TSTP Solution File: LDA004-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LDA004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:34:19 EDT 2023
% Result : Unsatisfiable 191.68s 35.99s
% Output : Refutation 192.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 23
% Syntax : Number of formulae : 599 ( 309 unt; 11 typ; 0 def)
% Number of atoms : 984 ( 669 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 4800 ( 534 ~; 340 |; 0 &;3926 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 11 con; 0-2 aty)
% Number of variables : 516 ( 0 ^; 516 !; 0 ?; 516 :)
% Comments :
%------------------------------------------------------------------------------
thf(left_type,type,
left: $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(f_type,type,
f: $i > $i > $i ).
thf(n2_type,type,
n2: $i ).
thf(n1_type,type,
n1: $i ).
thf(n3_type,type,
n3: $i ).
thf(u_type,type,
u: $i ).
thf(u1_type,type,
u1: $i ).
thf(u2_type,type,
u2: $i ).
thf(u3_type,type,
u3: $i ).
thf(5,axiom,
( n2
= ( f @ n1 @ n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
thf(20,plain,
( n2
= ( f @ n1 @ n1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
( ( f @ n1 @ n1 )
= n2 ),
inference(lifteq,[status(thm)],[20]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
= ( f @ A @ ( f @ B @ C ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ n2 @ ( f @ A @ C ) )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ n1 @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,16]) ).
thf(108,plain,
! [A: $i] :
( ( f @ n1 @ ( f @ n1 @ A ) )
= ( f @ n2 @ ( f @ n1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( n1 )),bind(B,$thf( n1 ))]]) ).
thf(138,plain,
! [A: $i] :
( ( f @ n1 @ ( f @ n1 @ A ) )
= ( f @ n2 @ ( f @ n1 @ A ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(9,axiom,
( u2
= ( f @ u @ n2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
thf(28,plain,
( u2
= ( f @ u @ n2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
( ( f @ u @ n2 )
= u2 ),
inference(lifteq,[status(thm)],[28]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( left @ A @ ( f @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(17,plain,
! [B: $i,A: $i] : ( left @ A @ ( f @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( left @ A @ u2 )
| ( ( f @ u @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,17]) ).
thf(333,plain,
left @ u @ u2,
inference(pattern_uni,[status(thm)],[332:[bind(A,$thf( u )),bind(B,$thf( n2 ))]]) ).
thf(6,axiom,
( n3
= ( f @ n2 @ n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(22,plain,
( n3
= ( f @ n2 @ n1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
( ( f @ n2 @ n1 )
= n3 ),
inference(lifteq,[status(thm)],[22]) ).
thf(7,axiom,
( u
= ( f @ n2 @ n2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
thf(24,plain,
( u
= ( f @ n2 @ n2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
( ( f @ n2 @ n2 )
= u ),
inference(lifteq,[status(thm)],[24]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ u @ ( f @ A @ C ) )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ n2 @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,16]) ).
thf(102,plain,
! [A: $i] :
( ( f @ u @ ( f @ n2 @ A ) )
= ( f @ n2 @ ( f @ n2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( n2 )),bind(B,$thf( n2 ))]]) ).
thf(136,plain,
! [A: $i] :
( ( f @ u @ ( f @ n2 @ A ) )
= ( f @ n2 @ ( f @ n2 @ A ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(869,plain,
! [A: $i] :
( ( ( f @ u @ n3 )
= ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ n2 @ n1 )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[23,136]) ).
thf(870,plain,
( ( f @ u @ n3 )
= ( f @ n2 @ ( f @ n2 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[869:[bind(A,$thf( n1 ))]]) ).
thf(10,axiom,
( u3
= ( f @ u @ n3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
thf(30,plain,
( u3
= ( f @ u @ n3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
( ( f @ u @ n3 )
= u3 ),
inference(lifteq,[status(thm)],[30]) ).
thf(1152,plain,
( ( f @ n2 @ n3 )
= u3 ),
inference(rewrite,[status(thm)],[870,23,31]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ ( f @ A @ B ) @ u )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ n2 @ n2 )
!= ( f @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25,16]) ).
thf(104,plain,
! [A: $i] :
( ( f @ ( f @ n2 @ A ) @ u )
= ( f @ n2 @ ( f @ A @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( n2 )),bind(B,$thf( B )),bind(C,$thf( n2 ))]]) ).
thf(137,plain,
! [A: $i] :
( ( f @ ( f @ n2 @ A ) @ u )
= ( f @ n2 @ ( f @ A @ n2 ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(1617,plain,
! [A: $i] :
( ( ( f @ u3 @ u )
= ( f @ n2 @ ( f @ A @ n2 ) ) )
| ( ( f @ n2 @ n3 )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1152,137]) ).
thf(1618,plain,
( ( f @ u3 @ u )
= ( f @ n2 @ ( f @ n3 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[1617:[bind(A,$thf( n3 ))]]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ( left @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ( left @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ( left @ A @ C ) ),
inference(cnf,[status(esa)],[18]) ).
thf(1,negated_conjecture,
~ ( left @ a @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(13,plain,
~ ( left @ a @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,plain,
~ ( left @ a @ b ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ( ( left @ A @ C )
!= ( left @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[19,14]) ).
thf(55,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ~ ( left @ A @ b ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( b ))]]) ).
thf(62,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ~ ( left @ A @ b ) ),
inference(simp,[status(thm)],[55]) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( left @ C @ b )
| ( ( left @ A @ ( f @ A @ B ) )
!= ( left @ a @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,62]) ).
thf(367,plain,
! [A: $i] :
~ ( left @ ( f @ a @ A ) @ b ),
inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( a )),bind(B,$thf( E )),bind(C,$thf( f @ a @ E ))]]) ).
thf(380,plain,
! [A: $i] :
~ ( left @ ( f @ a @ A ) @ b ),
inference(simp,[status(thm)],[367]) ).
thf(956,plain,
! [C: $i,B: $i,A: $i] :
( ( left @ A @ ( f @ A @ B ) )
!= ( left @ ( f @ a @ C ) @ b ) ),
inference(paramod_ordered,[status(thm)],[17,380]) ).
thf(965,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( f @ a @ C ) )
| ( ( f @ A @ B )
!= b ) ),
inference(simp,[status(thm)],[956]) ).
thf(983,plain,
! [B: $i,A: $i] :
( ( f @ ( f @ a @ B ) @ A )
!= b ),
inference(simp,[status(thm)],[965]) ).
thf(2205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
!= b )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ ( f @ a @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16,983]) ).
thf(2206,plain,
! [B: $i,A: $i] :
( ( f @ a @ ( f @ A @ B ) )
!= b ),
inference(pattern_uni,[status(thm)],[2205:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( f @ a @ G )),bind(E,$thf( B ))]]) ).
thf(2258,plain,
! [B: $i,A: $i] :
( ( f @ a @ ( f @ A @ B ) )
!= b ),
inference(simp,[status(thm)],[2206]) ).
thf(2294,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n3 @ n2 ) ) )
!= b )
| ( ( f @ u3 @ u )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1618,2258]) ).
thf(2295,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n3 @ n2 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[2294:[bind(A,$thf( u3 )),bind(B,$thf( u ))]]) ).
thf(1187,plain,
! [A: $i] :
( ( ( f @ u @ u3 )
= ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ n2 @ n3 )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1152,136]) ).
thf(1188,plain,
( ( f @ u @ u3 )
= ( f @ n2 @ ( f @ n2 @ n3 ) ) ),
inference(pattern_uni,[status(thm)],[1187:[bind(A,$thf( n3 ))]]) ).
thf(1275,plain,
( ( f @ u @ u3 )
= ( f @ n2 @ u3 ) ),
inference(rewrite,[status(thm)],[1188,1152]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ ( f @ A @ B ) @ u2 )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ u @ n2 )
!= ( f @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,16]) ).
thf(155,plain,
! [A: $i] :
( ( f @ ( f @ u @ A ) @ u2 )
= ( f @ u @ ( f @ A @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( u )),bind(B,$thf( B )),bind(C,$thf( n2 ))]]) ).
thf(175,plain,
! [A: $i] :
( ( f @ ( f @ u @ A ) @ u2 )
= ( f @ u @ ( f @ A @ n2 ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(51310,plain,
! [A: $i] :
( ( ( f @ ( f @ n2 @ u3 ) @ u2 )
= ( f @ u @ ( f @ A @ n2 ) ) )
| ( ( f @ u @ u3 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1275,175]) ).
thf(51311,plain,
( ( f @ ( f @ n2 @ u3 ) @ u2 )
= ( f @ u @ ( f @ u3 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[51310:[bind(A,$thf( u3 ))]]) ).
thf(61765,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ ( f @ u3 @ n2 ) ) )
| ( ( f @ ( f @ n2 @ u3 ) @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51311,17]) ).
thf(61766,plain,
left @ ( f @ n2 @ u3 ) @ ( f @ u @ ( f @ u3 @ n2 ) ),
inference(pattern_uni,[status(thm)],[61765:[bind(A,$thf( f @ n2 @ u3 )),bind(B,$thf( u2 ))]]) ).
thf(3759,plain,
! [A: $i] :
( ( ( f @ n1 @ n2 )
= ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n1 @ n1 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,138]) ).
thf(3760,plain,
( ( f @ n1 @ n2 )
= ( f @ n2 @ ( f @ n1 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[3759:[bind(A,$thf( n1 ))]]) ).
thf(3968,plain,
( ( f @ n1 @ n2 )
= ( f @ n2 @ n2 ) ),
inference(rewrite,[status(thm)],[3760,21]) ).
thf(3973,plain,
! [A: $i] :
( ( ( f @ n1 @ ( f @ n2 @ n2 ) )
= ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n1 @ n2 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3968,138]) ).
thf(3974,plain,
( ( f @ n1 @ ( f @ n2 @ n2 ) )
= ( f @ n2 @ ( f @ n1 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[3973:[bind(A,$thf( n2 ))]]) ).
thf(4807,plain,
( ( f @ n1 @ u )
= ( f @ n2 @ ( f @ n2 @ n2 ) ) ),
inference(rewrite,[status(thm)],[3974,3968,25]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ ( f @ A @ B ) @ n2 )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ n1 @ n1 )
!= ( f @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,16]) ).
thf(110,plain,
! [A: $i] :
( ( f @ ( f @ n1 @ A ) @ n2 )
= ( f @ n1 @ ( f @ A @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( n1 )),bind(B,$thf( B )),bind(C,$thf( n1 ))]]) ).
thf(139,plain,
! [A: $i] :
( ( f @ ( f @ n1 @ A ) @ n2 )
= ( f @ n1 @ ( f @ A @ n1 ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(9998,plain,
! [A: $i] :
( ( ( f @ n1 @ ( f @ A @ n1 ) )
= ( f @ n2 @ n2 ) )
| ( ( f @ n1 @ n1 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,139]) ).
thf(9999,plain,
( ( f @ n1 @ ( f @ n1 @ n1 ) )
= ( f @ n2 @ n2 ) ),
inference(pattern_uni,[status(thm)],[9998:[bind(A,$thf( n1 ))]]) ).
thf(10357,plain,
( ( f @ n2 @ ( f @ n1 @ n1 ) )
= u ),
inference(rewrite,[status(thm)],[9999,25,138]) ).
thf(10409,plain,
! [A: $i] :
( ( ( f @ u @ u )
= ( f @ n2 @ ( f @ A @ n2 ) ) )
| ( ( f @ n2 @ ( f @ n1 @ n1 ) )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10357,137]) ).
thf(10410,plain,
( ( f @ u @ u )
= ( f @ n2 @ ( f @ ( f @ n1 @ n1 ) @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[10409:[bind(A,$thf( f @ n1 @ n1 ))]]) ).
thf(834,plain,
! [A: $i] :
( ( ( f @ u @ u )
= ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ n2 @ n2 )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,136]) ).
thf(835,plain,
( ( f @ u @ u )
= ( f @ n2 @ ( f @ n2 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( n2 ))]]) ).
thf(995,plain,
( ( f @ u @ u )
= ( f @ n2 @ u ) ),
inference(rewrite,[status(thm)],[835,25]) ).
