%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE027+3 : 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 : n001.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 07:43:02 AM UTC 2026
% Result : Theorem 97.19s 20.84s
% Output : Refutation 99.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 25
% Syntax : Number of formulae : 547 ( 157 unt; 0 typ; 6 def)
% Number of atoms : 1490 ( 883 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 5338 ( 717 ~; 558 |; 38 &;3988 @)
% ( 4 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 603 ( 1 ^; 586 !; 10 ?; 603 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(one_decl,type,
one: $i ).
thf(complement_decl,type,
complement: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ? [D: $i] : ( D @ test )
& ( C @ test ) )
=> ( ( B @ ( C @ c @ multiplication ) @ ( A @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ ( C @ multiplication ) @ addition ) )
= ( B @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ? [C: $i] : ( C @ test )
& ( B @ test ) )
=> ( ( A @ ( B @ c @ multiplication ) @ ( sk2 @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ ( B @ multiplication ) @ addition ) )
= ( A @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ? [B: $i] : ( B @ test )
& ( A @ test ) )
=> ( ( sk3 @ ( A @ c @ multiplication ) @ ( sk2 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ ( A @ multiplication ) @ addition ) )
= ( sk3 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ test ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
( ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
& ( sk5 @ test )
& ( sk4 @ test ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
sk4 @ test,
inference(cnfConj,[status(thm)],[23]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(59,plain,
! [A: $i] :
( ( A @ test )
=> ( ! [B: $i] :
( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ! [B: $i] :
( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(miniscope,[status(thm)],[58]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ( A @ c )
= C )
| ~ ( C @ ( A @ complement ) )
| ~ ( A @ test ) )
& ( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[60]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
!= B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(64,plain,
! [A: $i] :
( ( A @ c @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[63]) ).
thf(1216,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,64]) ).
thf(1217,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1216]) ).
thf(1218,plain,
sk4 @ c @ ( sk4 @ complement ),
inference(pattern_uni,[status(thm)],[1217:[bind(A,$thf( sk4 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
<=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(68,plain,
( ! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(miniscope,[status(thm)],[67]) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ complement ) )
| ( ( D @ ( C @ addition ) )
!= one )
| ( ( C @ ( D @ multiplication ) )
!= zero )
| ( ( D @ ( C @ multiplication ) )
!= zero ) )
& ( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) )
& ( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) )
& ( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(1755,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1218,74]) ).
thf(1756,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1755]) ).
thf(1757,plain,
( ( sk4 @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1756:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(85,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(86,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[86]) ).
thf(26,plain,
( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(27,plain,
( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(114,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[87,27]) ).
thf(140,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A
!= ( sk4 @ c ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(156,plain,
( ( sk2 != zero )
| ( ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(18,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(91,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[92]) ).
thf(341,plain,
( ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[156,93]) ).
thf(349,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[87,341]) ).
thf(359,plain,
! [A: $i] :
( ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero )
| ( A != sk4 )
| ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[349]) ).
thf(384,plain,
( ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[359]) ).
thf(2055,plain,
( ( ( sk4 @ ( sk4 @ c @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1757,384]) ).
thf(2056,plain,
( ( ( sk4 @ ( sk4 @ c @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2055]) ).
thf(2124,plain,
( ( sk4 != sk1 )
| ( ( sk4 @ c )
!= sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2056]) ).
thf(25,plain,
sk5 @ test,
inference(cnfConj,[status(thm)],[23]) ).
thf(1219,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,64]) ).
thf(1220,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1219]) ).
thf(1221,plain,
sk5 @ c @ ( sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1220:[bind(A,$thf( sk5 ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(46,plain,
! [A: $i] :
( ( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(47,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ! [A: $i] :
( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ test )
| ~ ( B @ ( C @ complement ) ) )
& ( ( A @ ( A @ sk6 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(1243,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1221,51]) ).
thf(1244,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1245,plain,
sk5 @ c @ test,
inference(pattern_uni,[status(thm)],[1244:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(1246,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,64]) ).
thf(1247,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1246]) ).
thf(1248,plain,
sk5 @ c @ c @ ( sk5 @ c @ complement ),
inference(pattern_uni,[status(thm)],[1247:[bind(A,$thf( sk5 @ c ))]]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(3347,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1248,76]) ).
thf(3348,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3347]) ).
thf(3349,plain,
( ( sk5 @ c @ ( sk5 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3348:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(7426,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3349,57]) ).
thf(7427,plain,
( ( sk5 @ c @ c @ ( sk5 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[7426:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
thf(1230,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1218,51]) ).
thf(1231,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1230]) ).
thf(1232,plain,
sk4 @ c @ test,
inference(pattern_uni,[status(thm)],[1231:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(1233,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1232,64]) ).
thf(1234,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1233]) ).
thf(1235,plain,
sk4 @ c @ c @ ( sk4 @ c @ complement ),
inference(pattern_uni,[status(thm)],[1234:[bind(A,$thf( sk4 @ c ))]]) ).
thf(1557,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1235,51]) ).
thf(1558,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1557]) ).
thf(1559,plain,
sk4 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[1558:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(111,plain,
( ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(159,plain,
( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(446,plain,
( ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= sk1 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[159]) ).
thf(518,plain,
( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= sk1 ),
inference(simp,[status(thm)],[446]) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(787,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,49]) ).
thf(788,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[787]) ).
thf(789,plain,
sk5 @ ( sk5 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[788:[bind(A,$thf( sk5 ))]]) ).
thf(3293,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[789,76]) ).
thf(3294,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3293]) ).
