%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP669-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:21:42 AM UTC 2026
% Result : Unsatisfiable 84.32s 20.39s
% Output : Refutation 71.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 378 ( 99 unt; 0 typ; 0 def)
% Number of atoms : 953 ( 952 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 4993 ( 856 ~; 575 |; 0 &;3562 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 470 ( 0 ^; 470 !; 0 ?; 470 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_decl,type,
mult: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(ld_decl,type,
ld: $i > $i > $i ).
thf(rd_decl,type,
rd: $i > $i > $i ).
thf(unit_decl,type,
unit: $i ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( unit @ mult ) )
= A ),
inference(lifteq,[status(thm)],[25]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ mult ) @ rd ) )
= A ),
inference(lifteq,[status(thm)],[21]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( C @ ( B @ mult ) ) )
| ( ( C @ ( A @ rd ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[26,22]) ).
thf(420,plain,
! [A: $i] :
( ( A @ ( A @ rd ) )
= unit ),
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( A @ mult ) )
= B ),
inference(lifteq,[status(thm)],[15]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(12,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ mult ) ) ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( b @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) )
| ( ( b @ ( B @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,14]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= a )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( B @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(105,plain,
! [A: $i] :
( ( ( A @ ( c @ ( b @ mult ) @ ( a @ mult ) @ ld ) )
!= a )
| ( ( b @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ rd ) @ mult ) )
= A ),
inference(lifteq,[status(thm)],[19]) ).
thf(6,axiom,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
thf(23,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
! [A: $i] :
( ( unit @ ( A @ mult ) )
= A ),
inference(lifteq,[status(thm)],[23]) ).
thf(57,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) )
| ( ( b @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,14]) ).
thf(69,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( A
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(101,plain,
( ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( unit @ ( b @ ( a @ mult ) @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[69]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
= ( A @ ( C @ ( B @ mult ) @ ( A @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
= ( A @ ( C @ ( B @ mult ) @ ( A @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ mult ) @ ( A @ mult ) @ mult ) )
= ( A @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(11172,plain,
( ( ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(rewrite,[status(thm)],[101,32,24]) ).
thf(11182,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[24,11172]) ).
thf(11411,plain,
( ( ( a @ ( c @ mult ) )
!= unit )
| ( ( b @ ( a @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[11182]) ).
thf(11509,plain,
( ( ( a @ ( c @ mult ) )
!= unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[11411]) ).
thf(12093,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( a @ ( c @ mult ) )
!= unit )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[24,11509]) ).
thf(12161,plain,
( ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[12093]) ).
thf(14840,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[20,12161]) ).
thf(14883,plain,
! [A: $i] :
( ( A != a )
| ( ( A @ ( unit @ rd ) )
!= c )
| ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b ) ),
inference(simp,[status(thm)],[14840]) ).
thf(14912,plain,
( ( ( a @ ( unit @ rd ) )
!= c )
| ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b ) ),
inference(simp,[status(thm)],[14883]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,14]) ).
thf(316,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[291]) ).
thf(384,plain,
( ( b @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(1237,plain,
( ( b @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(rewrite,[status(thm)],[384,32]) ).
thf(53,plain,
( ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(123,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,53]) ).
thf(144,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( A @ ( a @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[123]) ).
thf(22893,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( A @ ( a @ mult ) )
!= a ) ),
inference(rewrite,[status(thm)],[144,24]) ).
thf(126,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( A != b )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,53]) ).
thf(176,plain,
( ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(26613,plain,
( ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(rewrite,[status(thm)],[176,32]) ).
thf(71,plain,
! [A: $i] :
( ( unit != a )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( A
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(103,plain,
( ( unit != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[71]) ).
thf(11796,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( unit != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[26,103]) ).
thf(11912,plain,
! [A: $i] :
( ( A != b )
| ( unit != a )
| ( unit != a )
| ( ( c @ ( b @ mult ) )
!= b )
| ( a != a )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[11796]) ).
thf(12045,plain,
( ( unit != a )
| ( ( c @ ( b @ mult ) )
!= b )
| ( ( b @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[11912]) ).
thf(12886,plain,
( ( b != b )
| ( ( b @ ( c @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( unit != a )
| ( ( c @ ( b @ mult ) )
!= b ) ),
inference(eqfactor_ordered,[status(thm)],[12045]) ).
thf(12901,plain,
( ( c != b )
| ( c != b )
| ( unit != a )
| ( ( c @ ( b @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12886]) ).
thf(12934,plain,
( ( c != b )
| ( unit != a )
| ( ( c @ ( b @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12901]) ).
thf(122,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,53]) ).
thf(156,plain,
! [A: $i] :
( ( ( c @ ( b @ mult ) )
!= unit )
| ( A != a )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a )
| ( A != a ) ),
inference(simp,[status(thm)],[122]) ).
thf(194,plain,
( ( ( c @ ( b @ mult ) )
!= unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[156]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( B != b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[16,194]) ).
thf(218,plain,
! [A: $i] :
( ( ( b @ ( A @ ld ) )
!= ( b @ ( a @ mult ) ) )
| ( A != c )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[212]) ).
thf(234,plain,
( ( ( b @ ( c @ ld ) )
!= ( b @ ( a @ mult ) ) )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[218]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ ( B @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,14]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= ( c @ ( b @ mult ) ) )
| ( A != a )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( B @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(115,plain,
! [A: $i] :
( ( ( A @ ( a @ ld ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(1165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( D @ ( C @ mult ) @ ( B @ mult ) ) )
| ( ( B @ ( A @ mult ) )
= ( B @ ( D @ mult ) @ ( C @ ( B @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,32]) ).
thf(1166,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ ( A @ mult ) @ mult ) )
= ( unit @ ( B @ mult ) @ ( A @ ( unit @ mult ) @ mult ) ) ),
inference(pattern_uni,[status(thm)],[1165:[bind(A,$thf( F @ ( E @ mult ) )),bind(B,$thf( unit )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(1198,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ ( A @ mult ) @ mult ) )
= ( unit @ ( B @ mult ) @ ( A @ ( unit @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[1166]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ mult ) @ ( B @ mult ) @ ( A @ mult ) )
= ( B @ ( C @ ( B @ ( A @ mult ) @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ mult ) @ ( B @ mult ) @ ( A @ mult ) )
= ( B @ ( C @ ( B @ ( A @ mult ) @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ mult ) @ mult ) @ mult ) )
= ( B @ ( C @ mult ) @ ( B @ mult ) @ ( A @ mult ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( C @ ( B @ mult ) ) )
| ( ( C @ ( D @ ( A @ mult ) @ mult ) )
= ( C @ ( D @ mult ) @ ( C @ mult ) @ ( B @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,30]) ).