thf(16269,plain,
( ( f @ n2 @ ( f @ n1 @ ( f @ n1 @ n1 ) ) )
= ( f @ n2 @ u ) ),
inference(rewrite,[status(thm)],[10410,995,139]) ).
thf(16343,plain,
( ( ( f @ n2 @ ( f @ n1 @ n2 ) )
= ( f @ n2 @ u ) )
| ( ( f @ n1 @ n1 )
!= ( f @ n1 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[21,16269]) ).
thf(16344,plain,
( ( f @ n2 @ ( f @ n1 @ n2 ) )
= ( f @ n2 @ u ) ),
inference(pattern_uni,[status(thm)],[16343:[]]) ).
thf(16870,plain,
( ( f @ n2 @ ( f @ n2 @ n2 ) )
= ( f @ n2 @ u ) ),
inference(rewrite,[status(thm)],[16344,3968]) ).
thf(16871,plain,
( ( f @ n1 @ u )
= ( f @ n2 @ u ) ),
inference(rewrite,[status(thm)],[4807,16870]) ).
thf(17646,plain,
! [A: $i] :
( ( ( f @ ( f @ n2 @ u ) @ n2 )
= ( f @ n1 @ ( f @ A @ n1 ) ) )
| ( ( f @ n1 @ u )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16871,139]) ).
thf(17647,plain,
( ( f @ ( f @ n2 @ u ) @ n2 )
= ( f @ n1 @ ( f @ u @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[17646:[bind(A,$thf( u ))]]) ).
thf(8,axiom,
( u1
= ( f @ u @ n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
thf(26,plain,
( u1
= ( f @ u @ n1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
( ( f @ u @ n1 )
= u1 ),
inference(lifteq,[status(thm)],[26]) ).
thf(39851,plain,
( ( f @ ( f @ n2 @ u ) @ n2 )
= ( f @ n1 @ u1 ) ),
inference(rewrite,[status(thm)],[17647,27]) ).
thf(40027,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n1 @ u1 ) )
| ( ( f @ ( f @ n2 @ u ) @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39851,17]) ).
thf(40028,plain,
left @ ( f @ n2 @ u ) @ ( f @ n1 @ u1 ),
inference(pattern_uni,[status(thm)],[40027:[bind(A,$thf( f @ n2 @ u )),bind(B,$thf( n2 ))]]) ).
thf(10010,plain,
! [A: $i] :
( ( ( f @ ( f @ n2 @ n2 ) @ n2 )
= ( f @ n1 @ ( f @ A @ n1 ) ) )
| ( ( f @ n1 @ n2 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3968,139]) ).
thf(10011,plain,
( ( f @ ( f @ n2 @ n2 ) @ n2 )
= ( f @ n1 @ ( f @ n2 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[10010:[bind(A,$thf( n2 ))]]) ).
thf(12026,plain,
( ( f @ u @ n2 )
= ( f @ n1 @ n3 ) ),
inference(rewrite,[status(thm)],[10011,23,25]) ).
thf(12027,plain,
( ( f @ n1 @ n3 )
= u2 ),
inference(rewrite,[status(thm)],[29,12026]) ).
thf(12427,plain,
! [A: $i] :
( ( ( f @ n1 @ u2 )
= ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n1 @ n3 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12027,138]) ).
thf(12428,plain,
( ( f @ n1 @ u2 )
= ( f @ n2 @ ( f @ n1 @ n3 ) ) ),
inference(pattern_uni,[status(thm)],[12427:[bind(A,$thf( n3 ))]]) ).
thf(14415,plain,
( ( f @ n1 @ u2 )
= ( f @ n2 @ u2 ) ),
inference(rewrite,[status(thm)],[12428,12027]) ).
thf(14417,plain,
! [A: $i] :
( ( ( f @ n1 @ ( f @ n2 @ u2 ) )
= ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n1 @ u2 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14415,138]) ).
thf(14418,plain,
( ( f @ n1 @ ( f @ n2 @ u2 ) )
= ( f @ n2 @ ( f @ n1 @ u2 ) ) ),
inference(pattern_uni,[status(thm)],[14417:[bind(A,$thf( u2 ))]]) ).
thf(18070,plain,
( ( f @ n1 @ ( f @ n2 @ u2 ) )
= ( f @ n2 @ ( f @ n2 @ u2 ) ) ),
inference(rewrite,[status(thm)],[14418,14415]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ n3 @ ( f @ A @ C ) )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ n2 @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,16]) ).
thf(124,plain,
! [A: $i] :
( ( f @ n3 @ ( f @ n2 @ A ) )
= ( f @ n2 @ ( f @ n1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( n2 )),bind(B,$thf( n1 ))]]) ).
thf(144,plain,
! [A: $i] :
( ( f @ n3 @ ( f @ n2 @ A ) )
= ( f @ n2 @ ( f @ n1 @ A ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(26546,plain,
! [C: $i,B: $i,A: $i] :
( ( left @ B @ ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n3 @ ( f @ n2 @ A ) )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[144,17]) ).
thf(26547,plain,
! [A: $i] : ( left @ n3 @ ( f @ n2 @ ( f @ n1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[26546:[bind(A,$thf( E )),bind(B,$thf( n3 )),bind(C,$thf( f @ n2 @ E ))]]) ).
thf(27051,plain,
! [A: $i] : ( left @ n3 @ ( f @ n2 @ ( f @ n1 @ A ) ) ),
inference(simp,[status(thm)],[26547]) ).
thf(34478,plain,
! [A: $i] :
( ( left @ n3 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ) )
| ( ( f @ n1 @ ( f @ n2 @ u2 ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18070,27051]) ).
thf(34479,plain,
left @ n3 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ),
inference(pattern_uni,[status(thm)],[34478:[bind(A,$thf( f @ n2 @ u2 ))]]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ u1 @ ( f @ A @ C ) )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ u @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,16]) ).
thf(114,plain,
! [A: $i] :
( ( f @ u1 @ ( f @ u @ A ) )
= ( f @ u @ ( f @ n1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( u )),bind(B,$thf( n1 ))]]) ).
thf(140,plain,
! [A: $i] :
( ( f @ u1 @ ( f @ u @ A ) )
= ( f @ u @ ( f @ n1 @ A ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(18897,plain,
! [A: $i] :
( ( ( f @ u1 @ u3 )
= ( f @ u @ ( f @ n1 @ A ) ) )
| ( ( f @ u @ n3 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31,140]) ).
thf(18898,plain,
( ( f @ u1 @ u3 )
= ( f @ u @ ( f @ n1 @ n3 ) ) ),
inference(pattern_uni,[status(thm)],[18897:[bind(A,$thf( n3 ))]]) ).
thf(12,axiom,
( b
= ( f @ u1 @ u3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
thf(34,plain,
( b
= ( f @ u1 @ u3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(35,plain,
( ( f @ u1 @ u3 )
= b ),
inference(lifteq,[status(thm)],[34]) ).
thf(21377,plain,
( ( f @ u @ u2 )
= b ),
inference(rewrite,[status(thm)],[18898,35,12027]) ).
thf(51437,plain,
! [A: $i] :
( ( ( f @ u @ ( f @ A @ n2 ) )
= ( f @ b @ u2 ) )
| ( ( f @ u @ u2 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21377,175]) ).
thf(51438,plain,
( ( f @ u @ ( f @ u2 @ n2 ) )
= ( f @ b @ u2 ) ),
inference(pattern_uni,[status(thm)],[51437:[bind(A,$thf( u2 ))]]) ).
thf(12583,plain,
! [A: $i] :
( ( ( f @ u2 @ n2 )
= ( f @ n1 @ ( f @ A @ n1 ) ) )
| ( ( f @ n1 @ n3 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12027,139]) ).
thf(12584,plain,
( ( f @ u2 @ n2 )
= ( f @ n1 @ ( f @ n3 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[12583:[bind(A,$thf( n3 ))]]) ).
thf(52507,plain,
( ( f @ u @ ( f @ n1 @ ( f @ n3 @ n1 ) ) )
= ( f @ b @ u2 ) ),
inference(rewrite,[status(thm)],[51438,12584]) ).
thf(18828,plain,
! [C: $i,B: $i,A: $i] :
( ( left @ B @ ( f @ u @ ( f @ n1 @ A ) ) )
| ( ( f @ u1 @ ( f @ u @ A ) )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[140,17]) ).
thf(18829,plain,
! [A: $i] : ( left @ u1 @ ( f @ u @ ( f @ n1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[18828:[bind(A,$thf( E )),bind(B,$thf( u1 )),bind(C,$thf( f @ u @ E ))]]) ).
thf(19235,plain,
! [A: $i] : ( left @ u1 @ ( f @ u @ ( f @ n1 @ A ) ) ),
inference(simp,[status(thm)],[18829]) ).
thf(52679,plain,
! [A: $i] :
( ( left @ u1 @ ( f @ b @ u2 ) )
| ( ( f @ u @ ( f @ n1 @ ( f @ n3 @ n1 ) ) )
!= ( f @ u @ ( f @ n1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[52507,19235]) ).
thf(52680,plain,
left @ u1 @ ( f @ b @ u2 ),
inference(pattern_uni,[status(thm)],[52679:[bind(A,$thf( f @ n3 @ n1 ))]]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ ( f @ A @ B ) @ u1 )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ u @ n1 )
!= ( f @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,16]) ).
thf(116,plain,
! [A: $i] :
( ( f @ ( f @ u @ A ) @ u1 )
= ( f @ u @ ( f @ A @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( u )),bind(B,$thf( B )),bind(C,$thf( n1 ))]]) ).
thf(141,plain,
! [A: $i] :
( ( f @ ( f @ u @ A ) @ u1 )
= ( f @ u @ ( f @ A @ n1 ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(20714,plain,
! [A: $i] :
( ( ( f @ ( f @ n2 @ u3 ) @ u1 )
= ( f @ u @ ( f @ A @ n1 ) ) )
| ( ( f @ u @ u3 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1275,141]) ).
thf(20715,plain,
( ( f @ ( f @ n2 @ u3 ) @ u1 )
= ( f @ u @ ( f @ u3 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[20714:[bind(A,$thf( u3 ))]]) ).
thf(43989,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ ( f @ u3 @ n1 ) ) )
| ( ( f @ ( f @ n2 @ u3 ) @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20715,17]) ).
thf(43990,plain,
left @ ( f @ n2 @ u3 ) @ ( f @ u @ ( f @ u3 @ n1 ) ),
inference(pattern_uni,[status(thm)],[43989:[bind(A,$thf( f @ n2 @ u3 )),bind(B,$thf( u1 ))]]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ u2 @ ( f @ A @ C ) )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ u @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,16]) ).
thf(153,plain,
! [A: $i] :
( ( f @ u2 @ ( f @ u @ A ) )
= ( f @ u @ ( f @ n2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( u )),bind(B,$thf( n2 ))]]) ).
thf(174,plain,
! [A: $i] :
( ( f @ u2 @ ( f @ u @ A ) )
= ( f @ u @ ( f @ n2 @ A ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(47081,plain,
! [A: $i] :
( ( f @ u2 @ ( f @ u @ A ) )
= ( f @ n2 @ ( f @ n2 @ A ) ) ),
inference(rewrite,[status(thm)],[174,136]) ).
thf(47296,plain,
! [C: $i,B: $i,A: $i] :
( ( left @ B @ ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ u2 @ ( f @ u @ A ) )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[47081,17]) ).
thf(47297,plain,
! [A: $i] : ( left @ u2 @ ( f @ n2 @ ( f @ n2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[47296:[bind(A,$thf( E )),bind(B,$thf( u2 )),bind(C,$thf( f @ u @ E ))]]) ).
thf(47913,plain,
! [A: $i] : ( left @ u2 @ ( f @ n2 @ ( f @ n2 @ A ) ) ),
inference(simp,[status(thm)],[47297]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ A @ B ) )
!= ( left @ a @ b ) ),
inference(paramod_ordered,[status(thm)],[17,14]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( f @ A @ B )
!= b ) ),
inference(simp,[status(thm)],[331]) ).
thf(381,plain,
! [A: $i] :
( ( f @ a @ A )
!= b ),
inference(simp,[status(thm)],[369]) ).