thf(3295,plain,
( ( sk5 @ sk6 @ ( sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3294:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(3448,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3295,57]) ).
thf(3449,plain,
( ( sk5 @ ( sk5 @ sk6 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3448:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(1758,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1221,74]) ).
thf(1759,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1758]) ).
thf(1760,plain,
( ( sk5 @ ( sk5 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1759:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(82,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(83,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[83]) ).
thf(2221,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ c @ multiplication ) )
!= ( one @ ( A @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1760,84]) ).
thf(2279,plain,
! [A: $i] :
( ( sk5 != one )
| ( ( sk5 @ c )
!= A )
| ( zero = A ) ),
inference(simp,[status(thm)],[2221]) ).
thf(2330,plain,
( ( sk5 != one )
| ( ( sk5 @ c )
= zero ) ),
inference(simp,[status(thm)],[2279]) ).
thf(8474,plain,
( ( ( sk5 @ c )
!= ( sk5 @ c ) )
| ( zero @ test )
| ( sk5 != one ) ),
inference(paramod_ordered,[status(thm)],[2330,1245]) ).
thf(8475,plain,
( ( zero @ test )
| ( sk5 != one ) ),
inference(pattern_uni,[status(thm)],[8474:[]]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1249,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,49]) ).
thf(1250,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1249]) ).
thf(1251,plain,
sk5 @ c @ ( sk5 @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1250:[bind(A,$thf( sk5 @ c ))]]) ).
thf(3299,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1251,76]) ).
thf(3300,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3299]) ).
thf(3301,plain,
( ( sk5 @ c @ sk6 @ ( sk5 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3300:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 @ c @ sk6 ))]]) ).
thf(7039,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ sk6 @ ( sk5 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3301,57]) ).
thf(7040,plain,
( ( sk5 @ c @ ( sk5 @ c @ sk6 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[7039:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 @ c @ sk6 ))]]) ).
thf(284,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( A @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,27]) ).
thf(294,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( A
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(308,plain,
( ( one @ ( sk1 @ ( sk4 @ multiplication ) @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(863,plain,
( ( one @ ( sk1 @ multiplication ) @ ( sk4 @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[308,33]) ).
thf(865,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( ( A @ ( sk4 @ multiplication ) )
!= ( one @ ( sk1 @ multiplication ) @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,863]) ).
thf(980,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( A
!= ( one @ ( sk1 @ multiplication ) ) )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[865]) ).
thf(1056,plain,
( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( zero @ ( one @ ( sk1 @ multiplication ) @ addition ) ) ),
inference(simp,[status(thm)],[980]) ).
thf(1068,plain,
( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( one @ ( sk1 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[1056,93]) ).
thf(1634,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1248,51]) ).
thf(1635,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1634]) ).
thf(1636,plain,
sk5 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[1635:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
thf(1644,plain,
! [A: $i] :
( ( ( sk5 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1636,49]) ).
thf(1645,plain,
! [A: $i] :
( ( ( sk5 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1644]) ).
thf(1646,plain,
sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1645:[bind(A,$thf( sk5 @ c @ c ))]]) ).
thf(10884,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1646,74]) ).
thf(10885,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10884]) ).
thf(10886,plain,
( ( sk5 @ c @ c @ sk6 @ ( sk5 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10885:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c @ c @ sk6 ))]]) ).
thf(1562,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1559,64]) ).
thf(1563,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1562]) ).
thf(1564,plain,
sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[1563:[bind(A,$thf( sk4 @ c @ c ))]]) ).
thf(10280,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1564,51]) ).
thf(10281,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[10280]) ).
thf(10282,plain,
sk4 @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[10281:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(10307,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10282,64]) ).
thf(10308,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[10307]) ).
thf(10309,plain,
sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[10308:[bind(A,$thf( sk4 @ c @ c @ c ))]]) ).
thf(20233,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10309,76]) ).
thf(20234,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[20233]) ).
thf(20235,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[20234:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(1641,plain,
! [A: $i] :
( ( ( sk5 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1636,64]) ).
thf(1642,plain,
! [A: $i] :
( ( ( sk5 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1641]) ).
thf(1643,plain,
sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[1642:[bind(A,$thf( sk5 @ c @ c ))]]) ).
thf(10792,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1643,51]) ).
thf(10793,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[10792]) ).
thf(10794,plain,
sk5 @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[10793:[bind(A,$thf( sk5 @ c @ c @ c )),bind(B,$thf( sk5 @ c @ c ))]]) ).
thf(10815,plain,
! [A: $i] :
( ( ( sk5 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10794,64]) ).
thf(10816,plain,
! [A: $i] :
( ( ( sk5 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[10815]) ).
thf(10817,plain,
sk5 @ c @ c @ c @ c @ ( sk5 @ c @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[10816:[bind(A,$thf( sk5 @ c @ c @ c ))]]) ).
thf(21137,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ c @ ( sk5 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10817,74]) ).
thf(21138,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ c @ ( sk5 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[21137]) ).
thf(21139,plain,
( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[21138:[bind(A,$thf( sk5 @ c @ c @ c @ c )),bind(B,$thf( sk5 @ c @ c @ c ))]]) ).
thf(784,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,49]) ).
thf(785,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[784]) ).
thf(786,plain,
sk4 @ ( sk4 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[785:[bind(A,$thf( sk4 ))]]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(2412,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[786,75]) ).
thf(2413,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2412]) ).
thf(2414,plain,
( ( sk4 @ ( sk4 @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2413:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(2529,plain,
( ( ( sk4 @ ( sk4 @ sk6 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[2414,384]) ).