thf(911,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ ( A @ mult ) @ mult ) )
= ( unit @ ( B @ mult ) @ ( unit @ mult ) @ ( A @ mult ) ) ),
inference(pattern_uni,[status(thm)],[910:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).
thf(979,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ ( A @ mult ) @ mult ) )
= ( unit @ ( B @ mult ) @ ( unit @ mult ) @ ( A @ mult ) ) ),
inference(simp,[status(thm)],[911]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ mult ) @ ( B @ mult ) @ ( A @ mult ) )
= ( C @ ( A @ ( B @ ( A @ mult ) @ mult ) @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ mult ) @ ( B @ mult ) @ ( A @ mult ) )
= ( C @ ( A @ ( B @ ( A @ mult ) @ mult ) @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( A @ mult ) @ mult ) @ mult ) )
= ( C @ ( A @ mult ) @ ( B @ mult ) @ ( A @ mult ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( C @ ( B @ mult ) ) )
| ( ( D @ ( B @ ( A @ mult ) @ mult ) )
= ( D @ ( B @ mult ) @ ( C @ mult ) @ ( B @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( B @ ( unit @ ( A @ mult ) @ mult ) )
= ( B @ ( unit @ mult ) @ ( A @ mult ) @ ( unit @ mult ) ) ),
inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(512,plain,
! [B: $i,A: $i] :
( ( B @ ( unit @ ( A @ mult ) @ mult ) )
= ( B @ ( unit @ mult ) @ ( A @ mult ) @ ( unit @ mult ) ) ),
inference(simp,[status(thm)],[475]) ).
thf(1737,plain,
! [B: $i,A: $i] :
( ( B @ ( unit @ mult ) @ ( A @ mult ) )
= ( B @ ( A @ mult ) ) ),
inference(rewrite,[status(thm)],[512,24,26]) ).
thf(6116,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ mult ) @ ( A @ mult ) )
= ( B @ ( A @ mult ) ) ),
inference(rewrite,[status(thm)],[979,24,1737]) ).
thf(7797,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( unit @ mult ) @ mult ) )
= ( B @ ( A @ mult ) ) ),
inference(rewrite,[status(thm)],[1198,6116,24]) ).
thf(7941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( unit @ mult ) @ mult ) )
!= ( D @ ( C @ ld ) @ ( C @ mult ) ) )
| ( ( B @ ( A @ mult ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[7797,16]) ).
thf(7942,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( unit @ mult ) @ ld ) @ ( B @ mult ) )
= A ),
inference(pattern_uni,[status(thm)],[7941:[bind(A,$thf( J )),bind(B,$thf( H @ ( J @ ( unit @ mult ) @ ld ) )),bind(C,$thf( J @ ( unit @ mult ) )),bind(D,$thf( H ))]]) ).
thf(8235,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( unit @ mult ) @ ld ) @ ( B @ mult ) )
= A ),
inference(simp,[status(thm)],[7942]) ).
thf(9100,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ld ) @ ( B @ mult ) )
= A ),
inference(rewrite,[status(thm)],[8235,26]) ).
thf(12102,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( a @ ( c @ mult ) )
!= unit )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[9100,11509]) ).
thf(12168,plain,
! [A: $i] :
( ( ( b @ ( A @ ld ) )
!= ( b @ ( a @ mult ) ) )
| ( A != c )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[12102]) ).
thf(12172,plain,
( ( ( b @ ( c @ ld ) )
!= ( b @ ( a @ mult ) ) )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[12168]) ).
thf(12097,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( A != unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[20,11509]) ).
thf(12126,plain,
! [A: $i] :
( ( A != a )
| ( ( A @ ( unit @ rd ) )
!= c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12097]) ).
thf(12174,plain,
( ( ( a @ ( unit @ rd ) )
!= c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12126]) ).
thf(16204,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( a @ ( unit @ rd ) )
!= c )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[20,12174]) ).
thf(16235,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) ) )
| ( ( A @ ( b @ rd ) )
!= c )
| ( ( a @ ( unit @ rd ) )
!= c ) ),
inference(simp,[status(thm)],[16204]) ).
thf(16280,plain,
( ( ( b @ ( a @ mult ) @ ( b @ rd ) )
!= c )
| ( ( a @ ( unit @ rd ) )
!= c ) ),
inference(simp,[status(thm)],[16235]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ mult ) @ ( A @ ld ) )
= B ),
inference(lifteq,[status(thm)],[17]) ).
thf(305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( A @ ( C @ ld ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[20,18]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ rd ) @ ld ) )
= B ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ rd ) )),bind(D,$thf( F ))]]) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ rd ) @ ld ) )
= B ),
inference(simp,[status(thm)],[306]) ).
thf(1251,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ mult ) @ rd ) )
!= ( b @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) ) )
| ( A
!= ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,1237]) ).
thf(1296,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[1251]) ).
thf(1329,plain,
( ( b @ ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[1296]) ).
thf(2591,plain,
( ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(rewrite,[status(thm)],[1329,30]) ).
thf(2607,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( B
!= ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,2591]) ).
thf(2718,plain,
! [A: $i] :
( ( ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) @ ( A @ ld ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[2607]) ).
thf(2933,plain,
( ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) @ ( b @ ( a @ mult ) @ ld ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) ),
inference(simp,[status(thm)],[2718]) ).
thf(12117,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( a @ ( c @ mult ) )
!= unit )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[26,11509]) ).
thf(12165,plain,
( ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[12117]) ).
thf(209,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( A != b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[24,194]) ).
thf(223,plain,
( ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[209]) ).
thf(243,plain,
( ( unit != unit )
| ( ( c @ ( b @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( b != a ) ),
inference(eqfactor_ordered,[status(thm)],[223]) ).
