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= unit ) ),
inference(simp,[status(thm)],[88]) ).
thf(190,plain,
! [A: $i] :
( ( A
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[27,174]) ).
thf(230,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= unit )
| ( ( mult @ a @ c )
!= c ) ),
inference(simp,[status(thm)],[190]) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( mult @ A @ unit )
!= ( mult @ B @ ( ld @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,17]) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A != B )
| ( ( ld @ B @ C )
!= unit ) ),
inference(simp,[status(thm)],[316]) ).
thf(362,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( ld @ A @ B )
!= unit ) ),
inference(simp,[status(thm)],[321]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ B @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A != b )
| ( ( ld @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[307]) ).
thf(367,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( ld @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[327]) ).
thf(65,plain,
! [A: $i] :
( ( A
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(91,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= unit )
| ( ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
!= ( mult @ a @ c ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(217,plain,
! [A: $i] :
( ( unit != a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit )
| ( ( i @ A )
!= ( mult @ b @ a ) )
| ( A != a ) ),
inference(simp,[status(thm)],[193]) ).
thf(251,plain,
( ( unit != a )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ b @ a )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(63965,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ ( mult @ unit @ unit ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[63818,39129]) ).
thf(63966,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ ( mult @ unit @ unit ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[63965:[bind(A,$thf( i @ ( i @ ( mult @ unit @ unit ) ) ))]]) ).
thf(68510,plain,
( ( i @ ( i @ ( i @ ( i @ ( mult @ unit @ unit ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[63966,788]) ).
thf(767,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ A @ C )
= B )
| ( ( mult @ unit @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,23]) ).
thf(768,plain,
! [A: $i] :
( ( rd @ A @ A )
= unit ),
inference(pattern_uni,[status(thm)],[767:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(26775,plain,
! [A: $i] :
( ( ( rd @ unit @ ( i @ A ) )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26651,13002]) ).
thf(26776,plain,
( ( rd @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) ) )
= unit ),
inference(pattern_uni,[status(thm)],[26775:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ))]]) ).
thf(32846,plain,
( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[26776,788]) ).
thf(198,plain,
! [A: $i] :
( ( A
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ unit )
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[25,174]) ).
thf(223,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= ( mult @ a @ c ) )
| ( unit != c ) ),
inference(simp,[status(thm)],[198]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( mult @ B @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[17,174]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ a )
!= a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[311]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ a )
!= a )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[328]) ).
thf(61229,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( ( mult @ a @ b )
!= unit )
| ( A
!= ( mult @ b @ a ) ) ),
inference(rewrite,[status(thm)],[368,17]) ).
thf(2380,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( A != a )
| ( ( rd @ ( mult @ A @ B ) @ B )
!= ( rd @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,1981]) ).
thf(2386,plain,
! [B: $i,A: $i] :
( ( unit != b )
| ( ( mult @ a @ A )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[2380]) ).
thf(2390,plain,
! [A: $i] :
( ( unit != b )
| ( ( mult @ a @ A )
!= A ) ),
inference(simp,[status(thm)],[2386]) ).
thf(5642,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( A != a )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ ( i @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,4973]) ).
thf(5659,plain,
! [B: $i,A: $i] :
( ( unit != b )
| ( ( rd @ a @ A )
!= ( i @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[5642]) ).
thf(5677,plain,
! [A: $i] :
( ( unit != b )
| ( ( rd @ a @ A )
!= ( i @ A ) ) ),
inference(simp,[status(thm)],[5659]) ).
thf(8880,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( A
!= ( i @ C ) )
| ( ( rd @ B @ ( ld @ A @ B ) )
!= ( rd @ a @ C ) ) ),
inference(paramod_ordered,[status(thm)],[794,5677]) ).
thf(8881,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ ( ld @ A @ a ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[8880:[bind(A,$thf( D )),bind(B,$thf( a )),bind(C,$thf( ld @ D @ a ))]]) ).
thf(8922,plain,
! [A: $i] :
( ( unit != b )
| ( ( i @ ( ld @ A @ a ) )
!= A ) ),
inference(simp,[status(thm)],[8881]) ).
thf(101,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A != b )
| ( unit != a ) ),
inference(simp,[status(thm)],[59]) ).