thf(2530,plain,
( ( ( sk4 @ ( sk4 @ sk6 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2529]) ).
thf(2607,plain,
( ( sk4 != sk1 )
| ( ( sk4 @ sk6 )
!= sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2530]) ).
thf(113,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[87,27]) ).
thf(132,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[113]) ).
thf(148,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[132]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(94,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(10991,plain,
( ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) )
!= zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(rewrite,[status(thm)],[148,96,87]) ).
thf(3274,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[786,76]) ).
thf(3275,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3274]) ).
thf(3276,plain,
( ( sk4 @ sk6 @ ( sk4 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3275:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(1698,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[789,74]) ).
thf(1699,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1698]) ).
thf(1700,plain,
( ( sk5 @ sk6 @ ( sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1699:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(1938,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk5 @ sk6 @ ( sk5 @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[84,1700]) ).
thf(1999,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= one )
| ( A != sk5 )
| ( A = zero ) ),
inference(simp,[status(thm)],[1938]) ).
thf(2035,plain,
( ( ( sk5 @ sk6 )
!= one )
| ( sk5 = zero ) ),
inference(simp,[status(thm)],[1999]) ).
thf(3366,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ sk6 @ ( sk4 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3276,57]) ).
thf(3367,plain,
( ( sk4 @ ( sk4 @ sk6 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3366:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(1565,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1559,49]) ).
thf(1566,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1565]) ).
thf(1567,plain,
sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1566:[bind(A,$thf( sk4 @ c @ c ))]]) ).
thf(10696,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1567,75]) ).
thf(10697,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10696]) ).
thf(10698,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10697:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c @ c @ sk6 ))]]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21222,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ c @ ( sk5 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10817,51]) ).
thf(21223,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ c @ ( sk5 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[21222]) ).
thf(21224,plain,
sk5 @ c @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[21223:[bind(A,$thf( sk5 @ c @ c @ c @ c )),bind(B,$thf( sk5 @ c @ c @ c ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[29]) ).
thf(117,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,27]) ).
thf(128,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( sk4 != zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[117]) ).
thf(144,plain,
( ( sk4 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[128]) ).
thf(169,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[30,144]) ).
thf(170,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[169]) ).
thf(172,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk4 != zero )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[170]) ).
thf(174,plain,
sk4 != zero,
inference(simp,[status(thm)],[172]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(53,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[53]) ).
thf(3377,plain,
! [A: $i] :
( ( ( sk4 @ sk6 @ ( sk4 @ addition ) )
!= ( A @ ( A @ addition ) ) )
| ( one = A ) ),
inference(paramod_ordered,[status(thm)],[3276,54]) ).
thf(3402,plain,
! [A: $i] :
( ( ( sk4 @ sk6 )
!= A )
| ( sk4 != A )
| ( one = A ) ),
inference(simp,[status(thm)],[3377]) ).
thf(3425,plain,
( ( ( sk4 @ sk6 )
!= sk4 )
| ( sk4 = one ) ),
inference(simp,[status(thm)],[3402]) ).
thf(10310,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10282,49]) ).
thf(10311,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[10310]) ).
thf(10312,plain,
sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[10311:[bind(A,$thf( sk4 @ c @ c @ c ))]]) ).
thf(20416,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10312,74]) ).
thf(20417,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[20416]) ).
thf(20418,plain,
( ( sk4 @ c @ c @ c @ sk6 @ ( sk4 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[20417:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c @ sk6 ))]]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[77]) ).
thf(2203,plain,
( ( ( sk5 @ ( sk5 @ c @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1760,384]) ).
thf(2204,plain,
( ( ( sk5 @ ( sk5 @ c @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2203]) ).
thf(2301,plain,
( ( sk5 != sk1 )
| ( ( sk5 @ c )
!= sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2204]) ).
thf(112,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[87,27]) ).
thf(136,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk4 )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(152,plain,
( ( sk1 != zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(15824,plain,
( ( sk1 != zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( zero @ ( sk4 @ multiplication ) @ addition ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(rewrite,[status(thm)],[152,96]) ).
thf(10727,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1643,74]) ).
thf(10728,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10727]) ).
thf(10729,plain,
( ( sk5 @ c @ c @ ( sk5 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10728:[bind(A,$thf( sk5 @ c @ c @ c )),bind(B,$thf( sk5 @ c @ c ))]]) ).
thf(20302,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10309,51]) ).
thf(20303,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[20302]) ).
thf(20304,plain,
sk4 @ c @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[20303:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(2481,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1235,75]) ).
thf(2482,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2481]) ).
thf(2483,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2482:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(10782,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1643,75]) ).
thf(10783,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10782]) ).
thf(10784,plain,
( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10783:[bind(A,$thf( sk5 @ c @ c @ c )),bind(B,$thf( sk5 @ c @ c ))]]) ).
thf(20431,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10312,76]) ).
thf(20432,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[20431]) ).
thf(20433,plain,
( ( sk4 @ c @ c @ c @ sk6 @ ( sk4 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[20432:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c @ sk6 ))]]) ).
thf(344,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( A @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,341]) ).
thf(355,plain,
! [A: $i] :
( ( sk1 != one )
| ( A != sk4 )
| ( sk2 != zero )
| ( A != sk1 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[344]) ).
thf(380,plain,
( ( sk1 != one )
| ( sk4 != sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[355]) ).
thf(3331,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1218,76]) ).
thf(3332,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3331]) ).