thf(393,plain,
! [A: $i] :
( ( f @ u1 @ u3 )
!= ( f @ a @ A ) ),
inference(paramod_ordered,[status(thm)],[35,381]) ).
thf(400,plain,
! [A: $i] :
( ( u1 != a )
| ( u3 != A ) ),
inference(simp,[status(thm)],[393]) ).
thf(408,plain,
u1 != a,
inference(simp,[status(thm)],[400]) ).
thf(147,plain,
( ( u2 = u )
| ( ( f @ u @ n2 )
!= ( f @ n2 @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[25,29]) ).
thf(161,plain,
( ( u2 = u )
| ( u != n2 )
| ( n2 != n2 ) ),
inference(simp,[status(thm)],[147]) ).
thf(170,plain,
( ( u2 = u )
| ( u != n2 ) ),
inference(simp,[status(thm)],[161]) ).
thf(51604,plain,
! [A: $i] :
( ( ( f @ u3 @ u2 )
= ( f @ u @ ( f @ A @ n2 ) ) )
| ( ( f @ u @ n3 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31,175]) ).
thf(51605,plain,
( ( f @ u3 @ u2 )
= ( f @ u @ ( f @ n3 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[51604:[bind(A,$thf( n3 ))]]) ).
thf(54575,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ ( f @ n3 @ n2 ) ) )
| ( ( f @ u3 @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51605,17]) ).
thf(54576,plain,
left @ u3 @ ( f @ u @ ( f @ n3 @ n2 ) ),
inference(pattern_uni,[status(thm)],[54575:[bind(A,$thf( u3 )),bind(B,$thf( u2 ))]]) ).
thf(47117,plain,
! [A: $i] :
( ( ( f @ u2 @ ( f @ n2 @ u3 ) )
= ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ u @ u3 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1275,47081]) ).
thf(47118,plain,
( ( f @ u2 @ ( f @ n2 @ u3 ) )
= ( f @ n2 @ ( f @ n2 @ u3 ) ) ),
inference(pattern_uni,[status(thm)],[47117:[bind(A,$thf( u3 ))]]) ).
thf(59539,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ u3 ) ) )
!= b )
| ( ( f @ u2 @ ( f @ n2 @ u3 ) )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[47118,2258]) ).
thf(59540,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ u3 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[59539:[bind(A,$thf( u2 )),bind(B,$thf( f @ n2 @ u3 ))]]) ).
thf(118,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( f @ ( f @ A @ ( f @ B @ C ) ) @ ( f @ D @ F ) )
= ( f @ D @ ( f @ E @ F ) ) )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[16,16]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( f @ ( f @ C @ ( f @ B @ D ) ) @ ( f @ ( f @ C @ B ) @ A ) )
= ( f @ ( f @ C @ B ) @ ( f @ ( f @ C @ D ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( f @ I @ H )),bind(E,$thf( f @ I @ J )),bind(F,$thf( F ))]]) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( f @ ( f @ C @ ( f @ B @ D ) ) @ ( f @ ( f @ C @ B ) @ A ) )
= ( f @ ( f @ C @ B ) @ ( f @ ( f @ C @ D ) @ A ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(2315,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ u3 )
!= b )
| ( ( f @ u @ n3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,2258]) ).
thf(2316,plain,
( ( f @ a @ u3 )
!= b ),
inference(pattern_uni,[status(thm)],[2315:[bind(A,$thf( u )),bind(B,$thf( n3 ))]]) ).
thf(4007,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ n2 ) )
| ( ( f @ n1 @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3968,17]) ).
thf(4008,plain,
left @ n1 @ ( f @ n2 @ n2 ),
inference(pattern_uni,[status(thm)],[4007:[bind(A,$thf( n1 )),bind(B,$thf( n2 ))]]) ).
thf(4144,plain,
left @ n1 @ u,
inference(rewrite,[status(thm)],[4008,25]) ).
thf(4178,plain,
! [A: $i] :
( ~ ( left @ A @ b )
| ( ( left @ n1 @ u )
!= ( left @ a @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4144,62]) ).
thf(4194,plain,
! [A: $i] :
( ~ ( left @ A @ b )
| ( n1 != a )
| ( u != A ) ),
inference(simp,[status(thm)],[4178]) ).
thf(4209,plain,
( ~ ( left @ u @ b )
| ( n1 != a ) ),
inference(simp,[status(thm)],[4194]) ).
thf(21474,plain,
! [B: $i,A: $i] :
( ( left @ A @ b )
| ( ( f @ u @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21377,17]) ).
thf(21475,plain,
left @ u @ b,
inference(pattern_uni,[status(thm)],[21474:[bind(A,$thf( u )),bind(B,$thf( u2 ))]]) ).
thf(21856,plain,
( ~ $true
| ( n1 != a ) ),
inference(rewrite,[status(thm)],[4209,21475]) ).
thf(21857,plain,
n1 != a,
inference(simp,[status(thm)],[21856]) ).
thf(2303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ A @ n2 ) ) )
!= b )
| ( ( f @ ( f @ n2 @ A ) @ u )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[137,2258]) ).
thf(2304,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ A @ n2 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[2303:[bind(A,$thf( E )),bind(B,$thf( f @ n2 @ E )),bind(C,$thf( u ))]]) ).
thf(2345,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ A @ n2 ) ) )
!= b ),
inference(simp,[status(thm)],[2304]) ).
thf(15050,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n1 @ ( f @ n3 @ n1 ) ) ) )
!= b )
| ( ( f @ u2 @ n2 )
!= ( f @ A @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[12584,2345]) ).
thf(15051,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n1 @ ( f @ n3 @ n1 ) ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[15050:[bind(A,$thf( u2 ))]]) ).
thf(12425,plain,
( ( f @ u @ n2 )
= u2 ),
inference(rewrite,[status(thm)],[12026,12027]) ).
thf(47189,plain,
! [A: $i] :
( ( ( f @ u2 @ u2 )
= ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ u @ n2 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12425,47081]) ).
thf(47190,plain,
( ( f @ u2 @ u2 )
= ( f @ n2 @ ( f @ n2 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[47189:[bind(A,$thf( n2 ))]]) ).
thf(48009,plain,
( ( f @ u2 @ u2 )
= ( f @ n2 @ u ) ),
inference(rewrite,[status(thm)],[47190,16870]) ).
thf(48188,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ u ) )
| ( ( f @ u2 @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48009,17]) ).
thf(48189,plain,
left @ u2 @ ( f @ n2 @ u ),
inference(pattern_uni,[status(thm)],[48188:[bind(A,$thf( u2 )),bind(B,$thf( u2 ))]]) ).
thf(1587,plain,
! [C: $i,B: $i,A: $i] :
( ( left @ B @ ( f @ n2 @ ( f @ A @ n2 ) ) )
| ( ( f @ ( f @ n2 @ A ) @ u )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[137,17]) ).
thf(1588,plain,
! [A: $i] : ( left @ ( f @ n2 @ A ) @ ( f @ n2 @ ( f @ A @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[1587:[bind(A,$thf( E )),bind(B,$thf( f @ n2 @ E )),bind(C,$thf( u ))]]) ).
thf(1669,plain,
! [A: $i] : ( left @ ( f @ n2 @ A ) @ ( f @ n2 @ ( f @ A @ n2 ) ) ),
inference(simp,[status(thm)],[1588]) ).
thf(2431,plain,
! [A: $i] :
( ( left @ ( f @ n2 @ A ) @ ( f @ n2 @ u2 ) )
| ( ( f @ u @ n2 )
!= ( f @ A @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[29,1669]) ).
thf(2432,plain,
left @ ( f @ n2 @ u ) @ ( f @ n2 @ u2 ),
inference(pattern_uni,[status(thm)],[2431:[bind(A,$thf( u ))]]) ).
thf(4809,plain,
! [A: $i] :
( ( ( f @ n1 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) )
= ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n1 @ u )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4807,138]) ).
thf(4810,plain,
( ( f @ n1 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) )
= ( f @ n2 @ ( f @ n1 @ u ) ) ),
inference(pattern_uni,[status(thm)],[4809:[bind(A,$thf( u ))]]) ).
thf(5166,plain,
( ( f @ n1 @ ( f @ n2 @ u ) )
= ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ),
inference(rewrite,[status(thm)],[4810,4807,25]) ).
thf(3772,plain,
! [C: $i,B: $i,A: $i] :
( ( left @ B @ ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n1 @ ( f @ n1 @ A ) )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[138,17]) ).
thf(3773,plain,
! [A: $i] : ( left @ n1 @ ( f @ n2 @ ( f @ n1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3772:[bind(A,$thf( E )),bind(B,$thf( n1 )),bind(C,$thf( f @ n1 @ E ))]]) ).
thf(3938,plain,
! [A: $i] : ( left @ n1 @ ( f @ n2 @ ( f @ n1 @ A ) ) ),
inference(simp,[status(thm)],[3773]) ).
thf(5192,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) )
| ( ( f @ n1 @ ( f @ n2 @ u ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5166,3938]) ).
thf(5193,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ),
inference(pattern_uni,[status(thm)],[5192:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(5825,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u ) ) ),
inference(rewrite,[status(thm)],[5193,25]) ).
thf(21439,plain,
! [A: $i] :
( ( ( f @ u @ ( f @ A @ n1 ) )
= ( f @ b @ u1 ) )
| ( ( f @ u @ u2 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21377,141]) ).
thf(21440,plain,
( ( f @ u @ ( f @ u2 @ n1 ) )
= ( f @ b @ u1 ) ),
inference(pattern_uni,[status(thm)],[21439:[bind(A,$thf( u2 ))]]) ).
thf(25937,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ b @ u1 ) )
| ( ( f @ u @ ( f @ u2 @ n1 ) )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21440,17]) ).
thf(25938,plain,
left @ u @ ( f @ b @ u1 ),
inference(pattern_uni,[status(thm)],[25937:[bind(A,$thf( u )),bind(B,$thf( f @ u2 @ n1 ))]]) ).
thf(42,plain,
( ( u = n2 )
| ( ( f @ n1 @ n1 )
!= ( f @ n2 @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[25,21]) ).
thf(46,plain,
( ( u = n2 )
| ( n1 != n2 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[42]) ).
thf(52,plain,
( ( u = n2 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[46]) ).
thf(14576,plain,
! [A: $i] :
( ( ( f @ ( f @ n2 @ u2 ) @ n2 )
= ( f @ n1 @ ( f @ A @ n1 ) ) )
| ( ( f @ n1 @ u2 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14415,139]) ).
thf(14577,plain,
( ( f @ ( f @ n2 @ u2 ) @ n2 )
= ( f @ n1 @ ( f @ u2 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[14576:[bind(A,$thf( u2 ))]]) ).
thf(36331,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n1 @ ( f @ u2 @ n1 ) ) )
| ( ( f @ ( f @ n2 @ u2 ) @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14577,17]) ).
thf(36332,plain,
left @ ( f @ n2 @ u2 ) @ ( f @ n1 @ ( f @ u2 @ n1 ) ),
inference(pattern_uni,[status(thm)],[36331:[bind(A,$thf( f @ n2 @ u2 )),bind(B,$thf( n2 ))]]) ).
thf(18732,plain,
! [A: $i] :
( ( ( f @ u1 @ ( f @ n2 @ u3 ) )
= ( f @ u @ ( f @ n1 @ A ) ) )
| ( ( f @ u @ u3 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1275,140]) ).
thf(18733,plain,
( ( f @ u1 @ ( f @ n2 @ u3 ) )
= ( f @ u @ ( f @ n1 @ u3 ) ) ),
inference(pattern_uni,[status(thm)],[18732:[bind(A,$thf( u3 ))]]) ).
thf(15086,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n1 @ ( f @ n3 @ n1 ) ) )
| ( ( f @ u2 @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12584,17]) ).
thf(15087,plain,
left @ u2 @ ( f @ n1 @ ( f @ n3 @ n1 ) ),
inference(pattern_uni,[status(thm)],[15086:[bind(A,$thf( u2 )),bind(B,$thf( n2 ))]]) ).
thf(26665,plain,
! [A: $i] :
( ( ( f @ n3 @ n3 )
= ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n2 @ n1 )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[23,144]) ).