thf(167,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ b @ a ) @ c )
!= ( mult @ a @ c ) )
| ( unit != a ) ),
inference(simp,[status(thm)],[101]) ).
thf(23350,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[23175,9858]) ).
thf(23351,plain,
( ( rd @ ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[23350:[bind(A,$thf( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ))]]) ).
thf(28845,plain,
( ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[23351,700]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( A
!= ( mult @ a @ b ) )
| ( ( ld @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[303]) ).
thf(374,plain,
! [A: $i] :
( ( ( mult @ A @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( ld @ ( mult @ a @ b ) @ A )
!= a ) ),
inference(simp,[status(thm)],[335]) ).
thf(7077,plain,
! [B: $i,A: $i] :
( ( ( ld @ B @ unit )
= ( i @ ( mult @ A @ B ) ) )
| ( ( i @ ( i @ unit ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7024,963]) ).
thf(7078,plain,
! [A: $i] :
( ( ld @ A @ unit )
= ( i @ ( mult @ ( i @ unit ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[7077:[bind(A,$thf( i @ unit )),bind(B,$thf( B ))]]) ).
thf(7103,plain,
! [A: $i] :
( ( ld @ A @ unit )
= ( i @ ( mult @ ( i @ unit ) @ A ) ) ),
inference(simp,[status(thm)],[7078]) ).
thf(28026,plain,
! [A: $i] :
( ( i @ ( mult @ unit @ A ) )
= ( i @ A ) ),
inference(rewrite,[status(thm)],[7103,521,43]) ).
thf(131,plain,
! [A: $i] :
( ( unit != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( i @ A )
!= ( mult @ a @ b ) )
| ( A != a ) ),
inference(simp,[status(thm)],[71]) ).
thf(145,plain,
( ( unit != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(271,plain,
( ( ( mult @ a @ b )
!= unit )
| ( b != a )
| ( b != a ) ),
inference(simp,[status(thm)],[269]) ).
thf(282,plain,
( ( ( mult @ a @ b )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[271]) ).
thf(137,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( A
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
| ( A != a )
| ( unit != c ) ),
inference(simp,[status(thm)],[58]) ).
thf(150,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= a )
| ( unit != c ) ),
inference(simp,[status(thm)],[137]) ).
thf(9906,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ unit )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43,9858]) ).
thf(9907,plain,
( ( rd @ ( mult @ unit @ unit ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[9906:[bind(A,$thf( unit ))]]) ).
thf(10246,plain,
( ( mult @ unit @ unit )
= unit ),
inference(rewrite,[status(thm)],[9907,700]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ a )
!= a )
| ( c != c )
| ( ( mult @ a @ b )
!= unit )
| ( A != b )
| ( ( ld @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[311]) ).
thf(370,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( ( mult @ a @ b )
!= unit )
| ( ( ld @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[330]) ).
thf(41991,plain,
! [B: $i,A: $i] :
( ( unit != a )
| ( unit != B )
| ( ( mult @ unit @ ( rd @ A @ A ) )
!= ( mult @ B @ ( i @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[35133,33531]) ).
thf(42050,plain,
! [A: $i] :
( ( unit != a )
| ( unit != unit )
| ( ( rd @ A @ A )
!= ( i @ b ) ) ),
inference(simp,[status(thm)],[41991]) ).
thf(42087,plain,
! [A: $i] :
( ( unit != a )
| ( ( rd @ A @ A )
!= ( i @ b ) ) ),
inference(simp,[status(thm)],[42050]) ).
thf(121,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ unit ) )
| ( ( i @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) )
| ( A != c ) ),
inference(simp,[status(thm)],[78]) ).
thf(182,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ unit ) )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= ( i @ c ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(34432,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= a )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= ( i @ c ) ) ),
inference(rewrite,[status(thm)],[182,25]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( unit = B )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ unit @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,27]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( unit = B )
| ( ( i @ A )
!= unit )
| ( A != B ) ),
inference(simp,[status(thm)],[46]) ).
thf(50,plain,
! [A: $i] :
( ( unit = A )
| ( ( i @ A )
!= unit ) ),
inference(simp,[status(thm)],[48]) ).
thf(99,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ A @ unit )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(5684,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ b @ a ) ) ),
inference(rewrite,[status(thm)],[99,25]) ).