thf(3333,plain,
( ( sk4 @ ( sk4 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3332:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(3530,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3333,57]) ).
thf(3531,plain,
( ( sk4 @ c @ ( sk4 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3530:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(97,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(98,plain,
( ! [A: $i,B: $i] :
( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(miniscope,[status(thm)],[97]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ leq ) )
| ( ( D @ ( C @ addition ) )
!= D ) )
& ( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[98]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(2427,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[789,75]) ).
thf(2428,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2427]) ).
thf(2429,plain,
( ( sk5 @ ( sk5 @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2428:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(2679,plain,
( ( ( sk5 @ ( sk5 @ sk6 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[2429,384]) ).
thf(2680,plain,
( ( ( sk5 @ ( sk5 @ sk6 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2679]) ).
thf(2773,plain,
( ( sk5 != sk1 )
| ( ( sk5 @ sk6 )
!= sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2680]) ).
thf(139,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A
!= ( sk4 @ c ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(155,plain,
( ( sk2 != zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(19158,plain,
( ( sk2 != zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(rewrite,[status(thm)],[155,96]) ).
thf(1236,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1232,49]) ).
thf(1237,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1236]) ).
thf(1238,plain,
sk4 @ c @ ( sk4 @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1237:[bind(A,$thf( sk4 @ c ))]]) ).
thf(3296,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1238,76]) ).
thf(3297,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3296]) ).
thf(3298,plain,
( ( sk4 @ c @ sk6 @ ( sk4 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3297:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk6 ))]]) ).
thf(6914,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ sk6 @ ( sk4 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3298,57]) ).
thf(6915,plain,
( ( sk4 @ c @ ( sk4 @ c @ sk6 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[6914:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk6 ))]]) ).
thf(118,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,27]) ).
thf(129,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(145,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) ) )
| ( ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(8899,plain,
( ( ( sk2 @ ( sk4 @ c @ multiplication ) )
!= zero )
| ( ( zero @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[145,96,30]) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[74,384]) ).
thf(1675,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[1674]) ).
thf(1676,plain,
( ( sk2 != zero )
| ~ ( sk4 @ ( sk1 @ complement ) ) ),
inference(pattern_uni,[status(thm)],[1675:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(1683,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[786,74]) ).
thf(1684,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1683]) ).
thf(1685,plain,
( ( sk4 @ sk6 @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1684:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(1803,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk4 @ sk6 @ ( sk4 @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[45,1685]) ).
thf(1831,plain,
! [A: $i] :
( ( A
!= ( sk4 @ sk6 ) )
| ( sk4 != one )
| ( A = zero ) ),
inference(simp,[status(thm)],[1803]) ).
thf(1881,plain,
( ( sk4 != one )
| ( ( sk4 @ sk6 )
= zero ) ),
inference(simp,[status(thm)],[1831]) ).
thf(1796,plain,
! [A: $i] :
( ( ( sk4 @ sk6 @ ( sk4 @ multiplication ) )
!= ( one @ ( A @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1685,84]) ).
thf(1834,plain,
! [A: $i] :
( ( ( sk4 @ sk6 )
!= one )
| ( sk4 != A )
| ( zero = A ) ),
inference(simp,[status(thm)],[1796]) ).
thf(1884,plain,
( ( ( sk4 @ sk6 )
!= one )
| ( sk4 = zero ) ),
inference(simp,[status(thm)],[1834]) ).
thf(3266,plain,
( ( sk4 @ sk6 )
!= one ),
inference(simplifyReflect,[status(thm)],[1884,174]) ).
thf(3270,plain,
( ( ( sk4 @ sk6 )
!= ( sk4 @ sk6 ) )
| ( one != zero )
| ( sk4 != one ) ),
inference(paramod_ordered,[status(thm)],[1881,3266]) ).
thf(3271,plain,
( ( one != zero )
| ( sk4 != one ) ),
inference(pattern_uni,[status(thm)],[3270:[]]) ).
thf(10895,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1646,76]) ).
thf(10896,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[10895]) ).
thf(10897,plain,
( ( sk5 @ c @ c @ sk6 @ ( sk5 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[10896:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c @ c @ sk6 ))]]) ).
thf(15630,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ sk6 @ ( sk5 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10897,57]) ).
thf(15631,plain,
( ( sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[15630:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c @ c @ sk6 ))]]) ).
thf(1158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[57,93]) ).
thf(1159,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[1158:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(2080,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk4 @ ( sk4 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[45,1757]) ).
thf(2139,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( sk4 @ c )
!= one )
| ( A = zero ) ),
inference(simp,[status(thm)],[2080]) ).
thf(2181,plain,
( ( ( sk4 @ c )
!= one )
| ( sk4 = zero ) ),
inference(simp,[status(thm)],[2139]) ).
thf(6603,plain,
( ( sk4 @ c )
!= one ),
inference(simplifyReflect,[status(thm)],[2181,174]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
= B )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[60]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(simp,[status(thm)],[65]) ).
thf(6609,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk4 @ c ) )
| ( B != one )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[66,6603]) ).
thf(6610,plain,
! [A: $i] :
( ( A != one )
| ~ ( A @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(pattern_uni,[status(thm)],[6609:[bind(A,$thf( sk4 ))]]) ).
thf(6615,plain,
( ~ ( one @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(simp,[status(thm)],[6610]) ).
thf(7288,plain,
( ~ ( one @ ( sk4 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6615,24]) ).
thf(7289,plain,
~ ( one @ ( sk4 @ complement ) ),
inference(simp,[status(thm)],[7288]) ).