thf(26666,plain,
( ( f @ n3 @ n3 )
= ( f @ n2 @ ( f @ n1 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[26665:[bind(A,$thf( n1 ))]]) ).
thf(29426,plain,
( ( f @ n3 @ n3 )
= u ),
inference(rewrite,[status(thm)],[26666,10357]) ).
thf(29539,plain,
! [B: $i,A: $i] :
( ( left @ A @ u )
| ( ( f @ n3 @ n3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29426,17]) ).
thf(29540,plain,
left @ n3 @ u,
inference(pattern_uni,[status(thm)],[29539:[bind(A,$thf( n3 )),bind(B,$thf( n3 ))]]) ).
thf(36499,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n1 @ ( f @ u2 @ n1 ) ) )
!= b )
| ( ( f @ ( f @ n2 @ u2 ) @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14577,2258]) ).
thf(36500,plain,
( ( f @ a @ ( f @ n1 @ ( f @ u2 @ n1 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[36499:[bind(A,$thf( f @ n2 @ u2 )),bind(B,$thf( n2 ))]]) ).
thf(33348,plain,
! [A: $i] :
( ( left @ u1 @ ( f @ u @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ) )
| ( ( f @ n1 @ ( f @ n2 @ u2 ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18070,19235]) ).
thf(33349,plain,
left @ u1 @ ( f @ u @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ),
inference(pattern_uni,[status(thm)],[33348:[bind(A,$thf( f @ n2 @ u2 ))]]) ).
thf(33908,plain,
left @ u1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ),
inference(rewrite,[status(thm)],[33349,136]) ).
thf(16873,plain,
( ( f @ n1 @ ( f @ n2 @ u ) )
= ( f @ n2 @ ( f @ n2 @ u ) ) ),
inference(rewrite,[status(thm)],[5166,16870]) ).
thf(18934,plain,
! [A: $i] :
( ( ( f @ u1 @ ( f @ n2 @ u ) )
= ( f @ u @ ( f @ n1 @ A ) ) )
| ( ( f @ u @ u )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[995,140]) ).
thf(18935,plain,
( ( f @ u1 @ ( f @ n2 @ u ) )
= ( f @ u @ ( f @ n1 @ u ) ) ),
inference(pattern_uni,[status(thm)],[18934:[bind(A,$thf( u ))]]) ).
thf(42483,plain,
( ( f @ u1 @ ( f @ n2 @ u ) )
= ( f @ u @ ( f @ n2 @ u ) ) ),
inference(rewrite,[status(thm)],[18935,16871]) ).
thf(39971,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n1 @ u1 ) ) )
!= b )
| ( ( f @ ( f @ n2 @ u ) @ n2 )
!= ( f @ A @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[39851,2345]) ).
thf(39972,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n1 @ u1 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[39971:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(2300,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ n2 )
!= b )
| ( ( f @ n1 @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,2258]) ).
thf(2301,plain,
( ( f @ a @ n2 )
!= b ),
inference(pattern_uni,[status(thm)],[2300:[bind(A,$thf( n1 )),bind(B,$thf( n1 ))]]) ).
thf(51664,plain,
! [A: $i] :
( ( ( f @ ( f @ n2 @ u ) @ u2 )
= ( f @ u @ ( f @ A @ n2 ) ) )
| ( ( f @ u @ u )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[995,175]) ).
thf(51665,plain,
( ( f @ ( f @ n2 @ u ) @ u2 )
= ( f @ u @ ( f @ u @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[51664:[bind(A,$thf( u ))]]) ).
thf(64117,plain,
( ( f @ ( f @ n2 @ u ) @ u2 )
= ( f @ u @ u2 ) ),
inference(rewrite,[status(thm)],[51665,12425]) ).
thf(64364,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ u2 ) )
| ( ( f @ ( f @ n2 @ u ) @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[64117,17]) ).
thf(64365,plain,
left @ ( f @ n2 @ u ) @ ( f @ u @ u2 ),
inference(pattern_uni,[status(thm)],[64364:[bind(A,$thf( f @ n2 @ u )),bind(B,$thf( u2 ))]]) ).
thf(65184,plain,
left @ ( f @ n2 @ u ) @ b,
inference(rewrite,[status(thm)],[64365,21377]) ).
thf(65193,plain,
( ( left @ ( f @ n2 @ u ) @ b )
!= ( left @ a @ b ) ),
inference(paramod_ordered,[status(thm)],[65184,14]) ).
thf(65309,plain,
( ( ( f @ n2 @ u )
!= a )
| ( b != b ) ),
inference(simp,[status(thm)],[65193]) ).
thf(65398,plain,
( ( f @ n2 @ u )
!= a ),
inference(simp,[status(thm)],[65309]) ).
thf(4536,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) )
| ( ( f @ n1 @ n2 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3968,3938]) ).
thf(4537,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ n2 ) ),
inference(pattern_uni,[status(thm)],[4536:[bind(A,$thf( n2 ))]]) ).
thf(4669,plain,
left @ n1 @ ( f @ n2 @ u ),
inference(rewrite,[status(thm)],[4537,25]) ).
thf(61964,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ u @ ( f @ u3 @ n2 ) ) )
!= b )
| ( ( f @ ( f @ n2 @ u3 ) @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51311,2258]) ).
thf(61965,plain,
( ( f @ a @ ( f @ u @ ( f @ u3 @ n2 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[61964:[bind(A,$thf( f @ n2 @ u3 )),bind(B,$thf( u2 ))]]) ).
thf(18833,plain,
! [A: $i] :
( ( ( f @ u1 @ u1 )
= ( f @ u @ ( f @ n1 @ A ) ) )
| ( ( f @ u @ n1 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,140]) ).
thf(18834,plain,
( ( f @ u1 @ u1 )
= ( f @ u @ ( f @ n1 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[18833:[bind(A,$thf( n1 ))]]) ).
thf(20230,plain,
( ( f @ u1 @ u1 )
= ( f @ u @ n2 ) ),
inference(rewrite,[status(thm)],[18834,21]) ).
thf(20742,plain,
! [A: $i] :
( ( ( f @ u2 @ u1 )
= ( f @ u @ ( f @ A @ n1 ) ) )
| ( ( f @ u @ n2 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12425,141]) ).
thf(20743,plain,
( ( f @ u2 @ u1 )
= ( f @ u @ ( f @ n2 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[20742:[bind(A,$thf( n2 ))]]) ).
thf(21967,plain,
( ( f @ u2 @ u1 )
= ( f @ n2 @ ( f @ n2 @ n1 ) ) ),
inference(rewrite,[status(thm)],[20743,136]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ ( f @ A @ B ) @ n3 )
= ( f @ A @ ( f @ B @ C ) ) )
| ( ( f @ n2 @ n1 )
!= ( f @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,16]) ).
thf(126,plain,
! [A: $i] :
( ( f @ ( f @ n2 @ A ) @ n3 )
= ( f @ n2 @ ( f @ A @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( n2 )),bind(B,$thf( B )),bind(C,$thf( n1 ))]]) ).
thf(145,plain,
! [A: $i] :
( ( f @ ( f @ n2 @ A ) @ n3 )
= ( f @ n2 @ ( f @ A @ n1 ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(28550,plain,
! [A: $i] :
( ( ( f @ u @ n3 )
= ( f @ n2 @ ( f @ A @ n1 ) ) )
| ( ( f @ n2 @ ( f @ n1 @ n1 ) )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10357,145]) ).
thf(28551,plain,
( ( f @ u @ n3 )
= ( f @ n2 @ ( f @ ( f @ n1 @ n1 ) @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[28550:[bind(A,$thf( f @ n1 @ n1 ))]]) ).
thf(55758,plain,
( ( f @ n2 @ ( f @ n2 @ n1 ) )
= u3 ),
inference(rewrite,[status(thm)],[28551,21,31]) ).
thf(55759,plain,
( ( f @ u2 @ u1 )
= u3 ),
inference(rewrite,[status(thm)],[21967,55758]) ).
thf(47409,plain,
! [A: $i] :
( ( ( f @ u2 @ u3 )
= ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ u @ n3 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31,47081]) ).
thf(47410,plain,
( ( f @ u2 @ u3 )
= ( f @ n2 @ ( f @ n2 @ n3 ) ) ),
inference(pattern_uni,[status(thm)],[47409:[bind(A,$thf( n3 ))]]) ).
thf(50202,plain,
( ( f @ u2 @ u3 )
= ( f @ n2 @ u3 ) ),
inference(rewrite,[status(thm)],[47410,1152]) ).
thf(50382,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ u3 ) )
| ( ( f @ u2 @ u3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50202,17]) ).
thf(50383,plain,
left @ u2 @ ( f @ n2 @ u3 ),
inference(pattern_uni,[status(thm)],[50382:[bind(A,$thf( u2 )),bind(B,$thf( u3 ))]]) ).
thf(47466,plain,
! [A: $i] :
( ( ( f @ u2 @ ( f @ n2 @ u ) )
= ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ u @ u )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[995,47081]) ).
thf(47467,plain,
( ( f @ u2 @ ( f @ n2 @ u ) )
= ( f @ n2 @ ( f @ n2 @ u ) ) ),
inference(pattern_uni,[status(thm)],[47466:[bind(A,$thf( u ))]]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( left @ A @ u1 )
| ( ( f @ u @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,17]) ).
thf(339,plain,
left @ u @ u1,
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( u )),bind(B,$thf( n1 ))]]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( left @ A @ b )
| ( ( f @ u1 @ u3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,17]) ).
thf(341,plain,
left @ u1 @ b,
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( u1 )),bind(B,$thf( u3 ))]]) ).
thf(69,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ A @ b )
!= ( left @ a @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[62]) ).
thf(70,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ A @ b )
!= ( left @ a @ A ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(556,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ u1 @ b )
!= ( left @ A @ b ) ) ),
inference(paramod_ordered,[status(thm)],[341,70]) ).
thf(557,plain,
~ ( left @ a @ u1 ),
inference(pattern_uni,[status(thm)],[556:[bind(A,$thf( u1 ))]]) ).
thf(589,plain,
( ( left @ u @ u1 )
!= ( left @ a @ u1 ) ),
inference(paramod_ordered,[status(thm)],[339,557]) ).
thf(598,plain,
( ( u != a )
| ( u1 != u1 ) ),
inference(simp,[status(thm)],[589]) ).
thf(602,plain,
u != a,
inference(simp,[status(thm)],[598]) ).
thf(3813,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n1 @ A ) ) )
!= b )
| ( ( f @ n1 @ ( f @ n1 @ A ) )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[138,2258]) ).
thf(3814,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ n1 @ A ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[3813:[bind(A,$thf( E )),bind(B,$thf( n1 )),bind(C,$thf( f @ n1 @ E ))]]) ).
thf(3943,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ n1 @ A ) ) )
!= b ),
inference(simp,[status(thm)],[3814]) ).
thf(6180,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) )
!= b )
| ( ( f @ n1 @ ( f @ n1 @ A ) )
!= ( f @ n1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[138,3943]) ).
thf(6181,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[6180:[bind(A,$thf( D )),bind(B,$thf( f @ n1 @ D ))]]) ).
thf(6304,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) )
!= b ),
inference(simp,[status(thm)],[6181]) ).
thf(12484,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ u2 ) ) )
!= b )
| ( ( f @ n1 @ n3 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12027,6304]) ).
thf(12485,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ u2 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[12484:[bind(A,$thf( n3 ))]]) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( left @ A @ u3 )
| ( ( f @ n2 @ n3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1152,17]) ).
thf(1169,plain,
left @ n2 @ u3,
inference(pattern_uni,[status(thm)],[1168:[bind(A,$thf( n2 )),bind(B,$thf( n3 ))]]) ).
thf(26707,plain,
! [A: $i] :
( ( ( f @ n3 @ u3 )
= ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n2 @ n3 )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1152,144]) ).
thf(26708,plain,
( ( f @ n3 @ u3 )
= ( f @ n2 @ ( f @ n1 @ n3 ) ) ),
inference(pattern_uni,[status(thm)],[26707:[bind(A,$thf( n3 ))]]) ).
thf(31180,plain,
( ( f @ n3 @ u3 )
= ( f @ n2 @ u2 ) ),
inference(rewrite,[status(thm)],[26708,12027]) ).