thf(3654,plain,
! [B: $i,A: $i] :
( ( unit != b )
| ( unit != B )
| ( ( mult @ A @ ( i @ A ) )
!= ( mult @ a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[37,2390]) ).
thf(3655,plain,
( ( unit != b )
| ( ( i @ a )
!= unit ) ),
inference(pattern_uni,[status(thm)],[3654:[bind(A,$thf( a )),bind(B,$thf( i @ a ))]]) ).
thf(40398,plain,
! [B: $i,A: $i] :
( ( ( mult @ a @ b )
!= unit )
| ( A
!= ( mult @ b @ a ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( i @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,40342]) ).
thf(40472,plain,
! [A: $i] :
( ( ( mult @ a @ b )
!= unit )
| ( ( i @ A )
!= unit )
| ( A
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[40398]) ).
thf(40560,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( i @ ( mult @ b @ a ) )
!= unit ) ),
inference(simp,[status(thm)],[40472]) ).
thf(13235,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( i @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13176,9858]) ).
thf(13236,plain,
( ( rd @ ( mult @ unit @ ( i @ ( i @ unit ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[13235:[bind(A,$thf( i @ ( i @ unit ) ))]]) ).
thf(14297,plain,
( ( mult @ unit @ ( i @ ( i @ unit ) ) )
= unit ),
inference(rewrite,[status(thm)],[13236,700]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ C ) )
= ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( rd @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) )
= ( mult @ A @ ( mult @ B @ C ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(17287,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( A
!= ( i @ C ) )
| ( ( rd @ B @ ( ld @ A @ B ) )
!= ( rd @ b @ C ) ) ),
inference(paramod_ordered,[status(thm)],[794,8286]) ).
thf(17288,plain,
! [A: $i] :
( ( unit != a )
| ( ( i @ ( ld @ A @ b ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[17287:[bind(A,$thf( D )),bind(B,$thf( b )),bind(C,$thf( ld @ D @ b ))]]) ).
thf(17320,plain,
! [A: $i] :
( ( unit != a )
| ( ( i @ ( ld @ A @ b ) )
!= A ) ),
inference(simp,[status(thm)],[17288]) ).
thf(69,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ A @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(80,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ A @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ b @ a )
!= unit )
| ( A != a ) ),
inference(simp,[status(thm)],[69]) ).
thf(154,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ a @ c ) ) )
| ( ( mult @ b @ a )
!= unit ) ),
inference(simp,[status(thm)],[80]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( ( mult @ a @ ( mult @ B @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[17,15]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ B @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(simp,[status(thm)],[309]) ).
thf(54184,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ A @ c )
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(rewrite,[status(thm)],[346,17]) ).
thf(110,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ A @ a ) @ c ) )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( unit != b )
| ( A != a ) ),
inference(simp,[status(thm)],[67]) ).
thf(175,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ a @ a ) @ c ) ) )
| ( unit != b ) ),
inference(simp,[status(thm)],[110]) ).
thf(128,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= unit )
| ( ( i @ A )
!= a )
| ( A != c ) ),
inference(simp,[status(thm)],[74]) ).
thf(143,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= unit )
| ( ( i @ c )
!= a ) ),
inference(simp,[status(thm)],[128]) ).
thf(93,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ unit @ c ) ) )
| ( ( i @ A )
!= ( mult @ b @ a ) )
| ( A != a ) ),
inference(simp,[status(thm)],[77]) ).
thf(161,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ unit @ c ) ) )
| ( ( mult @ b @ a )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(20251,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ c ) )
| ( ( mult @ b @ a )
!= ( i @ a ) ) ),
inference(rewrite,[status(thm)],[161,27]) ).
thf(33448,plain,
! [A: $i] :
( ( unit != a )
| ( ( i @ unit )
!= A )
| ( ( rd @ unit @ unit )
!= ( rd @ b @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8817,27436]) ).
thf(33512,plain,
( ( unit != a )
| ( ( rd @ unit @ unit )
!= ( rd @ b @ ( i @ unit ) ) ) ),
inference(simp,[status(thm)],[33448]) ).
thf(39869,plain,
( ( unit != a )
| ( ( rd @ b @ unit )
!= unit ) ),
inference(rewrite,[status(thm)],[33512,43,38574]) ).