thf(7301,plain,
! [A: $i] :
( ( ( A @ ( A @ sk6 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ~ $true
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[49,7289]) ).
thf(7302,plain,
! [A: $i] :
( ( ( A @ ( A @ sk6 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[7301]) ).
thf(7322,plain,
! [A: $i] :
( ( A != one )
| ( ( A @ sk6 )
!= sk4 )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[7302]) ).
thf(7327,plain,
( ( ( one @ sk6 )
!= sk4 )
| ~ ( one @ test ) ),
inference(simp,[status(thm)],[7322]) ).
thf(8853,plain,
( ( ( sk5 @ c @ test )
!= ( one @ test ) )
| ( ( one @ sk6 )
!= sk4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1245,7327]) ).
thf(8854,plain,
( ( ( sk5 @ c @ test )
!= ( one @ test ) )
| ( ( one @ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[8853]) ).
thf(8884,plain,
( ( ( sk5 @ c )
!= one )
| ( ( one @ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[8854]) ).
thf(2487,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1221,75]) ).
thf(2488,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2487]) ).
thf(2489,plain,
( ( sk5 @ c @ ( sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2488:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(3009,plain,
( ( ( sk5 @ c @ ( sk5 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[2489,384]) ).
thf(3010,plain,
( ( ( sk5 @ c @ ( sk5 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[3009]) ).
thf(3119,plain,
( ( ( sk5 @ c )
!= sk1 )
| ( sk5 != sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[3010]) ).
thf(10654,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1567,76]) ).
thf(10655,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[10654]) ).
thf(10656,plain,
( ( sk4 @ c @ c @ sk6 @ ( sk4 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[10655:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c @ c @ sk6 ))]]) ).
thf(13433,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ sk6 @ ( sk4 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10656,57]) ).
thf(13434,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[13433:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c @ c @ sk6 ))]]) ).
thf(137,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk4 )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(153,plain,
( ( sk1 != zero )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(17942,plain,
( ( sk1 != zero )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( zero @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[153,96]) ).
thf(7311,plain,
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[786,7289]) ).
thf(7312,plain,
( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) ),
inference(simp,[status(thm)],[7311]) ).
thf(7318,plain,
( ( sk4 != one )
| ( ( sk4 @ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[7312]) ).
thf(3364,plain,
! [A: $i] :
( ( ( sk4 @ sk6 @ ( sk4 @ addition ) )
!= ( zero @ ( A @ addition ) ) )
| ( one = A ) ),
inference(paramod_ordered,[status(thm)],[3276,93]) ).
thf(3408,plain,
! [A: $i] :
( ( ( sk4 @ sk6 )
!= zero )
| ( sk4 != A )
| ( one = A ) ),
inference(simp,[status(thm)],[3364]) ).
thf(3428,plain,
( ( ( sk4 @ sk6 )
!= zero )
| ( sk4 = one ) ),
inference(simp,[status(thm)],[3408]) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1218,75]) ).
thf(2485,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2484]) ).
thf(2486,plain,
( ( sk4 @ c @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2485:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(2833,plain,
( ( ( sk4 @ c @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[2486,384]) ).
thf(2834,plain,
( ( ( sk4 @ c @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2833]) ).
thf(2962,plain,
( ( ( sk4 @ c )
!= sk1 )
| ( sk4 != sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2834]) ).
thf(2978,plain,
( ( ( sk4 @ c )
!= sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[2962]) ).
thf(2228,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk5 @ ( sk5 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[45,1760]) ).
thf(2306,plain,
! [A: $i] :
( ( A != sk5 )
| ( ( sk5 @ c )
!= one )
| ( A = zero ) ),
inference(simp,[status(thm)],[2228]) ).
thf(2317,plain,
( ( ( sk5 @ c )
!= one )
| ( sk5 = zero ) ),
inference(simp,[status(thm)],[2306]) ).
thf(21153,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ c @ ( sk5 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10817,76]) ).
thf(21154,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ c @ ( sk5 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[21153]) ).
thf(21155,plain,
( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[21154:[bind(A,$thf( sk5 @ c @ c @ c @ c )),bind(B,$thf( sk5 @ c @ c @ c ))]]) ).
thf(3328,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1235,76]) ).
thf(3329,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3328]) ).
thf(3330,plain,
( ( sk4 @ c @ ( sk4 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3329:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(7173,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3330,57]) ).
thf(7174,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[7173:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(1752,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1235,74]) ).
thf(1753,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1752]) ).
thf(1754,plain,
( ( sk4 @ c @ ( sk4 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1753:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ ( B @ addition ) @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( D @ ( B @ multiplication ) @ addition ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[87,42]) ).
thf(640,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(pattern_uni,[status(thm)],[639:[bind(A,$thf( F @ ( E @ addition ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(simp,[status(thm)],[640]) ).
thf(727,plain,
( ( zero @ ( zero @ addition ) )
= zero ),
inference(rewrite,[status(thm)],[685,87]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ( ( zero @ ( zero @ addition ) )
!= ( B @ ( C @ addition ) ) )
| ( ( A @ ( zero @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[727,36]) ).
thf(743,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) @ ( zero @ addition ) )
= ( A @ ( zero @ addition ) ) ),
inference(pattern_uni,[status(thm)],[742:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( zero ))]]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(simp,[status(thm)],[103]) ).
thf(7365,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ addition ) @ ( zero @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( ( A @ ( zero @ addition ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[743,104]) ).