thf(42036,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ u @ ( f @ n1 @ u3 ) ) )
!= b )
| ( ( f @ u1 @ ( f @ n2 @ u3 ) )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18733,2258]) ).
thf(42037,plain,
( ( f @ a @ ( f @ u @ ( f @ n1 @ u3 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[42036:[bind(A,$thf( u1 )),bind(B,$thf( f @ n2 @ u3 ))]]) ).
thf(21496,plain,
! [A: $i] :
( ( ( f @ u1 @ b )
= ( f @ u @ ( f @ n1 @ A ) ) )
| ( ( f @ u @ u2 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21377,140]) ).
thf(21497,plain,
( ( f @ u1 @ b )
= ( f @ u @ ( f @ n1 @ u2 ) ) ),
inference(pattern_uni,[status(thm)],[21496:[bind(A,$thf( u2 ))]]) ).
thf(27432,plain,
( ( f @ u1 @ b )
= ( f @ u @ ( f @ n2 @ u2 ) ) ),
inference(rewrite,[status(thm)],[21497,14415]) ).
thf(2285,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ u )
!= b )
| ( ( f @ n2 @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,2258]) ).
thf(2286,plain,
( ( f @ a @ u )
!= b ),
inference(pattern_uni,[status(thm)],[2285:[bind(A,$thf( n2 )),bind(B,$thf( n2 ))]]) ).
thf(36273,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n1 @ ( f @ u2 @ n1 ) ) ) )
!= b )
| ( ( f @ ( f @ n2 @ u2 ) @ n2 )
!= ( f @ A @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[14577,2345]) ).
thf(36274,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n1 @ ( f @ u2 @ n1 ) ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[36273:[bind(A,$thf( f @ n2 @ u2 ))]]) ).
thf(2306,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ u1 )
!= b )
| ( ( f @ u @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,2258]) ).
thf(2307,plain,
( ( f @ a @ u1 )
!= b ),
inference(pattern_uni,[status(thm)],[2306:[bind(A,$thf( u )),bind(B,$thf( n1 ))]]) ).
thf(34448,plain,
! [A: $i] :
( ( left @ n3 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) )
| ( ( f @ n1 @ u2 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14415,27051]) ).
thf(34449,plain,
left @ n3 @ ( f @ n2 @ ( f @ n2 @ u2 ) ),
inference(pattern_uni,[status(thm)],[34448:[bind(A,$thf( u2 ))]]) ).
thf(12509,plain,
! [B: $i,A: $i] :
( ( left @ A @ u2 )
| ( ( f @ n1 @ n3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12027,17]) ).
thf(12510,plain,
left @ n1 @ u2,
inference(pattern_uni,[status(thm)],[12509:[bind(A,$thf( n1 )),bind(B,$thf( n3 ))]]) ).
thf(18757,plain,
! [A: $i] :
( ( ( f @ u1 @ u2 )
= ( f @ u @ ( f @ n1 @ A ) ) )
| ( ( f @ u @ n2 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12425,140]) ).
thf(18758,plain,
( ( f @ u1 @ u2 )
= ( f @ u @ ( f @ n1 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[18757:[bind(A,$thf( n2 ))]]) ).
thf(19243,plain,
( ( f @ u1 @ u2 )
= ( f @ u @ ( f @ n2 @ n2 ) ) ),
inference(rewrite,[status(thm)],[18758,3968]) ).
thf(19333,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ ( f @ n2 @ n2 ) ) )
| ( ( f @ u1 @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19243,17]) ).
thf(19334,plain,
left @ u1 @ ( f @ u @ ( f @ n2 @ n2 ) ),
inference(pattern_uni,[status(thm)],[19333:[bind(A,$thf( u1 )),bind(B,$thf( u2 ))]]) ).
thf(19695,plain,
left @ u1 @ ( f @ n2 @ ( f @ n2 @ n2 ) ),
inference(rewrite,[status(thm)],[19334,136]) ).
thf(19702,plain,
( ( left @ u1 @ ( f @ n2 @ u ) )
| ( ( f @ n2 @ n2 )
!= ( f @ n2 @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[25,19695]) ).
thf(19703,plain,
left @ u1 @ ( f @ n2 @ u ),
inference(pattern_uni,[status(thm)],[19702:[]]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= u2 )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ u @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[16,29]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= u2 )
| ( ( f @ A @ B )
!= u )
| ( ( f @ A @ C )
!= n2 ) ),
inference(simp,[status(thm)],[157]) ).
thf(4511,plain,
! [B: $i,A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) )
| ( ( f @ n1 @ ( f @ n1 @ A ) )
!= ( f @ n1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[138,3938]) ).
thf(4512,plain,
! [A: $i] : ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[4511:[bind(A,$thf( D )),bind(B,$thf( f @ n1 @ D ))]]) ).
thf(4640,plain,
! [A: $i] : ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) ),
inference(simp,[status(thm)],[4512]) ).
thf(6383,plain,
! [B: $i,A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) ) )
| ( ( f @ n1 @ ( f @ n1 @ A ) )
!= ( f @ n1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[138,4640]) ).
thf(6384,plain,
! [A: $i] : ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[6383:[bind(A,$thf( D )),bind(B,$thf( f @ n1 @ D ))]]) ).
thf(6586,plain,
! [A: $i] : ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) ) ),
inference(simp,[status(thm)],[6384]) ).
thf(12590,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ) )
| ( ( f @ n1 @ n3 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12027,6586]) ).
thf(12591,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ),
inference(pattern_uni,[status(thm)],[12590:[bind(A,$thf( n3 ))]]) ).
thf(185,plain,
( ( u3 = n3 )
| ( ( f @ u @ n3 )
!= ( f @ n2 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,31]) ).
thf(192,plain,
( ( u3 = n3 )
| ( u != n2 )
| ( n3 != n1 ) ),
inference(simp,[status(thm)],[185]) ).
thf(11,axiom,
( a
= ( f @ ( f @ n3 @ n2 ) @ u2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
thf(32,plain,
( a
= ( f @ ( f @ n3 @ n2 ) @ u2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(33,plain,
( ( f @ ( f @ n3 @ n2 ) @ u2 )
= a ),
inference(lifteq,[status(thm)],[32]) ).
thf(7129,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) ) )
!= b )
| ( ( f @ n1 @ ( f @ n1 @ A ) )
!= ( f @ n1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[138,6304]) ).
thf(7130,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[7129:[bind(A,$thf( D )),bind(B,$thf( f @ n1 @ D ))]]) ).
thf(7301,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n1 @ A ) ) ) ) )
!= b ),
inference(simp,[status(thm)],[7130]) ).
thf(71,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( A != a )
| ( b != A ) ),
inference(simp,[status(thm)],[69]) ).
thf(73,plain,
( ~ ( left @ a @ a )
| ( b != a ) ),
inference(simp,[status(thm)],[71]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ( b != a )
| ( ( left @ A @ C )
!= ( left @ a @ a ) ) ),
inference(paramod_ordered,[status(thm)],[19,73]) ).
thf(91,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ~ ( left @ A @ a )
| ( b != a ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( a ))]]) ).
thf(92,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ~ ( left @ A @ a )
| ( b != a ) ),
inference(simp,[status(thm)],[91]) ).
thf(22063,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ ( f @ n2 @ n1 ) ) )
| ( ( f @ u2 @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21967,17]) ).
thf(22064,plain,
left @ u2 @ ( f @ n2 @ ( f @ n2 @ n1 ) ),
inference(pattern_uni,[status(thm)],[22063:[bind(A,$thf( u2 )),bind(B,$thf( u1 ))]]) ).
thf(23546,plain,
left @ u2 @ ( f @ n2 @ n3 ),
inference(rewrite,[status(thm)],[22064,23]) ).
thf(65202,plain,
! [A: $i] :
( ( left @ ( f @ n2 @ u ) @ b )
!= ( left @ ( f @ a @ A ) @ b ) ),
inference(paramod_ordered,[status(thm)],[65184,380]) ).
thf(65350,plain,
! [A: $i] :
( ( ( f @ n2 @ u )
!= ( f @ a @ A ) )
| ( b != b ) ),
inference(simp,[status(thm)],[65202]) ).
thf(65413,plain,
! [A: $i] :
( ( f @ n2 @ u )
!= ( f @ a @ A ) ),
inference(simp,[status(thm)],[65350]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( left @ A @ u )
| ( ( f @ n2 @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25,17]) ).
thf(330,plain,
left @ n2 @ u,
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( n2 )),bind(B,$thf( n2 ))]]) ).
thf(436,plain,
! [A: $i] :
( ~ ( left @ A @ b )
| ( ( left @ n2 @ u )
!= ( left @ a @ A ) ) ),
inference(paramod_ordered,[status(thm)],[330,62]) ).
thf(438,plain,
! [A: $i] :
( ~ ( left @ A @ b )
| ( n2 != a )
| ( u != A ) ),
inference(simp,[status(thm)],[436]) ).
thf(455,plain,
( ~ ( left @ u @ b )
| ( n2 != a ) ),
inference(simp,[status(thm)],[438]) ).
thf(21854,plain,
( ~ $true
| ( n2 != a ) ),
inference(rewrite,[status(thm)],[455,21475]) ).
thf(21855,plain,
n2 != a,
inference(simp,[status(thm)],[21854]) ).
thf(44179,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ u @ ( f @ u3 @ n1 ) ) )
!= b )
| ( ( f @ ( f @ n2 @ u3 ) @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20715,2258]) ).
thf(44180,plain,
( ( f @ a @ ( f @ u @ ( f @ u3 @ n1 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[44179:[bind(A,$thf( f @ n2 @ u3 )),bind(B,$thf( u1 ))]]) ).
thf(12449,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ u2 ) )
| ( ( f @ n1 @ n3 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12027,3938]) ).
thf(12450,plain,
left @ n1 @ ( f @ n2 @ u2 ),
inference(pattern_uni,[status(thm)],[12449:[bind(A,$thf( n3 ))]]) ).
thf(52981,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ b @ u2 ) )
!= b )
| ( ( f @ u @ ( f @ n1 @ ( f @ n3 @ n1 ) ) )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52507,2258]) ).
thf(52982,plain,
( ( f @ a @ ( f @ b @ u2 ) )
!= b ),
inference(pattern_uni,[status(thm)],[52981:[bind(A,$thf( u )),bind(B,$thf( f @ n1 @ ( f @ n3 @ n1 ) ))]]) ).
thf(12801,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ n1 @ u2 )
!= ( left @ A @ b ) ) ),
inference(paramod_ordered,[status(thm)],[12510,70]) ).
thf(12865,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( n1 != A )
| ( u2 != b ) ),
inference(simp,[status(thm)],[12801]) ).
thf(12866,plain,
( ~ ( left @ a @ n1 )
| ( u2 != b ) ),
inference(simp,[status(thm)],[12865]) ).
thf(52756,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ b @ u2 ) )
| ( ( f @ u @ ( f @ n1 @ ( f @ n3 @ n1 ) ) )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52507,17]) ).
thf(52757,plain,
left @ u @ ( f @ b @ u2 ),
inference(pattern_uni,[status(thm)],[52756:[bind(A,$thf( u )),bind(B,$thf( f @ n1 @ ( f @ n3 @ n1 ) ))]]) ).
thf(355,plain,
! [B: $i,A: $i] :
( ( left @ A @ a )
| ( ( f @ ( f @ n3 @ n2 ) @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33,17]) ).
thf(356,plain,
left @ ( f @ n3 @ n2 ) @ a,
inference(pattern_uni,[status(thm)],[355:[bind(A,$thf( f @ n3 @ n2 )),bind(B,$thf( u2 ))]]) ).
thf(1291,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ u3 ) )
| ( ( f @ u @ u3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1275,17]) ).
thf(1292,plain,
left @ u @ ( f @ n2 @ u3 ),
inference(pattern_uni,[status(thm)],[1291:[bind(A,$thf( u )),bind(B,$thf( u3 ))]]) ).
thf(6214,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) )
!= b )
| ( ( f @ n1 @ ( f @ n2 @ u ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5166,3943]) ).
thf(6215,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[6214:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(6946,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u ) ) ) )
!= b ),
inference(rewrite,[status(thm)],[6215,25]) ).