thf(81,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ A @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ b @ a )
!= unit )
| ( A != a ) ),
inference(simp,[status(thm)],[69]) ).
thf(155,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ a @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ b @ a )
!= unit ) ),
inference(simp,[status(thm)],[81]) ).
thf(16337,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ b @ a )
!= unit ) ),
inference(simp,[status(thm)],[155]) ).
thf(105,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( A
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
| ( unit != a )
| ( A != c ) ),
inference(simp,[status(thm)],[66]) ).
thf(171,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( unit != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= c ) ),
inference(simp,[status(thm)],[105]) ).
thf(79,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ A @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(2394,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ A @ c )
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ ( mult @ b @ a ) @ a ) ) ),
inference(rewrite,[status(thm)],[79,27]) ).
thf(68,plain,
! [A: $i] :
( ( A
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,15]) ).
thf(139,plain,
( ( unit != a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(47252,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( rd @ unit @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47054,9858]) ).
thf(47253,plain,
( ( rd @ ( mult @ unit @ ( i @ ( rd @ unit @ unit ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[47252:[bind(A,$thf( i @ ( rd @ unit @ unit ) ))]]) ).
thf(49348,plain,
( ( mult @ unit @ ( i @ ( rd @ unit @ unit ) ) )
= unit ),
inference(rewrite,[status(thm)],[47253,700]) ).
thf(35433,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ B @ unit )
= C )
| ( ( mult @ unit @ ( rd @ A @ A ) )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35133,19]) ).
thf(35434,plain,
! [A: $i] :
( ( rd @ A @ A )
= ( ld @ unit @ unit ) ),
inference(pattern_uni,[status(thm)],[35433:[bind(A,$thf( E )),bind(B,$thf( unit )),bind(C,$thf( rd @ E @ E ))]]) ).
thf(36133,plain,
! [A: $i] :
( ( rd @ A @ A )
= ( ld @ unit @ unit ) ),
inference(simp,[status(thm)],[35434]) ).
thf(36303,plain,
! [A: $i] :
( ( rd @ A @ A )
= ( i @ unit ) ),
inference(rewrite,[status(thm)],[36133,521]) ).
thf(57,plain,
! [A: $i] :
( ( A
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,15]) ).
thf(119,plain,
( ( ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
!= ( mult @ ( mult @ a @ b ) @ a ) )
| ( ( mult @ a @ c )
!= unit ) ),
inference(simp,[status(thm)],[57]) ).
thf(201,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( A != b )
| ( unit != a ) ),
inference(simp,[status(thm)],[196]) ).
thf(235,plain,
( ( ( mult @ ( mult @ b @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( unit != a ) ),
inference(simp,[status(thm)],[201]) ).
thf(15437,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15345,9858]) ).
thf(15438,plain,
( ( rd @ ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[15437:[bind(A,$thf( i @ ( i @ ( i @ ( i @ unit ) ) ) ))]]) ).
thf(18237,plain,
( ( mult @ unit @ ( i @ ( i @ ( i @ ( i @ unit ) ) ) ) )
= unit ),
inference(rewrite,[status(thm)],[15438,700]) ).
thf(41989,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( A != C )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ ( i @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,33531]) ).
thf(41990,plain,
! [A: $i] :
( ( unit != a )
| ( ( rd @ A @ ( i @ b ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[41989:[bind(A,$thf( D )),bind(B,$thf( i @ b )),bind(C,$thf( rd @ D @ ( i @ b ) ))]]) ).
thf(42076,plain,
! [A: $i] :
( ( unit != a )
| ( ( rd @ A @ ( i @ b ) )
!= A ) ),
inference(simp,[status(thm)],[41990]) ).
thf(13197,plain,
! [A: $i] :
( ( unit != b )
| ( ( mult @ unit @ A )
!= a )
| ( ( i @ ( i @ ( i @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13176,4973]) ).
thf(13198,plain,
( ( unit != b )
| ( ( mult @ unit @ ( i @ ( i @ unit ) ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[13197:[bind(A,$thf( i @ ( i @ unit ) ))]]) ).
thf(13328,plain,
( ( unit != b )
| ( ( i @ ( i @ unit ) )
!= a ) ),
inference(rewrite,[status(thm)],[13198,27]) ).