thf(247,plain,
( ( c != b )
| ( b != a )
| ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[243]) ).
thf(258,plain,
( ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[247]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( B != unit )
| ( c != b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[16,258]) ).
thf(401,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= b )
| ( A != a )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[394]) ).
thf(404,plain,
( ( ( unit @ ( a @ ld ) )
!= b )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[401]) ).
thf(12096,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( a @ ( c @ mult ) )
!= unit )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[20,11509]) ).
thf(12134,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) ) )
| ( ( A @ ( b @ rd ) )
!= c )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[12096]) ).
thf(12182,plain,
( ( ( b @ ( a @ mult ) @ ( b @ rd ) )
!= c )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[12134]) ).
thf(16305,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( b @ rd ) )
!= c )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[9100,12182]) ).
thf(16355,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= a )
| ( A != c )
| ( ( b @ ( a @ mult ) @ ( b @ rd ) )
!= c ) ),
inference(simp,[status(thm)],[16305]) ).
thf(16387,plain,
( ( ( unit @ ( c @ ld ) )
!= a )
| ( ( b @ ( a @ mult ) @ ( b @ rd ) )
!= c ) ),
inference(simp,[status(thm)],[16355]) ).
thf(2631,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( A
!= ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,2591]) ).
thf(2776,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( A @ ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) @ rd ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[2631]) ).
thf(2972,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) @ rd ) )
!= ( b @ ( a @ mult ) ) ),
inference(simp,[status(thm)],[2776]) ).
thf(14845,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( A != unit )
| ( c != b )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(paramod_ordered,[status(thm)],[9100,12161]) ).
thf(14874,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= b )
| ( A != a )
| ( c != b )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[14845]) ).
thf(14903,plain,
( ( ( unit @ ( a @ ld ) )
!= b )
| ( c != b )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[14874]) ).
thf(18220,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( unit @ ( a @ ld ) )
!= b )
| ( c != b )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[20,14903]) ).
thf(18255,plain,
! [A: $i] :
( ( A != a )
| ( ( A @ ( unit @ rd ) )
!= c )
| ( ( unit @ ( a @ ld ) )
!= b )
| ( c != b ) ),
inference(simp,[status(thm)],[18220]) ).
thf(18269,plain,
( ( ( a @ ( unit @ rd ) )
!= c )
| ( ( unit @ ( a @ ld ) )
!= b )
| ( c != b ) ),
inference(simp,[status(thm)],[18255]) ).
thf(65,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) )
| ( ( b @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,14]) ).
thf(79,plain,
! [A: $i] :
( ( A != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= unit )
| ( ( b @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(110,plain,
( ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( B @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(6713,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(rewrite,[status(thm)],[84,16]) ).
thf(136,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( A != b )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,53]) ).
thf(180,plain,
( ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(27028,plain,
( ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(rewrite,[status(thm)],[180,32]) ).
thf(215,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( A != b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[26,194]) ).
thf(228,plain,
( ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[215]) ).
thf(12103,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( A != unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[9100,11509]) ).
thf(12137,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= a )
| ( A != c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12103]) ).
thf(12185,plain,
( ( ( unit @ ( c @ ld ) )
!= a )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12137]) ).
thf(14930,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( A != b )
| ( unit != c )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(paramod_ordered,[status(thm)],[9100,12165]) ).
thf(14976,plain,
! [A: $i] :
( ( ( b @ ( A @ ld ) )
!= b )
| ( A != a )
| ( unit != c )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[14930]) ).
thf(14981,plain,
( ( ( b @ ( a @ ld ) )
!= b )
| ( unit != c )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[14976]) ).
thf(12865,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( unit != a )
| ( A != b )
| ( ( b @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[20,12045]) ).
thf(12888,plain,
! [A: $i] :
( ( A != c )
| ( ( A @ ( b @ rd ) )
!= b )
| ( unit != a )
| ( ( b @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12865]) ).
thf(12924,plain,
( ( ( c @ ( b @ rd ) )
!= b )
| ( unit != a )
| ( ( b @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12888]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= a )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( B
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(106,plain,
( ( ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ ld ) )
!= a )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[74]) ).
thf(121,plain,
( ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[53]) ).
thf(63,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ ( A @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,14]) ).
thf(90,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) ) )
| ( unit != a )
| ( ( b @ ( a @ ( A @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(116,plain,
( ( unit != a )
| ( ( b @ ( a @ ( c @ ( b @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(7832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( unit @ mult ) @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( D @ ( B @ ( A @ mult ) @ rd ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[7797,22]) ).
thf(7833,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ mult ) @ rd ) )
= ( B @ ( unit @ mult ) ) ),
inference(pattern_uni,[status(thm)],[7832:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( unit @ mult ) )),bind(D,$thf( B ))]]) ).
thf(8219,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ mult ) @ rd ) )
= ( B @ ( unit @ mult ) ) ),
inference(simp,[status(thm)],[7833]) ).
thf(8892,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ mult ) @ rd ) )
= B ),
inference(rewrite,[status(thm)],[8219,26]) ).
thf(434,plain,
( ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(rewrite,[status(thm)],[14,28]) ).
thf(1381,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( B
!= ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,434]) ).
thf(1425,plain,
! [A: $i] :
( ( ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) @ ( A @ ld ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[1381]) ).
thf(1651,plain,
( ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) @ ( b @ ( a @ mult ) @ ld ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) ),
inference(simp,[status(thm)],[1425]) ).
thf(91,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) ) )
| ( unit != a )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(117,plain,
( ( unit != a )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( c @ ( b @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(56,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ ( A @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,14]) ).
thf(68,plain,
! [A: $i] :
( ( unit != c )
| ( A != b )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(100,plain,
( ( unit != c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(10766,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( a @ ( b @ ( a @ mult ) @ mult ) ) )
| ( unit != c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( A
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,100]) ).
thf(10828,plain,
( ( unit != a )
| ( ( b @ ( a @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( unit != c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[10766]) ).
thf(10965,plain,
( ( unit != a )
| ( unit != c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[10828]) ).
thf(11074,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( unit != a )
| ( unit != c )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[26,10965]) ).