thf(47242,plain,
! [A: $i] :
( ( ( f @ u2 @ b )
= ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ u @ u2 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21377,47081]) ).
thf(47243,plain,
( ( f @ u2 @ b )
= ( f @ n2 @ ( f @ n2 @ u2 ) ) ),
inference(pattern_uni,[status(thm)],[47242:[bind(A,$thf( u2 ))]]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ~ ( left @ a @ D )
| ( b != a )
| ( ( left @ A @ C )
!= ( left @ D @ a ) ) ),
inference(paramod_ordered,[status(thm)],[19,92]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ a )
| ~ ( left @ a @ A )
| ( b != a ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( a )),bind(D,$thf( A ))]]) ).
thf(55995,plain,
! [A: $i] :
( ( ( f @ n3 @ u3 )
= ( f @ n2 @ ( f @ n1 @ A ) ) )
| ( ( f @ n2 @ ( f @ n2 @ n1 ) )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[55758,144]) ).
thf(55996,plain,
( ( f @ n3 @ u3 )
= ( f @ n2 @ ( f @ n1 @ ( f @ n2 @ n1 ) ) ) ),
inference(pattern_uni,[status(thm)],[55995:[bind(A,$thf( f @ n2 @ n1 ))]]) ).
thf(67551,plain,
( ( f @ n2 @ ( f @ n1 @ n3 ) )
= ( f @ n2 @ u2 ) ),
inference(rewrite,[status(thm)],[55996,23,31180]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= u1 )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ u @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[16,27]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= u1 )
| ( ( f @ A @ B )
!= u )
| ( ( f @ A @ C )
!= n1 ) ),
inference(simp,[status(thm)],[112]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ( left @ A @ u3 )
| ( ( f @ u @ n3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,17]) ).
thf(360,plain,
left @ u @ u3,
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( u )),bind(B,$thf( n3 ))]]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= u )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ n2 @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[25,16]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= u )
| ( ( f @ A @ B )
!= n2 )
| ( ( f @ A @ C )
!= n2 ) ),
inference(simp,[status(thm)],[105]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( left @ A @ n3 )
| ( ( f @ n2 @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,17]) ).
thf(343,plain,
left @ n2 @ n3,
inference(pattern_uni,[status(thm)],[342:[bind(A,$thf( n2 )),bind(B,$thf( n1 ))]]) ).
thf(26078,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ b @ u1 ) )
!= b )
| ( ( f @ u @ ( f @ u2 @ n1 ) )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21440,2258]) ).
thf(26079,plain,
( ( f @ a @ ( f @ b @ u1 ) )
!= b ),
inference(pattern_uni,[status(thm)],[26078:[bind(A,$thf( u )),bind(B,$thf( f @ u2 @ n1 ))]]) ).
thf(21500,plain,
! [B: $i,A: $i] :
( ( f @ ( f @ a @ B ) @ A )
!= ( f @ u @ u2 ) ),
inference(paramod_ordered,[status(thm)],[21377,983]) ).
thf(21778,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ B )
!= u )
| ( A != u2 ) ),
inference(simp,[status(thm)],[21500]) ).
thf(21845,plain,
! [A: $i] :
( ( f @ a @ A )
!= u ),
inference(simp,[status(thm)],[21778]) ).
thf(10128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ a @ ( f @ n1 @ ( f @ A @ n1 ) ) )
!= b )
| ( ( f @ ( f @ n1 @ A ) @ n2 )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[139,2258]) ).
thf(10129,plain,
! [A: $i] :
( ( f @ a @ ( f @ n1 @ ( f @ A @ n1 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[10128:[bind(A,$thf( E )),bind(B,$thf( f @ n1 @ E )),bind(C,$thf( n2 ))]]) ).
thf(10329,plain,
! [A: $i] :
( ( f @ a @ ( f @ n1 @ ( f @ A @ n1 ) ) )
!= b ),
inference(simp,[status(thm)],[10129]) ).
thf(69478,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n1 @ n2 ) )
!= b )
| ( ( f @ n1 @ n1 )
!= ( f @ A @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[21,10329]) ).
thf(69479,plain,
( ( f @ a @ ( f @ n1 @ n2 ) )
!= b ),
inference(pattern_uni,[status(thm)],[69478:[bind(A,$thf( n1 ))]]) ).
thf(69919,plain,
( ( f @ a @ ( f @ n2 @ n2 ) )
!= b ),
inference(rewrite,[status(thm)],[69479,3968]) ).
thf(148,plain,
( ( u2 = n2 )
| ( ( f @ u @ n2 )
!= ( f @ n1 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,21]) ).
thf(166,plain,
( ( u2 = n2 )
| ( u != n1 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[148]) ).
thf(590,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ A @ B ) )
!= ( left @ a @ u1 ) ),
inference(paramod_ordered,[status(thm)],[17,557]) ).
thf(596,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( f @ A @ B )
!= u1 ) ),
inference(simp,[status(thm)],[590]) ).
thf(601,plain,
! [A: $i] :
( ( f @ a @ A )
!= u1 ),
inference(simp,[status(thm)],[596]) ).
thf(40207,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n1 @ u1 ) )
!= b )
| ( ( f @ ( f @ n2 @ u ) @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39851,2258]) ).
thf(40208,plain,
( ( f @ a @ ( f @ n1 @ u1 ) )
!= b ),
inference(pattern_uni,[status(thm)],[40207:[bind(A,$thf( f @ n2 @ u )),bind(B,$thf( n2 ))]]) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ( left @ B @ ( f @ n2 @ ( f @ n2 @ A ) ) )
| ( ( f @ u @ ( f @ n2 @ A ) )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[136,17]) ).
thf(856,plain,
! [A: $i] : ( left @ u @ ( f @ n2 @ ( f @ n2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[855:[bind(A,$thf( E )),bind(B,$thf( u )),bind(C,$thf( f @ n2 @ E ))]]) ).
thf(906,plain,
! [A: $i] : ( left @ u @ ( f @ n2 @ ( f @ n2 @ A ) ) ),
inference(simp,[status(thm)],[856]) ).
thf(22170,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ n1 ) ) )
!= b )
| ( ( f @ u2 @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21967,2258]) ).
thf(22171,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ n1 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[22170:[bind(A,$thf( u2 )),bind(B,$thf( u1 ))]]) ).
thf(28947,plain,
( ( f @ a @ ( f @ n2 @ n3 ) )
!= b ),
inference(rewrite,[status(thm)],[22171,23]) ).
thf(58,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ~ ( left @ D @ E )
| ( left @ D @ F )
| ( ( left @ A @ C )
!= ( left @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ~ ( left @ D @ A )
| ( left @ D @ C ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(179,plain,
( ( u3 = u2 )
| ( ( f @ u @ n3 )
!= ( f @ u @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[29,31]) ).
thf(194,plain,
( ( u3 = u2 )
| ( u != u )
| ( n3 != n2 ) ),
inference(simp,[status(thm)],[179]) ).
thf(204,plain,
( ( u3 = u2 )
| ( n3 != n2 ) ),
inference(simp,[status(thm)],[194]) ).
thf(20886,plain,
! [A: $i] :
( ( ( f @ u3 @ u1 )
= ( f @ u @ ( f @ A @ n1 ) ) )
| ( ( f @ u @ n3 )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31,141]) ).
thf(20887,plain,
( ( f @ u3 @ u1 )
= ( f @ u @ ( f @ n3 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[20886:[bind(A,$thf( n3 ))]]) ).
thf(2318,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ n3 )
!= b )
| ( ( f @ n2 @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,2258]) ).
thf(2319,plain,
( ( f @ a @ n3 )
!= b ),
inference(pattern_uni,[status(thm)],[2318:[bind(A,$thf( n2 )),bind(B,$thf( n1 ))]]) ).
thf(65207,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ ( f @ n2 @ u ) @ b )
!= ( left @ A @ b ) ) ),
inference(paramod_ordered,[status(thm)],[65184,70]) ).
thf(65208,plain,
~ ( left @ a @ ( f @ n2 @ u ) ),
inference(pattern_uni,[status(thm)],[65207:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(78,plain,
( ( u1 = n3 )
| ( ( f @ u @ n1 )
!= ( f @ n2 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[27,23]) ).
thf(80,plain,
( ( u1 = n3 )
| ( u != n2 )
| ( n1 != n1 ) ),
inference(simp,[status(thm)],[78]) ).
thf(86,plain,
( ( u1 = n3 )
| ( u != n2 ) ),
inference(simp,[status(thm)],[80]) ).
thf(38233,plain,
! [A: $i] :
( ( left @ u1 @ ( f @ u @ ( f @ n2 @ ( f @ n2 @ u ) ) ) )
| ( ( f @ n1 @ ( f @ n2 @ u ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16873,19235]) ).
thf(38234,plain,
left @ u1 @ ( f @ u @ ( f @ n2 @ ( f @ n2 @ u ) ) ),
inference(pattern_uni,[status(thm)],[38233:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(39419,plain,
left @ u1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u ) ) ),
inference(rewrite,[status(thm)],[38234,136]) ).
thf(28567,plain,
! [A: $i] :
( ( ( f @ u3 @ n3 )
= ( f @ n2 @ ( f @ A @ n1 ) ) )
| ( ( f @ n2 @ n3 )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1152,145]) ).
thf(28568,plain,
( ( f @ u3 @ n3 )
= ( f @ n2 @ ( f @ n3 @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[28567:[bind(A,$thf( n3 ))]]) ).
thf(32102,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ ( f @ n3 @ n1 ) ) )
| ( ( f @ u3 @ n3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[28568,17]) ).
thf(32103,plain,
left @ u3 @ ( f @ n2 @ ( f @ n3 @ n1 ) ),
inference(pattern_uni,[status(thm)],[32102:[bind(A,$thf( u3 )),bind(B,$thf( n3 ))]]) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ u ) )
| ( ( f @ u @ u )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[995,17]) ).
thf(1011,plain,
left @ u @ ( f @ n2 @ u ),
inference(pattern_uni,[status(thm)],[1010:[bind(A,$thf( u )),bind(B,$thf( u ))]]) ).
thf(7173,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) ) )
!= b )
| ( ( f @ n1 @ ( f @ n2 @ u ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5166,6304]) ).
thf(7174,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[7173:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(8445,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u ) ) ) ) )
!= b ),
inference(rewrite,[status(thm)],[7174,25]) ).
thf(5609,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n2 @ u2 ) )
!= b )
| ( ( f @ u @ n2 )
!= ( f @ A @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[29,2345]) ).
thf(5610,plain,
( ( f @ a @ ( f @ n2 @ u2 ) )
!= b ),
inference(pattern_uni,[status(thm)],[5609:[bind(A,$thf( u ))]]) ).
thf(1606,plain,
! [A: $i] :
( ( ( f @ n3 @ u )
= ( f @ n2 @ ( f @ A @ n2 ) ) )
| ( ( f @ n2 @ n1 )
!= ( f @ n2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[23,137]) ).
thf(1607,plain,
( ( f @ n3 @ u )
= ( f @ n2 @ ( f @ n1 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[1606:[bind(A,$thf( n1 ))]]) ).
thf(1756,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ ( f @ n1 @ n2 ) ) )
| ( ( f @ n3 @ u )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1607,17]) ).
thf(1757,plain,
left @ n3 @ ( f @ n2 @ ( f @ n1 @ n2 ) ),
inference(pattern_uni,[status(thm)],[1756:[bind(A,$thf( n3 )),bind(B,$thf( u ))]]) ).
thf(3971,plain,
left @ n3 @ ( f @ n2 @ ( f @ n2 @ n2 ) ),
inference(rewrite,[status(thm)],[1757,3968]) ).
thf(4213,plain,
left @ n3 @ ( f @ n2 @ u ),
inference(rewrite,[status(thm)],[3971,25]) ).
thf(74,plain,
( ( u1 = u )
| ( ( f @ u @ n1 )
!= ( f @ n2 @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[27,25]) ).
thf(81,plain,
( ( u1 = u )
| ( u != n2 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[74]) ).
thf(23621,plain,
( ( left @ u2 @ u3 )
| ( ( f @ n2 @ n3 )
!= ( f @ n2 @ n3 ) ) ),
inference(paramod_ordered,[status(thm)],[1152,23546]) ).