thf(76,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(102,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= unit )
| ( ( i @ A )
!= a )
| ( A
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(168,plain,
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= unit )
| ( ( i @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
!= a ) ),
inference(simp,[status(thm)],[102]) ).
thf(45062,plain,
! [A: $i] :
( ( unit != b )
| ( unit != A )
| ( ( rd @ unit @ unit )
!= ( rd @ A @ ( i @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[38574,38784]) ).
thf(45124,plain,
( ( unit != b )
| ( ( rd @ unit @ ( i @ a ) )
!= ( rd @ unit @ unit ) ) ),
inference(simp,[status(thm)],[45062]) ).
thf(72788,plain,
( ( unit != b )
| ( ( i @ ( i @ a ) )
!= unit ) ),
inference(rewrite,[status(thm)],[45124,788,38574]) ).
thf(750,plain,
( ( unit != a )
| ( ( i @ unit )
!= ( i @ b ) ) ),
inference(paramod_ordered,[status(thm)],[43,618]) ).
thf(752,plain,
( ( unit != a )
| ( unit != b ) ),
inference(simp,[status(thm)],[750]) ).
thf(122,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ a @ c )
!= unit )
| ( ( i @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) )
| ( A != c ) ),
inference(simp,[status(thm)],[78]) ).
thf(183,plain,
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ a @ c )
!= unit )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= ( i @ c ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(3117,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != a )
| ( A != b )
| ( ( rd @ B @ ( ld @ A @ B ) )
!= ( rd @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[794,1985]) ).
thf(3128,plain,
! [B: $i,A: $i] :
( ( unit != a )
| ( A != B )
| ( ( ld @ b @ A )
!= B ) ),
inference(simp,[status(thm)],[3117]) ).
thf(3132,plain,
! [A: $i] :
( ( unit != a )
| ( ( ld @ b @ A )
!= A ) ),
inference(simp,[status(thm)],[3128]) ).
thf(126,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ a @ c ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(75,plain,
! [A: $i] :
( ( ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ unit @ a ) @ c ) ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(132,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( mult @ unit @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(9991,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ a @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(rewrite,[status(thm)],[132,27]) ).
thf(9992,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ a )
!= a )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ a ) ) ),
inference(simp,[status(thm)],[9991]) ).
thf(73,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ ( mult @ a @ b ) @ a ) @ ( mult @ a @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(95,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
!= unit )
| ( ( i @ A )
!= ( mult @ ( mult @ a @ b ) @ a ) )
| ( A
!= ( mult @ a @ c ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(163,plain,
( ( ( mult @ a @ ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) )
!= unit )
| ( ( mult @ ( mult @ a @ b ) @ a )
!= ( i @ ( mult @ a @ c ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( mult @ B @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( A != b )
| ( ( ld @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[311]) ).
thf(369,plain,
! [A: $i] :
( ( ( mult @ ( mult @ A @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( ld @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[329]) ).
thf(13265,plain,
! [A: $i] :
( ( unit != a )
| ( ( mult @ unit @ A )
!= b )
| ( ( i @ ( i @ ( i @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13176,4981]) ).
thf(13266,plain,
( ( unit != a )
| ( ( mult @ unit @ ( i @ ( i @ unit ) ) )
!= b ) ),
inference(pattern_uni,[status(thm)],[13265:[bind(A,$thf( i @ ( i @ unit ) ))]]) ).
thf(14251,plain,
( ( unit != a )
| ( ( i @ ( i @ unit ) )
!= b ) ),
inference(rewrite,[status(thm)],[13266,27]) ).
thf(38707,plain,
! [C: $i,B: $i,A: $i] :
( ( unit != b )
| ( B != C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ C @ ( i @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,28471]) ).
thf(38758,plain,
! [B: $i,A: $i] :
( ( unit != b )
| ( A != B )
| ( ( ld @ A @ B )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[38707]) ).
thf(38794,plain,
! [A: $i] :
( ( unit != b )
| ( ( ld @ A @ A )
!= ( i @ a ) ) ),
inference(simp,[status(thm)],[38758]) ).
thf(194,plain,
! [A: $i] :
( ( ( mult @ a @ c )
!= unit )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[35,174]) ).