thf(11082,plain,
! [A: $i] :
( ( A != b )
| ( unit != a )
| ( unit != a )
| ( unit != c )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[11074]) ).
thf(11109,plain,
( ( unit != a )
| ( unit != c )
| ( ( b @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[11082]) ).
thf(11140,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( c @ mult ) ) )
| ( unit != a )
| ( unit != c )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[26,11109]) ).
thf(11158,plain,
( ( b != b )
| ( unit != c )
| ( unit != a )
| ( unit != c ) ),
inference(simp,[status(thm)],[11140]) ).
thf(11170,plain,
( ( unit != a )
| ( unit != c ) ),
inference(simp,[status(thm)],[11158]) ).
thf(70,plain,
! [A: $i] :
( ( unit != a )
| ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(102,plain,
( ( unit != a )
| ( ( b @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
= ( A @ ( C @ ( B @ mult ) @ mult ) @ ( A @ mult ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
= ( A @ ( C @ ( B @ mult ) @ mult ) @ ( A @ mult ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(67,plain,
! [A: $i] :
( ( unit != c )
| ( A != b )
| ( ( b @ ( a @ ( A @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(99,plain,
( ( unit != c )
| ( ( b @ ( a @ ( b @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(10462,plain,
( ( unit != c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(rewrite,[status(thm)],[99,30]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ mult ) ) )
| ( B
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,14]) ).
thf(96,plain,
! [A: $i] :
( ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= b )
| ( A
!= ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(120,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ ld ) )
!= b ),
inference(simp,[status(thm)],[96]) ).
thf(1106,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ld ) )
!= b ),
inference(rewrite,[status(thm)],[120,32]) ).
thf(12951,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( c != b )
| ( unit != a )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[20,12934]) ).
thf(12977,plain,
! [A: $i] :
( ( A != c )
| ( ( A @ ( b @ rd ) )
!= b )
| ( c != b )
| ( unit != a ) ),
inference(simp,[status(thm)],[12951]) ).
thf(12991,plain,
( ( ( c @ ( b @ rd ) )
!= b )
| ( c != b )
| ( unit != a ) ),
inference(simp,[status(thm)],[12977]) ).
thf(12116,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( a @ ( c @ mult ) )
!= unit )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[26,11509]) ).
thf(12139,plain,
! [A: $i] :
( ( A != b )
| ( unit != a )
| ( ( a @ ( c @ mult ) )
!= unit )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12116]) ).
thf(12187,plain,
( ( unit != a )
| ( ( a @ ( c @ mult ) )
!= unit )
| ( ( b @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12139]) ).
thf(16504,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( b @ ( c @ mult ) ) )
| ( unit != a )
| ( ( a @ ( c @ mult ) )
!= unit )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[9100,12187]) ).
thf(16542,plain,
! [A: $i] :
( ( ( b @ ( A @ ld ) )
!= b )
| ( A != c )
| ( unit != a )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[16504]) ).
thf(16569,plain,
( ( ( b @ ( c @ ld ) )
!= b )
| ( unit != a )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[16542]) ).
thf(18335,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( a @ ( unit @ rd ) )
!= c )
| ( A != unit )
| ( c != b ) ),
inference(paramod_ordered,[status(thm)],[20,14912]) ).
thf(18360,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ ( unit @ rd ) )
!= a )
| ( ( a @ ( unit @ rd ) )
!= c )
| ( c != b ) ),
inference(simp,[status(thm)],[18335]) ).
thf(18386,plain,
( ( ( b @ ( unit @ rd ) )
!= a )
| ( ( a @ ( unit @ rd ) )
!= c )
| ( c != b ) ),
inference(simp,[status(thm)],[18360]) ).
thf(7844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( unit @ mult ) @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( B @ ( A @ mult ) @ ( C @ ld ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[7797,18]) ).
thf(7845,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ mult ) @ ( B @ ( unit @ mult ) @ ld ) )
= A ),
inference(pattern_uni,[status(thm)],[7844:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ ( unit @ mult ) )),bind(D,$thf( B ))]]) ).
thf(8220,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ mult ) @ ( B @ ( unit @ mult ) @ ld ) )
= A ),
inference(simp,[status(thm)],[7845]) ).
thf(8985,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ mult ) @ ( B @ ld ) )
= A ),
inference(rewrite,[status(thm)],[8220,26]) ).
thf(125,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( A @ ( c @ mult ) )
!= b )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,53]) ).
thf(137,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( A @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[125]) ).
thf(21182,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) ) )
| ( ( A @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= a ) ),
inference(rewrite,[status(thm)],[137,24]) ).
thf(2628,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,2591]) ).
thf(2771,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) ) )
| ( ( A @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= a ) ),
inference(simp,[status(thm)],[2628]) ).
thf(2968,plain,
( ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= a ),
inference(simp,[status(thm)],[2771]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ ( B @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,14]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( B @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(4416,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(rewrite,[status(thm)],[75,16]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
= ( A @ ( C @ ( B @ mult ) @ mult ) @ ( A @ mult ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(2420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ mult ) @ ( B @ ( A @ mult ) @ mult ) )
!= ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ( C @ ( B @ mult ) @ mult ) @ ( A @ mult ) @ ld ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[34,1106]) ).
thf(2421,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) @ ld ) )
!= b ),
inference(pattern_uni,[status(thm)],[2420:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( c ))]]) ).
thf(4922,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) @ ld ) ) )
| ( B != b ) ),
inference(paramod_ordered,[status(thm)],[379,2421]) ).
thf(5063,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( ( b @ ( A @ rd ) )
!= ( a @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[4922]) ).
thf(5138,plain,
( ( b @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= ( a @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) ) ),
inference(simp,[status(thm)],[5063]) ).
thf(55,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ ( A @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,14]) ).
thf(93,plain,
! [A: $i] :
( ( ( c @ ( b @ mult ) )
!= unit )
| ( A != a )
| ( ( b @ ( a @ ( A @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(118,plain,
( ( ( c @ ( b @ mult ) )
!= unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( B @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,53]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( B @ ( a @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[128]) ).