thf(23622,plain,
left @ u2 @ u3,
inference(pattern_uni,[status(thm)],[23621:[]]) ).
thf(23767,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ u2 @ u3 )
!= ( left @ A @ b ) ) ),
inference(paramod_ordered,[status(thm)],[23622,62]) ).
thf(23781,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( u2 != A )
| ( u3 != b ) ),
inference(simp,[status(thm)],[23767]) ).
thf(23805,plain,
( ~ ( left @ a @ u2 )
| ( u3 != b ) ),
inference(simp,[status(thm)],[23781]) ).
thf(2288,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ u2 )
!= b )
| ( ( f @ u @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,2258]) ).
thf(2289,plain,
( ( f @ a @ u2 )
!= b ),
inference(pattern_uni,[status(thm)],[2288:[bind(A,$thf( u )),bind(B,$thf( n2 ))]]) ).
thf(176,plain,
( ( u3 = u )
| ( ( f @ u @ n3 )
!= ( f @ n2 @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[31,25]) ).
thf(198,plain,
( ( u3 = u )
| ( u != n2 )
| ( n3 != n2 ) ),
inference(simp,[status(thm)],[176]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= n3 )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ n2 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,16]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= n3 )
| ( ( f @ A @ B )
!= n2 )
| ( ( f @ A @ C )
!= n1 ) ),
inference(simp,[status(thm)],[127]) ).
thf(12464,plain,
! [A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ) )
!= b )
| ( ( f @ n1 @ n3 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12027,7301]) ).
thf(12465,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[12464:[bind(A,$thf( n3 ))]]) ).
thf(38110,plain,
! [A: $i] :
( ( left @ n3 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u ) ) ) )
| ( ( f @ n1 @ ( f @ n2 @ u ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16873,27051]) ).
thf(38111,plain,
left @ n3 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u ) ) ),
inference(pattern_uni,[status(thm)],[38110:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(67253,plain,
( ( left @ u2 @ ( f @ n2 @ u ) )
!= ( left @ a @ ( f @ n2 @ u ) ) ),
inference(paramod_ordered,[status(thm)],[48189,65208]) ).
thf(67465,plain,
( ( u2 != a )
| ( ( f @ n2 @ u )
!= ( f @ n2 @ u ) ) ),
inference(simp,[status(thm)],[67253]) ).
thf(67529,plain,
u2 != a,
inference(simp,[status(thm)],[67465]) ).
thf(33327,plain,
! [A: $i] :
( ( left @ u1 @ ( f @ u @ ( f @ n2 @ u ) ) )
| ( ( f @ n1 @ u )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16871,19235]) ).
thf(33328,plain,
left @ u1 @ ( f @ u @ ( f @ n2 @ u ) ),
inference(pattern_uni,[status(thm)],[33327:[bind(A,$thf( u ))]]) ).
thf(33593,plain,
left @ u1 @ ( f @ n2 @ ( f @ n2 @ u ) ),
inference(rewrite,[status(thm)],[33328,136]) ).
thf(2297,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ a )
!= b )
| ( ( f @ ( f @ n3 @ n2 ) @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33,2258]) ).
thf(2298,plain,
( ( f @ a @ a )
!= b ),
inference(pattern_uni,[status(thm)],[2297:[bind(A,$thf( f @ n3 @ n2 )),bind(B,$thf( u2 ))]]) ).
thf(56,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ~ ( left @ E @ F )
| ( left @ D @ F )
| ( ( left @ A @ C )
!= ( left @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ~ ( left @ C @ D )
| ( left @ A @ D ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ~ ( left @ C @ D )
| ( left @ A @ D ) ),
inference(simp,[status(thm)],[57]) ).
thf(4179,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ n1 @ u )
!= ( left @ A @ b ) ) ),
inference(paramod_ordered,[status(thm)],[4144,62]) ).
thf(4181,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( n1 != A )
| ( u != b ) ),
inference(simp,[status(thm)],[4179]) ).
thf(4200,plain,
( ~ ( left @ a @ n1 )
| ( u != b ) ),
inference(simp,[status(thm)],[4181]) ).
thf(3969,plain,
( ( f @ n3 @ u )
= ( f @ n2 @ ( f @ n2 @ n2 ) ) ),
inference(rewrite,[status(thm)],[1607,3968]) ).
thf(4324,plain,
( ( f @ n3 @ u )
= ( f @ n2 @ u ) ),
inference(rewrite,[status(thm)],[3969,25]) ).
thf(25123,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ ( f @ n3 @ n1 ) ) )
| ( ( f @ u3 @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20887,17]) ).
thf(25124,plain,
left @ u3 @ ( f @ u @ ( f @ n3 @ n1 ) ),
inference(pattern_uni,[status(thm)],[25123:[bind(A,$thf( u3 )),bind(B,$thf( u1 ))]]) ).
thf(12518,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) )
| ( ( f @ n1 @ n3 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12027,4640]) ).
thf(12519,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ u2 ) ),
inference(pattern_uni,[status(thm)],[12518:[bind(A,$thf( n3 ))]]) ).
thf(44,plain,
( ( u = n3 )
| ( ( f @ n2 @ n1 )
!= ( f @ n2 @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[25,23]) ).
thf(48,plain,
( ( u = n3 )
| ( n2 != n2 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[44]) ).
thf(50,plain,
( ( u = n3 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[48]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= u3 )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ u @ n3 ) ) ),
inference(paramod_ordered,[status(thm)],[16,31]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= u3 )
| ( ( f @ A @ B )
!= u )
| ( ( f @ A @ C )
!= n3 ) ),
inference(simp,[status(thm)],[191]) ).
thf(2321,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ u ) )
!= b )
| ( ( f @ u @ u )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[995,2258]) ).
thf(2322,plain,
( ( f @ a @ ( f @ n2 @ u ) )
!= b ),
inference(pattern_uni,[status(thm)],[2321:[bind(A,$thf( u )),bind(B,$thf( u ))]]) ).
thf(4799,plain,
( ( u != n2 )
| ~ ( left @ a @ n3 )
| ( u1 != u1 ) ),
inference(paramod_ordered,[status(thm)],[86,557]) ).
thf(4800,plain,
( ( u != n2 )
| ~ ( left @ a @ n3 ) ),
inference(pattern_uni,[status(thm)],[4799:[]]) ).
thf(17995,plain,
( ( n1 != n2 )
| ~ ( left @ a @ n3 )
| ( u != u ) ),
inference(paramod_ordered,[status(thm)],[52,4800]) ).
thf(17996,plain,
( ( n1 != n2 )
| ~ ( left @ a @ n3 ) ),
inference(pattern_uni,[status(thm)],[17995:[]]) ).
thf(31303,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ u2 ) )
| ( ( f @ n3 @ u3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31180,17]) ).
thf(31304,plain,
left @ n3 @ ( f @ n2 @ u2 ),
inference(pattern_uni,[status(thm)],[31303:[bind(A,$thf( n3 )),bind(B,$thf( u3 ))]]) ).
thf(32235,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n3 @ n1 ) ) )
!= b )
| ( ( f @ u3 @ n3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[28568,2258]) ).
thf(32236,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n3 @ n1 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[32235:[bind(A,$thf( u3 )),bind(B,$thf( n3 ))]]) ).
thf(1980,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ n2 @ ( f @ n3 @ n2 ) ) )
| ( ( f @ u3 @ u )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1618,17]) ).
thf(1981,plain,
left @ u3 @ ( f @ n2 @ ( f @ n3 @ n2 ) ),
inference(pattern_uni,[status(thm)],[1980:[bind(A,$thf( u3 )),bind(B,$thf( u ))]]) ).
thf(5273,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) )
!= b )
| ( ( f @ n1 @ ( f @ n2 @ u ) )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5166,2258]) ).
thf(5274,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[5273:[bind(A,$thf( n1 )),bind(B,$thf( f @ n2 @ u ))]]) ).
thf(5453,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ u ) ) )
!= b ),
inference(rewrite,[status(thm)],[5274,25]) ).
thf(120,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( f @ ( f @ D @ E ) @ ( f @ A @ ( f @ B @ C ) ) )
= ( f @ D @ ( f @ E @ F ) ) )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[16,16]) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( f @ ( f @ ( f @ C @ B ) @ A ) @ ( f @ C @ ( f @ B @ D ) ) )
= ( f @ ( f @ C @ B ) @ ( f @ A @ ( f @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( f @ I @ H )),bind(E,$thf( E )),bind(F,$thf( f @ I @ J ))]]) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( f @ ( f @ ( f @ C @ B ) @ A ) @ ( f @ C @ ( f @ B @ D ) ) )
= ( f @ ( f @ C @ B ) @ ( f @ A @ ( f @ C @ D ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(7702,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) ) ) )
| ( ( f @ n1 @ ( f @ n2 @ u ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5166,6586]) ).
thf(7703,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[7702:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(9046,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u ) ) ) ) ),
inference(rewrite,[status(thm)],[7703,25]) ).
thf(14585,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ) ) )
| ( ( f @ n1 @ u2 )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14415,6586]) ).
thf(14586,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u2 ) ) ) ),
inference(pattern_uni,[status(thm)],[14585:[bind(A,$thf( u2 ))]]) ).
thf(77,plain,
( ( u1 = n2 )
| ( ( f @ u @ n1 )
!= ( f @ n1 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[21,27]) ).
thf(82,plain,
( ( u1 = n2 )
| ( u != n1 )
| ( n1 != n1 ) ),
inference(simp,[status(thm)],[77]) ).
thf(87,plain,
( ( u1 = n2 )
| ( u != n1 ) ),
inference(simp,[status(thm)],[82]) ).
thf(2309,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ b )
!= b )
| ( ( f @ u1 @ u3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,2258]) ).
thf(2310,plain,
( ( f @ a @ b )
!= b ),
inference(pattern_uni,[status(thm)],[2309:[bind(A,$thf( u1 )),bind(B,$thf( u3 ))]]) ).
thf(2324,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ ( f @ n2 @ A ) ) )
!= b )
| ( ( f @ u @ ( f @ n2 @ A ) )
!= ( f @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[136,2258]) ).
thf(2325,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ A ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[2324:[bind(A,$thf( E )),bind(B,$thf( u )),bind(C,$thf( f @ n2 @ E ))]]) ).
thf(2347,plain,
! [A: $i] :
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ A ) ) )
!= b ),
inference(simp,[status(thm)],[2325]) ).
thf(2282,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n2 @ u3 ) )
!= b )
| ( ( f @ u @ u3 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1275,2258]) ).
thf(2283,plain,
( ( f @ a @ ( f @ n2 @ u3 ) )
!= b ),
inference(pattern_uni,[status(thm)],[2282:[bind(A,$thf( u )),bind(B,$thf( u3 ))]]) ).
thf(36,plain,
( ( n3 = n2 )
| ( ( f @ n1 @ n1 )
!= ( f @ n2 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,21]) ).
thf(38,plain,
( ( n3 = n2 )
| ( n1 != n2 )
| ( n1 != n1 ) ),
inference(simp,[status(thm)],[36]) ).
thf(40,plain,
( ( n3 = n2 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[38]) ).
thf(20319,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ n2 ) )
| ( ( f @ u1 @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20230,17]) ).
thf(20320,plain,
left @ u1 @ ( f @ u @ n2 ),
inference(pattern_uni,[status(thm)],[20319:[bind(A,$thf( u1 )),bind(B,$thf( u1 ))]]) ).
thf(21264,plain,
left @ u1 @ u2,
inference(rewrite,[status(thm)],[20320,12425]) ).
thf(150,plain,
( ( u2 = u1 )
| ( ( f @ u @ n1 )
!= ( f @ u @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[29,27]) ).
thf(164,plain,
( ( u2 = u1 )
| ( u != u )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[150]) ).
thf(171,plain,
( ( u2 = u1 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[164]) ).
thf(19434,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ u @ ( f @ n2 @ n2 ) ) )
!= b )
| ( ( f @ u1 @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19243,2258]) ).
thf(19435,plain,
( ( f @ a @ ( f @ u @ ( f @ n2 @ n2 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[19434:[bind(A,$thf( u1 )),bind(B,$thf( u2 ))]]) ).