thf(224,plain,
! [A: $i] :
( ( ( mult @ a @ c )
!= unit )
| ( ( mult @ a @ b )
!= unit )
| ( ( i @ A )
!= ( mult @ ( mult @ b @ a ) @ a ) )
| ( A != c ) ),
inference(simp,[status(thm)],[194]) ).
thf(254,plain,
( ( ( mult @ a @ c )
!= unit )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( mult @ b @ a ) @ a )
!= ( i @ c ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(60229,plain,
! [A: $i] :
( ( ( rd @ ( mult @ unit @ A ) @ unit )
= unit )
| ( ( i @ ( i @ ( mult @ unit @ unit ) ) )
!= ( i @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60001,9858]) ).
thf(60230,plain,
( ( rd @ ( mult @ unit @ ( i @ ( mult @ unit @ unit ) ) ) @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[60229:[bind(A,$thf( i @ ( mult @ unit @ unit ) ))]]) ).
thf(66028,plain,
( ( mult @ unit @ ( i @ ( mult @ unit @ unit ) ) )
= unit ),
inference(rewrite,[status(thm)],[60230,700]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ a @ b ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(52693,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= a )
| ( ( mult @ ( mult @ ( mult @ b @ a ) @ a ) @ c )
!= ( mult @ a @ c ) )
| ( A
!= ( mult @ a @ b ) ) ),
inference(rewrite,[status(thm)],[341,17]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( ( mult @ B @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( A
!= ( mult @ b @ a ) )
| ( ( ld @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[312]) ).
thf(364,plain,
! [A: $i] :
( ( ( mult @ A @ c )
!= ( mult @ a @ c ) )
| ( ( mult @ a @ b )
!= unit )
| ( ( ld @ ( mult @ b @ a ) @ A )
!= a ) ),
inference(simp,[status(thm)],[323]) ).
thf(137025,plain,
$false,
inference(e,[status(thm)],[61535,365,11895,30638,42102,4290,249,170,379,4973,120,247,38784,11962,39606,153,174,1196,22223,24,44834,37,25,257,1985,4151,372,37087,17894,20,152,20716,29,164,34045,38574,42081,12436,19924,47054,60001,2392,8289,23175,44799,380,6296,366,24426,15345,270,28471,5017,20931,260,28,160,561,392,3134,33,788,21,33531,47501,30584,27436,519,156,55572,18219,35133,38798,40342,4389,70282,39129,1776,16468,63818,173,13,129,8142,371,10851,794,180,17,149,618,3130,30695,166,32,34,40655,375,176,22,45343,57102,36409,27,53630,54,8286,4218,181,58993,13176,86,50714,159,230,362,367,46173,91,700,251,521,68510,768,51650,32846,223,61229,2390,35,8922,167,26651,28845,13861,374,749,9858,28026,754,145,18,282,150,10246,16,370,44638,42087,22872,34432,50,5684,3655,40560,14297,31,17320,1981,154,54184,175,143,43,6928,7024,20251,39869,48836,35088,961,963,4089,26,16337,171,23,2394,139,49348,36303,119,235,18237,42076,13328,36,168,30,72788,13165,752,5677,183,19,58341,3132,239,126,4981,960,52190,5681,15,9992,163,1004,369,14251,38794,254,66028,52693,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP696-1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n004.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Fri May 19 01:41:40 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/0.97 % [INFO] Parsing done (108ms).
% 1.28/0.98 % [INFO] Running in sequential loop mode.
% 1.59/1.18 % [INFO] eprover registered as external prover.
% 1.59/1.18 % [INFO] cvc4 registered as external prover.
% 1.69/1.18 % [INFO] Scanning for conjecture ...
% 1.82/1.24 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.86/1.26 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.86/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.86/1.27 % [INFO] Type checking passed.
% 1.86/1.27 % [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 ...
% 159.99/32.18 % External prover 'e' found a proof!
% 159.99/32.18 % [INFO] Killing All external provers ...
% 159.99/32.18 % Time passed: 31648ms (effective reasoning time: 31197ms)
% 159.99/32.18 % Solved by 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)>
% 159.99/32.18 % Axioms used in derivation (11): c05, c11, c08, c01, c03, c06, c02, c07, c10, c09, c04
% 159.99/32.18 % No. of inferences in proof: 595
% 159.99/32.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 31648 ms resp. 31197 ms w/o parsing
% 160.10/32.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 160.10/32.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------