thf(24681,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( A @ ( a @ mult ) )
!= a ) ),
inference(rewrite,[status(thm)],[165,9100]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( unit @ ( C @ mult ) ) )
| ( B = C ) ),
inference(paramod_ordered,[status(thm)],[16,24]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= unit )
| ( A != C )
| ( B = C ) ),
inference(simp,[status(thm)],[39]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) )
!= unit )
| ( A = B ) ),
inference(simp,[status(thm)],[45]) ).
thf(17263,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( b @ ( c @ mult ) ) )
| ( ( c @ ( b @ rd ) )
!= b )
| ( unit != a )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[9100,12924]) ).
thf(17288,plain,
! [A: $i] :
( ( ( b @ ( A @ ld ) )
!= b )
| ( A != c )
| ( ( c @ ( b @ rd ) )
!= b )
| ( unit != a ) ),
inference(simp,[status(thm)],[17263]) ).
thf(17305,plain,
( ( ( b @ ( c @ ld ) )
!= b )
| ( ( c @ ( b @ rd ) )
!= b )
| ( unit != a ) ),
inference(simp,[status(thm)],[17288]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( B != unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[16,194]) ).
thf(221,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= c )
| ( A != b )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[213]) ).
thf(236,plain,
( ( ( unit @ ( b @ ld ) )
!= c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[221]) ).
thf(15341,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( b @ ( c @ ld ) )
!= ( b @ ( a @ mult ) ) )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[9100,12172]) ).
thf(15373,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= a )
| ( A != c )
| ( ( b @ ( c @ ld ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[15341]) ).
thf(15382,plain,
( ( ( unit @ ( c @ ld ) )
!= a )
| ( ( b @ ( c @ ld ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[15373]) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( A != unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[20,194]) ).
thf(320,plain,
! [A: $i] :
( ( A != c )
| ( ( A @ ( unit @ rd ) )
!= b )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[304]) ).
thf(350,plain,
( ( ( c @ ( unit @ rd ) )
!= b )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[320]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( A != unit )
| ( c != b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[20,258]) ).
thf(399,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ ( unit @ rd ) )
!= a )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[393]) ).
thf(406,plain,
( ( ( b @ ( unit @ rd ) )
!= a )
| ( c != b )
| ( b != a ) ),
inference(simp,[status(thm)],[399]) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( unit @ ( C @ mult ) ) )
| ( A = C ) ),
inference(paramod_ordered,[status(thm)],[20,24]) ).
thf(288,plain,
! [A: $i] :
( ( unit @ ( A @ rd ) )
= A ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( D )),bind(B,$thf( unit )),bind(C,$thf( unit @ ( D @ rd ) ))]]) ).
thf(377,plain,
! [A: $i] :
( ( unit @ ( A @ rd ) )
= A ),
inference(simp,[status(thm)],[288]) ).
thf(2052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( C @ ( B @ mult ) ) )
| ( ( B @ ( D @ mult ) @ ( A @ mult ) )
= ( B @ ( D @ ( C @ mult ) @ mult ) @ ( B @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,34]) ).
thf(2053,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ mult ) @ ( A @ mult ) )
= ( unit @ ( B @ ( A @ mult ) @ mult ) @ ( unit @ mult ) ) ),
inference(pattern_uni,[status(thm)],[2052:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(2174,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ mult ) @ ( A @ mult ) )
= ( unit @ ( B @ ( A @ mult ) @ mult ) @ ( unit @ mult ) ) ),
inference(simp,[status(thm)],[2053]) ).
thf(12202,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ ( A @ mult ) @ mult ) )
= ( B @ ( A @ mult ) ) ),
inference(rewrite,[status(thm)],[2174,6116,26]) ).
thf(12407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( unit @ ( B @ ( A @ mult ) @ mult ) )
!= ( D @ ( E @ ( D @ ( C @ mult ) @ mult ) @ mult ) ) )
| ( ( B @ ( A @ mult ) )
= ( D @ ( E @ mult ) @ ( D @ mult ) @ ( C @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[12202,30]) ).
thf(12408,plain,
! [B: $i,A: $i] :
( ( A @ ( unit @ ( B @ mult ) @ mult ) )
= ( unit @ ( A @ mult ) @ ( unit @ mult ) @ ( B @ mult ) ) ),
inference(pattern_uni,[status(thm)],[12407:[bind(A,$thf( unit @ ( F @ mult ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( unit )),bind(E,$thf( B ))]]) ).
thf(12778,plain,
! [B: $i,A: $i] :
( ( A @ ( unit @ ( B @ mult ) @ mult ) )
= ( unit @ ( A @ mult ) @ ( unit @ mult ) @ ( B @ mult ) ) ),
inference(simp,[status(thm)],[12408]) ).
thf(21561,plain,
! [B: $i,A: $i] :
( ( unit @ ( A @ mult ) @ ( B @ mult ) )
= ( A @ ( B @ mult ) ) ),
inference(rewrite,[status(thm)],[12778,24,1737]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= c )
| ( A != b )
| ( ( b @ ( a @ ( B @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(107,plain,
! [A: $i] :
( ( ( A @ ( b @ ld ) )
!= c )
| ( ( b @ ( a @ ( A @ ( a @ mult ) @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(14290,plain,
! [A: $i] :
( ( ( A @ ( b @ ld ) )
!= c )
| ( ( b @ ( a @ mult ) @ ( A @ mult ) @ ( a @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(rewrite,[status(thm)],[107,28]) ).
thf(4930,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ mult ) @ ( A @ ld ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) @ ld ) ) )
| ( B != b ) ),
inference(paramod_ordered,[status(thm)],[18,2421]) ).
thf(5034,plain,
! [A: $i] :
( ( ( b @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( A
!= ( a @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[4930]) ).
thf(5114,plain,
( ( b @ ( a @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[5034]) ).
thf(2301,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( A != unit )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[20,228]) ).
thf(2316,plain,
! [A: $i] :
( ( A != c )
| ( ( A @ ( unit @ rd ) )
!= b )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( b != a ) ),
inference(simp,[status(thm)],[2301]) ).
thf(2343,plain,
( ( ( c @ ( unit @ rd ) )
!= b )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( b != a ) ),
inference(simp,[status(thm)],[2316]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= c )
| ( A != b )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( B @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(108,plain,
! [A: $i] :
( ( ( A @ ( b @ ld ) )
!= c )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(62,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,14]) ).