thf(7366,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) @ ( zero @ leq ) )
| ( ( A @ ( zero @ addition ) )
!= ( A @ ( zero @ addition ) ) ) ),
inference(pattern_uni,[status(thm)],[7365:[bind(A,$thf( E )),bind(B,$thf( zero )),bind(C,$thf( E @ ( zero @ addition ) ))]]) ).
thf(7387,plain,
! [A: $i] : ( A @ ( zero @ addition ) @ ( zero @ leq ) ),
inference(simp,[status(thm)],[7366]) ).
thf(9264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ addition ) )
!= ( C @ ( zero @ addition ) ) )
| ( B @ ( A @ addition ) @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[57,7387]) ).
thf(9265,plain,
! [A: $i] : ( zero @ ( A @ addition ) @ ( zero @ leq ) ),
inference(pattern_uni,[status(thm)],[9264:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(10202,plain,
! [A: $i] : ( A @ ( zero @ leq ) ),
inference(rewrite,[status(thm)],[9265,93]) ).
thf(10272,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1564,75]) ).
thf(10273,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10272]) ).
thf(10274,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10273:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(2351,plain,
! [A: $i] :
( ( ( A @ c @ ( A @ complement ) )
!= ( sk4 @ ( sk1 @ complement ) ) )
| ( sk2 != zero )
| ~ $true
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[64,1676]) ).
thf(2352,plain,
! [A: $i] :
( ( ( A @ c @ ( A @ complement ) )
!= ( sk4 @ ( sk1 @ complement ) ) )
| ( sk2 != zero )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[2351]) ).
thf(2370,plain,
! [A: $i] :
( ( ( A @ c )
!= sk4 )
| ( A != sk1 )
| ( sk2 != zero )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[2352]) ).
thf(2376,plain,
( ( ( sk1 @ c )
!= sk4 )
| ( sk2 != zero )
| ~ ( sk1 @ test ) ),
inference(simp,[status(thm)],[2370]) ).
thf(3232,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1251,75]) ).
thf(3233,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[3232]) ).
thf(3234,plain,
( ( sk5 @ c @ ( sk5 @ c @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[3233:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 @ c @ sk6 ))]]) ).
thf(2391,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[75,384]) ).
thf(2392,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[2391]) ).
thf(2393,plain,
( ( sk2 != zero )
| ~ ( sk1 @ ( sk4 @ complement ) ) ),
inference(pattern_uni,[status(thm)],[2392:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(135,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(151,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(14247,plain,
( ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( zero @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[151,96,87]) ).
thf(3206,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1251,74]) ).
thf(3207,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[3206]) ).
thf(3208,plain,
( ( sk5 @ c @ sk6 @ ( sk5 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[3207:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 @ c @ sk6 ))]]) ).
thf(2440,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1238,75]) ).
thf(2441,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2440]) ).
thf(2442,plain,
( ( sk4 @ c @ ( sk4 @ c @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2441:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk6 ))]]) ).
thf(7293,plain,
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[789,7289]) ).
thf(7294,plain,
( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) ),
inference(simp,[status(thm)],[7293]) ).
thf(7315,plain,
( ( sk5 != one )
| ( ( sk5 @ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[7294]) ).
thf(10739,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1643,76]) ).
thf(10740,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[10739]) ).
thf(10741,plain,
( ( sk5 @ c @ c @ ( sk5 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[10740:[bind(A,$thf( sk5 @ c @ c @ c )),bind(B,$thf( sk5 @ c @ c ))]]) ).
thf(2508,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1248,75]) ).
thf(2509,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2508]) ).
thf(2510,plain,
( ( sk5 @ c @ c @ ( sk5 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2509:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
thf(10234,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1564,76]) ).
thf(10235,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[10234]) ).
thf(10236,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[10235:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(1943,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ multiplication ) )
!= ( A @ ( one @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1700,45]) ).
thf(1983,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= A )
| ( sk5 != one )
| ( zero = A ) ),
inference(simp,[status(thm)],[1943]) ).
thf(2030,plain,
( ( sk5 != one )
| ( ( sk5 @ sk6 )
= zero ) ),
inference(simp,[status(thm)],[1983]) ).
thf(4211,plain,
( ( ( sk5 @ sk6 )
!= ( sk4 @ sk6 ) )
| ( one != zero )
| ( sk5 != one ) ),
inference(paramod_ordered,[status(thm)],[2030,3266]) ).
thf(4228,plain,
( ( sk5 != sk4 )
| ( one != zero )
| ( sk5 != one ) ),
inference(simp,[status(thm)],[4211]) ).
thf(130,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk4 @ c )
!= zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(146,plain,
( ( ( sk4 @ c )
!= zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(9349,plain,
( ( ( sk4 @ c )
!= zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(rewrite,[status(thm)],[146,96]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) )
| ~ ( B @ test )
| ~ ( A @ test ) ),
inference(cnf,[status(esa)],[79]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( B @ test )
| ~ ( A @ test )
| ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(342,plain,
( ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= sk1 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[341]) ).
thf(377,plain,
( ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= sk1 ) ),
inference(simp,[status(thm)],[342]) ).
thf(38,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(350,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= ( zero @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[87,341]) ).
thf(364,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk4 )
| ( sk2 != zero )
| ( sk1 != zero )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[350]) ).
thf(387,plain,
( ( sk2 != zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[364]) ).
thf(10643,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1567,74]) ).
thf(10644,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10643]) ).
thf(10645,plain,
( ( sk4 @ c @ c @ sk6 @ ( sk4 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10644:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c @ c @ sk6 ))]]) ).