thf(24756,plain,
( ( f @ a @ ( f @ n2 @ ( f @ n2 @ n2 ) ) )
!= b ),
inference(rewrite,[status(thm)],[19435,136]) ).
thf(4826,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) )
| ( ( f @ n1 @ u )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4807,3938]) ).
thf(4827,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ),
inference(pattern_uni,[status(thm)],[4826:[bind(A,$thf( u ))]]) ).
thf(5010,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ u ) ),
inference(rewrite,[status(thm)],[4827,25]) ).
thf(34457,plain,
! [A: $i] :
( ( left @ n3 @ ( f @ n2 @ ( f @ n2 @ u ) ) )
| ( ( f @ n1 @ u )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16871,27051]) ).
thf(34458,plain,
left @ n3 @ ( f @ n2 @ ( f @ n2 @ u ) ),
inference(pattern_uni,[status(thm)],[34457:[bind(A,$thf( u ))]]) ).
thf(25241,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ u @ ( f @ n3 @ n1 ) ) )
!= b )
| ( ( f @ u3 @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20887,2258]) ).
thf(25242,plain,
( ( f @ a @ ( f @ u @ ( f @ n3 @ n1 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[25241:[bind(A,$thf( u3 )),bind(B,$thf( u1 ))]]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( left @ A @ n2 )
| ( ( f @ n1 @ n1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,17]) ).
thf(354,plain,
left @ n1 @ n2,
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( n1 )),bind(B,$thf( n1 ))]]) ).
thf(667,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ n1 @ n2 )
!= ( left @ A @ b ) ) ),
inference(paramod_ordered,[status(thm)],[354,62]) ).
thf(675,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( n1 != A )
| ( n2 != b ) ),
inference(simp,[status(thm)],[667]) ).
thf(684,plain,
( ~ ( left @ a @ n1 )
| ( n2 != b ) ),
inference(simp,[status(thm)],[675]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ C )
| ~ ( left @ a @ D )
| ( ( left @ A @ C )
!= ( left @ D @ b ) ) ),
inference(paramod_ordered,[status(thm)],[19,62]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( left @ A @ B )
| ~ ( left @ B @ b )
| ~ ( left @ a @ A ) ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( b )),bind(D,$thf( A ))]]) ).
thf(432,plain,
! [B: $i,A: $i] :
( ~ ( left @ B @ b )
| ~ ( left @ a @ A )
| ( ( left @ n2 @ u )
!= ( left @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[330,68]) ).
thf(433,plain,
( ~ ( left @ u @ b )
| ~ ( left @ a @ n2 ) ),
inference(pattern_uni,[status(thm)],[432:[bind(A,$thf( n2 )),bind(B,$thf( u ))]]) ).
thf(63695,plain,
( ~ $true
| ~ ( left @ a @ n2 ) ),
inference(rewrite,[status(thm)],[433,21475]) ).
thf(63696,plain,
~ ( left @ a @ n2 ),
inference(simp,[status(thm)],[63695]) ).
thf(63731,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ A @ B ) )
!= ( left @ a @ n2 ) ),
inference(paramod_ordered,[status(thm)],[17,63696]) ).
thf(63796,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( f @ A @ B )
!= n2 ) ),
inference(simp,[status(thm)],[63731]) ).
thf(63832,plain,
! [A: $i] :
( ( f @ a @ A )
!= n2 ),
inference(simp,[status(thm)],[63796]) ).
thf(20926,plain,
! [A: $i] :
( ( ( f @ ( f @ n2 @ u ) @ u1 )
= ( f @ u @ ( f @ A @ n1 ) ) )
| ( ( f @ u @ u )
!= ( f @ u @ A ) ) ),
inference(paramod_ordered,[status(thm)],[995,141]) ).
thf(20927,plain,
( ( f @ ( f @ n2 @ u ) @ u1 )
= ( f @ u @ ( f @ u @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[20926:[bind(A,$thf( u ))]]) ).
thf(45581,plain,
( ( f @ ( f @ n2 @ u ) @ u1 )
= ( f @ u @ u1 ) ),
inference(rewrite,[status(thm)],[20927,27]) ).
thf(180,plain,
( ( u3 = n2 )
| ( ( f @ u @ n3 )
!= ( f @ n1 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[31,21]) ).
thf(195,plain,
( ( u3 = n2 )
| ( u != n1 )
| ( n3 != n1 ) ),
inference(simp,[status(thm)],[180]) ).
thf(15176,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ n1 @ ( f @ n3 @ n1 ) ) )
!= b )
| ( ( f @ u2 @ n2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12584,2258]) ).
thf(15177,plain,
( ( f @ a @ ( f @ n1 @ ( f @ n3 @ n1 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[15176:[bind(A,$thf( u2 )),bind(B,$thf( n2 ))]]) ).
thf(54746,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ u @ ( f @ n3 @ n2 ) ) )
!= b )
| ( ( f @ u3 @ u2 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51605,2258]) ).
thf(54747,plain,
( ( f @ a @ ( f @ u @ ( f @ n3 @ n2 ) ) )
!= b ),
inference(pattern_uni,[status(thm)],[54746:[bind(A,$thf( u3 )),bind(B,$thf( u2 ))]]) ).
thf(29538,plain,
! [A: $i] :
( ( f @ n3 @ n3 )
!= ( f @ a @ A ) ),
inference(paramod_ordered,[status(thm)],[29426,21845]) ).
thf(29870,plain,
! [A: $i] :
( ( n3 != a )
| ( n3 != A ) ),
inference(simp,[status(thm)],[29538]) ).
thf(29976,plain,
n3 != a,
inference(simp,[status(thm)],[29870]) ).
thf(396,plain,
! [A: $i] :
( ( b != a )
| ( ( f @ ( f @ n3 @ n2 ) @ u2 )
!= ( f @ a @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33,381]) ).
thf(407,plain,
! [A: $i] :
( ( b != a )
| ( ( f @ n3 @ n2 )
!= a )
| ( u2 != A ) ),
inference(simp,[status(thm)],[396]) ).
thf(415,plain,
( ( b != a )
| ( ( f @ n3 @ n2 )
!= a ) ),
inference(simp,[status(thm)],[407]) ).
thf(27543,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ ( f @ n2 @ u2 ) ) )
| ( ( f @ u1 @ b )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27432,17]) ).
thf(27544,plain,
left @ u1 @ ( f @ u @ ( f @ n2 @ u2 ) ),
inference(pattern_uni,[status(thm)],[27543:[bind(A,$thf( u1 )),bind(B,$thf( b ))]]) ).
thf(27978,plain,
left @ u1 @ ( f @ n2 @ ( f @ n2 @ u2 ) ),
inference(rewrite,[status(thm)],[27544,136]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= n2 )
| ( ( f @ ( f @ A @ B ) @ ( f @ A @ C ) )
!= ( f @ n1 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[16,21]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( f @ A @ ( f @ B @ C ) )
= n2 )
| ( ( f @ A @ B )
!= n1 )
| ( ( f @ A @ C )
!= n1 ) ),
inference(simp,[status(thm)],[106]) ).
thf(159,plain,
( ( u2 = n3 )
| ( ( f @ u @ n2 )
!= ( f @ n2 @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,29]) ).
thf(163,plain,
( ( u2 = n3 )
| ( u != n2 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[159]) ).
thf(45972,plain,
! [B: $i,A: $i] :
( ( ( f @ a @ ( f @ u @ u1 ) )
!= b )
| ( ( f @ ( f @ n2 @ u ) @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45581,2258]) ).
thf(45973,plain,
( ( f @ a @ ( f @ u @ u1 ) )
!= b ),
inference(pattern_uni,[status(thm)],[45972:[bind(A,$thf( f @ n2 @ u )),bind(B,$thf( u1 ))]]) ).
thf(45780,plain,
! [B: $i,A: $i] :
( ( left @ A @ ( f @ u @ u1 ) )
| ( ( f @ ( f @ n2 @ u ) @ u1 )
!= ( f @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45581,17]) ).
thf(45781,plain,
left @ ( f @ n2 @ u ) @ ( f @ u @ u1 ),
inference(pattern_uni,[status(thm)],[45780:[bind(A,$thf( f @ n2 @ u )),bind(B,$thf( u1 ))]]) ).
thf(6424,plain,
! [A: $i] :
( ( left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) ) )
| ( ( f @ n1 @ ( f @ n2 @ u ) )
!= ( f @ n1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5166,4640]) ).
thf(6425,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ n2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[6424:[bind(A,$thf( f @ n2 @ u ))]]) ).
thf(7310,plain,
left @ n1 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ ( f @ n2 @ u ) ) ) ),
inference(rewrite,[status(thm)],[6425,25]) ).
thf(30060,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ n3 @ u )
!= ( left @ A @ b ) ) ),
inference(paramod_ordered,[status(thm)],[29540,62]) ).
thf(30083,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( n3 != A )
| ( u != b ) ),
inference(simp,[status(thm)],[30060]) ).
thf(30088,plain,
( ~ ( left @ a @ n3 )
| ( u != b ) ),
inference(simp,[status(thm)],[30083]) ).
thf(21865,plain,
! [A: $i] :
( ~ ( left @ a @ A )
| ( ( left @ u @ b )
!= ( left @ A @ b ) ) ),
inference(paramod_ordered,[status(thm)],[21475,70]) ).
thf(21866,plain,
~ ( left @ a @ u ),
inference(pattern_uni,[status(thm)],[21865:[bind(A,$thf( u ))]]) ).
thf(177888,plain,
$false,
inference(e,[status(thm)],[138,333,2295,61766,40028,34479,52680,1618,43990,47913,408,170,54576,59540,142,2316,1275,21857,15051,48189,2432,20715,24,5825,25938,25,52,14,36332,18733,15087,3938,29540,36500,33908,20,16873,42483,39972,2301,65398,4669,61965,20230,55759,50383,47467,27051,602,12485,1169,31180,42037,27432,2286,36274,380,12425,381,2307,34449,50202,12510,19703,28,160,70,12591,192,33,7301,21,137,92,65184,2345,19235,23546,65413,21855,44180,12450,52982,3968,12866,21377,52757,356,141,339,1292,6304,55758,6946,47243,96,29426,67551,16269,47118,48009,13,129,73,360,128,343,26079,21845,69919,166,17,601,40208,906,32,34,4144,28947,22,51605,10329,59,204,27,144,20887,4640,2319,65208,86,39419,1669,32103,1011,8445,5610,4213,81,23805,140,2289,198,330,983,130,12465,14577,35,38111,12584,67529,19695,52507,33593,51311,145,2298,557,63,18,4200,39851,4324,25124,12519,16870,50,199,16,2322,4800,31,17996,31304,32236,1981,5453,175,3943,143,9046,14586,87,12027,2310,2347,19243,2283,40,21264,26,171,23622,24756,23,139,5010,995,14415,34458,25242,6586,684,21440,10357,2258,16871,30,63832,19,45581,136,341,195,15177,54747,29976,47081,415,21475,1152,27978,63696,131,15,163,68,62,18070,45973,28568,45781,354,7310,30088,64117,21866]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LDA004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 20:36:51 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.96 % [INFO] Parsing done (119ms).
% 1.18/0.97 % [INFO] Running in sequential loop mode.
% 1.49/1.16 % [INFO] eprover registered as external prover.
% 1.49/1.17 % [INFO] cvc4 registered as external prover.
% 1.49/1.17 % [INFO] Scanning for conjecture ...
% 1.76/1.22 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.87/1.24 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.87/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.25 % [INFO] Type checking passed.
% 1.87/1.26 % [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 ...
% 191.68/35.98 % External prover 'e' found a proof!
% 191.68/35.98 % [INFO] Killing All external provers ...
% 191.68/35.99 % Time passed: 35471ms (effective reasoning time: 35016ms)
% 191.68/35.99 % 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)>
% 191.68/35.99 % Axioms used in derivation (11): clause_5, clause_8, clause_9, clause_4, a3, clause_6, a1, clause_11, a2, clause_7, clause_10
% 191.68/35.99 % No. of inferences in proof: 588
% 191.68/35.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 35471 ms resp. 35016 ms w/o parsing
% 192.07/36.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 192.07/36.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------