thf(98,plain,
( ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= b )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[62]) ).
thf(10147,plain,
( ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= b )
| ( ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= unit ) ),
inference(rewrite,[status(thm)],[98,32]) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,434]) ).
thf(1596,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( A @ ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) @ rd ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[1357]) ).
thf(1643,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) @ rd ) )
!= ( b @ ( a @ mult ) ) ),
inference(simp,[status(thm)],[1596]) ).
thf(13021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( C @ mult ) ) )
| ( ( C @ ( c @ ( b @ mult ) @ ( a @ mult ) @ ld ) )
!= a )
| ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,105]) ).
thf(13022,plain,
! [A: $i] :
( ( ( b @ ( A @ rd ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ ld ) )
!= a )
| ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(pattern_uni,[status(thm)],[13021:[bind(A,$thf( D )),bind(B,$thf( b )),bind(C,$thf( b @ ( D @ rd ) ))]]) ).
thf(13418,plain,
( ( b @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ ld ) )
!= a ),
inference(simp,[status(thm)],[13022]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( B @ ( c @ mult ) )
!= b )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,53]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( B @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= a ) ),
inference(simp,[status(thm)],[130]) ).
thf(24937,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) ) )
| ( ( A @ ( c @ mult ) )
!= b )
| ( b != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= a ) ),
inference(rewrite,[status(thm)],[168,9100]) ).
thf(2604,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) @ ( a @ mult ) ) )
| ( B
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,2591]) ).
thf(2692,plain,
! [A: $i] :
( ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[2604]) ).
thf(2914,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ld ) )
!= ( b @ ( a @ ( c @ mult ) @ mult ) @ ( b @ mult ) ) ),
inference(simp,[status(thm)],[2692]) ).
thf(1984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( B @ ( D @ mult ) ) )
| ( ( A @ ( C @ ( B @ mult ) @ mult ) )
= ( B @ ( D @ ( C @ mult ) @ mult ) @ ( B @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,34]) ).
thf(1985,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( unit @ mult ) @ mult ) )
= ( unit @ ( A @ ( B @ mult ) @ mult ) @ ( unit @ mult ) ) ),
inference(pattern_uni,[status(thm)],[1984:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2269,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( unit @ mult ) @ mult ) )
= ( unit @ ( A @ ( B @ mult ) @ mult ) @ ( unit @ mult ) ) ),
inference(simp,[status(thm)],[1985]) ).
thf(15391,plain,
! [B: $i,A: $i] :
( ( unit @ ( A @ ( B @ mult ) @ mult ) )
= ( A @ ( B @ mult ) ) ),
inference(rewrite,[status(thm)],[2269,7797,26]) ).
thf(15519,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( unit @ ( A @ ( B @ mult ) @ mult ) )
!= ( C @ ( E @ ( D @ mult ) @ ( C @ mult ) @ mult ) ) )
| ( ( A @ ( B @ mult ) )
= ( C @ ( E @ mult ) @ ( D @ ( C @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[15391,32]) ).
thf(15520,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ mult ) @ ( A @ ( unit @ mult ) @ mult ) )
= ( B @ ( A @ mult ) @ ( unit @ mult ) ) ),
inference(pattern_uni,[status(thm)],[15519:[bind(A,$thf( G @ ( F @ mult ) )),bind(B,$thf( unit )),bind(C,$thf( unit )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(16087,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ mult ) @ ( A @ ( unit @ mult ) @ mult ) )
= ( B @ ( A @ mult ) @ ( unit @ mult ) ) ),
inference(simp,[status(thm)],[15520]) ).
thf(25159,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( unit @ mult ) @ mult ) )
= ( B @ ( A @ mult ) ) ),
inference(rewrite,[status(thm)],[16087,21561,26]) ).
thf(16220,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( a @ ( unit @ rd ) )
!= c )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[26,12174]) ).
thf(16240,plain,
! [A: $i] :
( ( A != b )
| ( unit != a )
| ( ( a @ ( unit @ rd ) )
!= c )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[16220]) ).
thf(16285,plain,
( ( unit != a )
| ( ( a @ ( unit @ rd ) )
!= c )
| ( ( b @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[16240]) ).
thf(14925,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[20,12165]) ).
thf(14974,plain,
! [A: $i] :
( ( A != a )
| ( ( A @ ( unit @ rd ) )
!= c )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c ) ),
inference(simp,[status(thm)],[14925]) ).
thf(15004,plain,
( ( ( a @ ( unit @ rd ) )
!= c )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c ) ),
inference(simp,[status(thm)],[14974]) ).
thf(7907,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( unit @ mult ) @ mult ) )
!= ( C @ ( E @ mult ) @ ( D @ ( C @ mult ) @ mult ) ) )
| ( ( B @ ( A @ mult ) )
= ( C @ ( E @ ( D @ mult ) @ mult ) @ ( C @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[7797,34]) ).
thf(7908,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ mult ) @ ( A @ mult ) )
= ( unit @ ( B @ ( A @ mult ) @ mult ) @ ( unit @ mult ) ) ),
inference(pattern_uni,[status(thm)],[7907:[bind(A,$thf( A )),bind(B,$thf( unit @ ( F @ mult ) )),bind(C,$thf( unit )),bind(D,$thf( A )),bind(E,$thf( F ))]]) ).
thf(8229,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ mult ) @ ( A @ mult ) )
= ( unit @ ( B @ ( A @ mult ) @ mult ) @ ( unit @ mult ) ) ),
inference(simp,[status(thm)],[7908]) ).
thf(20089,plain,
! [B: $i,A: $i] :
( ( unit @ ( B @ ( A @ mult ) @ mult ) )
= ( B @ ( A @ mult ) ) ),
inference(rewrite,[status(thm)],[8229,6116,26]) ).
thf(13621,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ rd ) @ ld ) )
!= ( b @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) @ ( c @ ( b @ mult ) @ ( a @ mult ) @ ld ) ) )
| ( B != a ) ),
inference(paramod_ordered,[status(thm)],[379,13418]) ).
thf(13760,plain,
! [A: $i] :
( ( A
!= ( b @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) ) )
| ( ( a @ ( A @ rd ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[13621]) ).