thf(3446,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ addition ) )
!= ( zero @ ( A @ addition ) ) )
| ( one = A ) ),
inference(paramod_ordered,[status(thm)],[3295,93]) ).
thf(3494,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= zero )
| ( sk5 != A )
| ( one = A ) ),
inference(simp,[status(thm)],[3446]) ).
thf(3512,plain,
( ( ( sk5 @ sk6 )
!= zero )
| ( sk5 = one ) ),
inference(simp,[status(thm)],[3494]) ).
thf(119,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( zero @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,27]) ).
thf(142,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk4 @ c )
!= zero )
| ( ( zero @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(157,plain,
( ( ( sk4 @ c )
!= zero )
| ( ( zero @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(20545,plain,
( ( ( sk4 @ c )
!= zero )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(rewrite,[status(thm)],[157,93]) ).
thf(134,plain,
! [A: $i] :
( ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= zero )
| ( A != sk4 )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[113]) ).
thf(150,plain,
( ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[134]) ).
thf(131,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk4 @ c )
!= zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(147,plain,
( ( ( sk4 @ c )
!= zero )
| ( ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(10371,plain,
( ( ( sk4 @ c )
!= zero )
| ( ( zero @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[147,96]) ).
thf(133,plain,
! [A: $i] :
( ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= zero )
| ( A != sk4 )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(149,plain,
( ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(11594,plain,
( ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[149,1159]) ).
thf(2073,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ c @ multiplication ) )
!= ( one @ ( A @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1757,84]) ).
thf(2132,plain,
! [A: $i] :
( ( sk4 != one )
| ( ( sk4 @ c )
!= A )
| ( zero = A ) ),
inference(simp,[status(thm)],[2073]) ).
thf(2175,plain,
( ( sk4 != one )
| ( ( sk4 @ c )
= zero ) ),
inference(simp,[status(thm)],[2132]) ).
thf(7309,plain,
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1221,7289]) ).
thf(7310,plain,
( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( one @ ( sk4 @ complement ) ) ),
inference(simp,[status(thm)],[7309]) ).
thf(7319,plain,
( ( ( sk5 @ c )
!= one )
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[7310]) ).
thf(10818,plain,
! [A: $i] :
( ( ( sk5 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10794,49]) ).
thf(10819,plain,
! [A: $i] :
( ( ( sk5 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[10818]) ).
thf(10820,plain,
sk5 @ c @ c @ c @ ( sk5 @ c @ c @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[10819:[bind(A,$thf( sk5 @ c @ c @ c ))]]) ).
thf(7367,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[54,104]) ).
thf(7368,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[7367:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(7388,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[7368]) ).
thf(14754,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10741,57]) ).
thf(14755,plain,
( ( sk5 @ c @ c @ c @ ( sk5 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[14754:[bind(A,$thf( sk5 @ c @ c @ c )),bind(B,$thf( sk5 @ c @ c ))]]) ).
thf(115,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( zero @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[87,27]) ).
thf(120,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= zero )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(7719,plain,
( ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= zero )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[120,96,87]) ).
thf(7720,plain,
( ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= zero )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[7719]) ).
thf(8861,plain,
( ( ( sk5 @ test )
!= ( one @ test ) )
| ( ( one @ sk6 )
!= sk4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,7327]) ).
thf(8862,plain,
( ( ( sk5 @ test )
!= ( one @ test ) )
| ( ( one @ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[8861]) ).
thf(8882,plain,
( ( sk5 != one )
| ( ( one @ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[8862]) ).
thf(3334,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1221,76]) ).
thf(3335,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3334]) ).
thf(3336,plain,
( ( sk5 @ ( sk5 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3335:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(348,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( A @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[45,341]) ).
thf(358,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk4 != one )
| ( sk2 != zero )
| ( A != sk1 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[348]) ).
thf(383,plain,
( ( sk4 != one )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[358]) ).
thf(10935,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1646,75]) ).
thf(10936,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10935]) ).
thf(10937,plain,
( ( sk5 @ c @ c @ ( sk5 @ c @ c @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10936:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c @ c @ sk6 ))]]) ).
thf(20493,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10312,75]) ).
thf(20494,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[20493]) ).
thf(20495,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[20494:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c @ sk6 ))]]) ).
thf(20217,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10309,74]) ).
thf(20218,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[20217]) ).
thf(20219,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[20218:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(5558,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( zero @ test )
| ( sk4 != one ) ),
inference(paramod_ordered,[status(thm)],[2175,1232]) ).
thf(5559,plain,
( ( zero @ test )
| ( sk4 != one ) ),
inference(pattern_uni,[status(thm)],[5558:[]]) ).
thf(3460,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk5 @ sk6 @ ( sk5 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[54,3295]) ).
thf(3482,plain,
! [A: $i] :
( ( A
!= ( sk5 @ sk6 ) )
| ( A != sk5 )
| ( A = one ) ),
inference(simp,[status(thm)],[3460]) ).
thf(3506,plain,
( ( ( sk5 @ sk6 )
!= sk5 )
| ( sk5 = one ) ),
inference(simp,[status(thm)],[3482]) ).
thf(10222,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1564,74]) ).
thf(10223,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10222]) ).
thf(10224,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10223:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(12311,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10236,57]) ).
thf(12312,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[12311:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(3243,plain,
( ( ( sk4 @ sk6 )
!= ( sk4 @ sk6 ) )
| ( sk4 @ ( zero @ complement ) )
| ( sk4 != one ) ),
inference(paramod_ordered,[status(thm)],[1881,786]) ).