thf(13843,plain,
( ( a @ ( b @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) @ rd ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) ),
inference(simp,[status(thm)],[13760]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( C @ ( B @ ld ) @ ( B @ mult ) ) )
| ( A = C ) ),
inference(paramod_ordered,[status(thm)],[24,16]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ld ) )
!= unit )
| ( A != B )
| ( A = C ) ),
inference(simp,[status(thm)],[40]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= unit )
| ( A = B ) ),
inference(simp,[status(thm)],[46]) ).
thf(54,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( b @ ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,14]) ).
thf(88,plain,
( ( unit != b )
| ( ( a @ ( c @ ( b @ mult ) @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(7258,plain,
( ( unit != b )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(rewrite,[status(thm)],[88,32]) ).
thf(7269,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( unit != b )
| ( ( A @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) )
!= ( a @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,7258]) ).
thf(7372,plain,
! [A: $i] :
( ( unit != b )
| ( A != a )
| ( unit != b )
| ( ( A @ ( c @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[7269]) ).
thf(7498,plain,
( ( unit != b )
| ( ( a @ ( c @ mult ) )
!= ( a @ ( c @ mult ) ) ) ),
inference(simp,[status(thm)],[7372]) ).
thf(7796,plain,
unit != b,
inference(simp,[status(thm)],[7498]) ).
thf(2296,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( B != b )
| ( unit != c )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[16,228]) ).
thf(2331,plain,
! [A: $i] :
( ( ( b @ ( A @ ld ) )
!= b )
| ( A != a )
| ( unit != c )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[2296]) ).
thf(2354,plain,
( ( ( b @ ( a @ ld ) )
!= b )
| ( unit != c )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[2331]) ).
thf(16423,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( unit @ ( c @ ld ) )
!= a )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(paramod_ordered,[status(thm)],[26,12185]) ).
thf(16434,plain,
! [A: $i] :
( ( A != b )
| ( unit != a )
| ( ( unit @ ( c @ ld ) )
!= a )
| ( ( A @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[16423]) ).
thf(16485,plain,
( ( unit != a )
| ( ( unit @ ( c @ ld ) )
!= a )
| ( ( b @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[16434]) ).
thf(14844,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[9100,12161]) ).
thf(14877,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= a )
| ( A != c )
| ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b ) ),
inference(simp,[status(thm)],[14844]) ).
thf(14906,plain,
( ( ( unit @ ( c @ ld ) )
!= a )
| ( ( b @ ( a @ mult ) )
!= unit )
| ( c != b ) ),
inference(simp,[status(thm)],[14877]) ).
thf(18277,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( unit @ ( c @ ld ) )
!= a )
| ( A != unit )
| ( c != b ) ),
inference(paramod_ordered,[status(thm)],[20,14906]) ).
thf(18300,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ ( unit @ rd ) )
!= a )
| ( ( unit @ ( c @ ld ) )
!= a )
| ( c != b ) ),
inference(simp,[status(thm)],[18277]) ).
thf(18327,plain,
( ( ( b @ ( unit @ rd ) )
!= a )
| ( ( unit @ ( c @ ld ) )
!= a )
| ( c != b ) ),
inference(simp,[status(thm)],[18300]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) ) )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( A != b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[20,194]) ).
thf(318,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) ) )
| ( ( A @ ( b @ rd ) )
!= c )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[303]) ).
thf(386,plain,
( ( ( b @ ( a @ mult ) @ ( b @ rd ) )
!= c )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( b != a ) ),
inference(simp,[status(thm)],[318]) ).
thf(14929,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[9100,12165]) ).
thf(14958,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= a )
| ( A != c )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c ) ),
inference(simp,[status(thm)],[14929]) ).
thf(14992,plain,
( ( ( unit @ ( c @ ld ) )
!= a )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c ) ),
inference(simp,[status(thm)],[14958]) ).
thf(14841,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( A != unit )
| ( c != b )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(paramod_ordered,[status(thm)],[20,12161]) ).
thf(14887,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ ( unit @ rd ) )
!= a )
| ( c != b )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[14841]) ).
thf(14916,plain,
( ( ( b @ ( unit @ rd ) )
!= a )
| ( c != b )
| ( ( a @ ( c @ mult ) )
!= unit ) ),
inference(simp,[status(thm)],[14887]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(8401,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) @ ( a @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(rewrite,[status(thm)],[89,26]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) )
!= ( c @ ( b @ mult ) ) )
| ( A != a )
| ( ( b @ ( a @ ( B @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(114,plain,
! [A: $i] :
( ( ( A @ ( a @ ld ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ ( A @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(94,plain,
! [A: $i] :
( ( ( c @ ( b @ mult ) )
!= unit )
| ( A != a )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(119,plain,
( ( ( c @ ( b @ mult ) )
!= unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( b @ ( a @ mult ) )
!= ( a @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(18223,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( unit @ ( a @ ld ) )
!= b )
| ( c != b )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[9100,14903]) ).
thf(18247,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= a )
| ( A != c )
| ( ( unit @ ( a @ ld ) )
!= b )
| ( c != b ) ),
inference(simp,[status(thm)],[18223]) ).
thf(18263,plain,
( ( ( unit @ ( c @ ld ) )
!= a )
| ( ( unit @ ( a @ ld ) )
!= b )
| ( c != b ) ),
inference(simp,[status(thm)],[18247]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( C @ ( B @ mult ) ) )
| ( ( A @ ( B @ ld ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[24,18]) ).
thf(262,plain,
! [A: $i] :
( ( A @ ( A @ ld ) )
= unit ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).
thf(417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( D @ ( C @ mult ) ) )
| ( ( D @ ( B @ rd ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[16,22]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( B @ rd ) )
= A ),
inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ ld ) ))]]) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ld ) @ ( B @ rd ) )
= A ),
inference(simp,[status(thm)],[418]) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) ) )
| ( A
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,434]) ).
thf(1480,plain,
! [A: $i] :
( ( A
!= ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) ) )
| ( ( A @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= a ) ),
inference(simp,[status(thm)],[1351]) ).
thf(1693,plain,
( ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ rd ) )
!= a ),
inference(simp,[status(thm)],[1480]) ).
thf(66,plain,
! [A: $i] :
( ( ( unit @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(3633,plain,
! [A: $i] :
( ( A
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( ( a @ ( A @ ( a @ mult ) @ mult ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(rewrite,[status(thm)],[66,24]) ).
thf(2295,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( c @ ( b @ mult ) ) )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( B != unit )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[16,228]) ).
thf(2328,plain,
! [A: $i] :
( ( ( unit @ ( A @ ld ) )
!= c )
| ( A != b )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( b != a ) ),
inference(simp,[status(thm)],[2295]) ).
thf(2353,plain,
( ( ( unit @ ( b @ ld ) )
!= c )
| ( ( b @ ( a @ mult ) )
!= b )
| ( unit != c )
| ( b != a ) ),
inference(simp,[status(thm)],[2328]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( C @ ( unit @ mult ) ) )
| ( B = C ) ),
inference(paramod_ordered,[status(thm)],[16,26]) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( unit @ ld ) )
= A ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( unit )),bind(B,$thf( E )),bind(C,$thf( E @ ( unit @ ld ) ))]]) ).
thf(47,plain,
! [A: $i] :
( ( A @ ( unit @ ld ) )
= A ),
inference(simp,[status(thm)],[42]) ).
thf(1375,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ld ) @ ( A @ mult ) )
!= ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) @ ( a @ mult ) ) )
| ( B
!= ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,434]) ).
thf(1505,plain,
! [A: $i] :
( ( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( A @ ld ) )
!= ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[1375]) ).
thf(1713,plain,
( ( b @ ( a @ mult ) @ ( c @ mult ) @ ( b @ ( a @ mult ) @ mult ) @ ( a @ ld ) )
!= ( b @ ( a @ mult ) @ ( c @ ( b @ mult ) @ mult ) ) ),
inference(simp,[status(thm)],[1505]) ).
thf(12868,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ld ) @ ( B @ mult ) )
!= ( b @ ( c @ mult ) ) )
| ( unit != a )
| ( ( c @ ( b @ mult ) )
!= b )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[9100,12045]) ).
thf(12922,plain,
! [A: $i] :
( ( ( b @ ( A @ ld ) )
!= b )
| ( A != c )
| ( unit != a )
| ( ( c @ ( b @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12868]) ).
thf(12948,plain,
( ( ( b @ ( c @ ld ) )
!= b )
| ( unit != a )
| ( ( c @ ( b @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[12922]) ).
thf(80,plain,
! [A: $i] :
( ( A != a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b )
| ( A
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(111,plain,
( ( ( b @ ( a @ mult ) )
!= a )
| ( ( c @ ( b @ mult ) @ ( a @ mult ) )
!= unit )
| ( ( b @ ( a @ mult ) @ ( c @ mult ) )
!= b ) ),
inference(simp,[status(thm)],[80]) ).
thf(15338,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ rd ) @ mult ) )
!= ( a @ ( c @ mult ) ) )
| ( ( b @ ( c @ ld ) )
!= ( b @ ( a @ mult ) ) )
| ( A != unit ) ),
inference(paramod_ordered,[status(thm)],[20,12172]) ).
thf(15354,plain,
! [A: $i] :
( ( A != a )
| ( ( A @ ( unit @ rd ) )
!= c )
| ( ( b @ ( c @ ld ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[15338]) ).
thf(15386,plain,
( ( ( a @ ( unit @ rd ) )
!= c )
| ( ( b @ ( c @ ld ) )
!= ( b @ ( a @ mult ) ) ) ),
inference(simp,[status(thm)],[15354]) ).
thf(214,plain,
! [A: $i] :
( ( ( A @ ( unit @ mult ) )
!= ( b @ ( a @ mult ) ) )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( ( A @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(paramod_ordered,[status(thm)],[26,194]) ).
thf(224,plain,
! [A: $i] :
( ( A != b )
| ( unit != a )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( ( A @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[214]) ).
thf(232,plain,
( ( unit != a )
| ( ( c @ ( b @ mult ) )
!= unit )
| ( ( b @ ( c @ mult ) )
!= b )
| ( b != a ) ),
inference(simp,[status(thm)],[224]) ).
thf(36991,plain,
$false,
inference(e,[status(thm)],[420,105,14912,1237,22893,26613,12934,234,115,12172,16280,379,2933,12165,404,16387,2972,24,25,18269,110,6713,12161,20,27028,228,29,12185,14981,12924,106,121,116,8892,1651,117,11170,102,28,21,33,10462,1106,12991,16569,18386,8985,9100,21182,12045,2968,4416,5138,17,32,34,22,118,24681,27,12,49,17305,236,15382,350,406,377,12182,434,21561,14290,5114,2343,103,108,10147,1643,13418,24937,2914,25159,16285,15004,194,20089,12174,13843,50,12187,7796,2354,31,16485,18327,386,14992,14906,14916,8401,2591,26,258,114,23,119,11172,18263,2421,262,30,19,422,14903,1693,3633,11509,2353,47,15,1713,12948,111,1737,15386,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP669-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.47 % Computer : n019.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Fri Sep 25 15:35:04 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.45/1.30 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.57 % [INFO] Parsing done (262ms).
% 1.81/1.59 % [INFO] Running in sequential loop mode.
% 2.79/2.19 % [INFO] eprover registered as external prover.
% 2.93/2.20 % [INFO] Scanning for conjecture ...
% 3.10/2.33 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 3.10/2.38 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.26/2.40 % [INFO] Problem is propositional (TPTP CNF).
% 3.26/2.41 % [INFO] Type checking passed.
% 3.26/2.42 % [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 ...
% 84.32/20.38 % External prover 'e' found a proof!
% 84.32/20.39 % [INFO] Killing All external provers ...
% 84.32/20.39 % Time passed: 19711ms (effective reasoning time: 18790ms)
% 84.32/20.39 % Axioms used in derivation (10): c05, c08, c01, c03, c06, c02, c07, c10, c09, c04
% 84.32/20.39 % No. of inferences in proof: 378
% 84.32/20.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19711 ms resp. 18790 ms w/o parsing
% 71.26/20.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 71.26/20.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------