thf(3244,plain,
( ( sk4 @ ( zero @ complement ) )
| ( sk4 != one ) ),
inference(pattern_uni,[status(thm)],[3243:[]]) ).
thf(121,plain,
! [A: $i] :
( ( sk3 != zero )
| ( A
!= ( sk4 @ c ) )
| ( ( zero @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(160,plain,
( ( sk3 != zero )
| ( ( zero @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(23097,plain,
( ( sk3 != zero )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(rewrite,[status(thm)],[160,93]) ).
thf(1923,plain,
( ( ( sk5 @ sk6 @ ( sk5 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1700,384]) ).
thf(1924,plain,
( ( ( sk5 @ sk6 @ ( sk5 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[1923]) ).
thf(1976,plain,
( ( ( sk5 @ sk6 )
!= sk1 )
| ( sk5 != sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[1924]) ).
thf(1711,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1238,74]) ).
thf(1712,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1711]) ).
thf(1713,plain,
( ( sk4 @ c @ sk6 @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1712:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk6 ))]]) ).
thf(1782,plain,
( ( ( sk4 @ sk6 @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1685,384]) ).
thf(1783,plain,
( ( ( sk4 @ sk6 @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[1782]) ).
thf(1835,plain,
( ( ( sk4 @ sk6 )
!= sk1 )
| ( sk4 != sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[1783]) ).
thf(1885,plain,
( ( ( sk4 @ sk6 )
!= sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[1835]) ).
thf(8859,plain,
( ( ( sk4 @ test )
!= ( one @ test ) )
| ( ( one @ sk6 )
!= sk4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,7327]) ).
thf(8860,plain,
( ( ( sk4 @ test )
!= ( one @ test ) )
| ( ( one @ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[8859]) ).
thf(8876,plain,
( ( sk4 != one )
| ( ( one @ sk6 )
!= sk4 ) ),
inference(simp,[status(thm)],[8860]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) )
| ~ ( B @ test )
| ~ ( A @ test ) ),
inference(cnf,[status(esa)],[88]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( B @ test )
| ~ ( A @ test )
| ( ( B @ c @ ( A @ c @ multiplication ) )
= ( B @ ( A @ addition ) @ c ) ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(20299,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10309,75]) ).
thf(20300,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[20299]) ).
thf(20301,plain,
( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[20300:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(3625,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3336,57]) ).
thf(3626,plain,
( ( sk5 @ c @ ( sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3625:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(1767,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1248,74]) ).
thf(1768,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1767]) ).
thf(1769,plain,
( ( sk5 @ c @ ( sk5 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1768:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
thf(28370,plain,
$false,
inference(e,[status(thm)],[2124,7427,1559,518,3449,8475,88,7040,1068,10886,20235,10282,384,21139,2607,10991,3276,2035,3367,42,24,10698,37,25,21224,174,52,3425,1760,20418,46,93,78,1232,2301,15824,57,10309,10729,789,3295,20304,84,2483,10784,20433,74,1564,380,3301,85,3531,102,2773,1636,19158,6915,21,8899,2414,33,1238,28,1676,3271,3349,97,15631,10897,10794,1159,6603,8884,3119,1567,13434,17942,7318,1700,3428,2978,2317,96,21155,3333,7174,10656,7289,1251,1754,10202,34,45,64,10274,2376,3234,2489,2393,3266,14247,54,3330,3208,49,2442,7315,10741,2510,10236,4228,9349,81,377,76,39,91,66,3298,387,10645,1245,1643,3512,20545,150,10371,11594,2175,67,2429,1235,2486,1218,7319,31,10820,7388,14755,1221,2030,1881,7720,43,1685,87,104,1646,40,8882,3336,55,786,7327,58,2330,383,82,75,10937,20495,36,30,20219,1248,1757,51,10312,5559,79,3506,94,10224,12312,341,3244,23097,1976,1713,1885,8876,90,20301,3626,1769,10817]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.21/0.67 % Computer : n001.cluster.edu
% 0.21/0.67 % Model : x86_64 x86_64
% 0.21/0.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.67 % Memory : 8046.5625MB
% 0.21/0.67 % OS : Linux 6.8.0-71-generic
% 0.21/0.67 % CPULimit : 300
% 0.21/0.67 % WCLimit : 300
% 0.21/0.67 % DateTime : Fri Sep 25 19:20:27 UTC 2026
% 0.21/0.67 % CPUTime :
% 0.21/0.67 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
% 1.38/1.52 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.89/1.85 % [INFO] Parsing done (325ms).
% 1.89/1.88 % [INFO] Running in sequential loop mode.
% 3.00/2.41 % [INFO] eprover registered as external prover.
% 3.00/2.42 % [INFO] Scanning for conjecture ...
% 3.18/2.58 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.35/2.68 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.55/2.74 % [INFO] Problem is first-order (TPTP FOF).
% 3.55/2.75 % [INFO] Type checking passed.
% 3.55/2.76 % [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 ...
% 97.19/20.83 % External prover 'e' found a proof!
% 97.19/20.83 % [INFO] Killing All external provers ...
% 97.19/20.84 % Time passed: 19963ms (effective reasoning time: 18951ms)
% 97.19/20.84 % 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)>
% 97.19/20.84 % Axioms used in derivation (18): test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, test_deMorgan2, additive_identity, additive_idempotence, additive_associativity, order, additive_commutativity, right_annihilation, test_deMorgan1, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 97.19/20.84 % No. of inferences in proof: 541
% 97.19/20.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19963 ms resp. 18951 ms w/o parsing
% 99.12/21.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 99.12/21.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------