TSTP Solution File: KLE147+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE147+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:25:10 EDT 2023
% Result : Theorem 153.73s 36.99s
% Output : Refutation 154.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 28
% Syntax : Number of formulae : 718 ( 315 unt; 9 typ; 0 def)
% Number of atoms : 1357 ( 993 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 6800 ( 799 ~; 569 |; 2 &;5419 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 1193 ( 0 ^;1193 !; 0 ?;1193 :)
% Comments :
%------------------------------------------------------------------------------
thf(strong_iteration_type,type,
strong_iteration: $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(star_type,type,
star: $i > $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(one_type,type,
one: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(13,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(56,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(57,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[57]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(43,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[44]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ zero @ B ) ) ),
inference(paramod_ordered,[status(thm)],[58,45]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( one != zero )
| ( A != B ) ),
inference(simp,[status(thm)],[79]) ).
thf(83,plain,
! [A: $i] :
( ( A = zero )
| ( one != zero ) ),
inference(simp,[status(thm)],[81]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) )
= ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) )
= ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i] :
( ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) )
= ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(95,plain,
! [A: $i] :
( ( A
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,23]) ).
thf(105,plain,
( ( ( star @ sk2 )
!= one )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(110,plain,
( ( star @ sk2 )
!= one ),
inference(simp,[status(thm)],[105]) ).
thf(2953,plain,
! [A: $i] :
( ( one != zero )
| ( A
!= ( star @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[83,110]) ).
thf(2954,plain,
one != zero,
inference(pattern_uni,[status(thm)],[2953:[bind(A,$thf( star @ sk2 ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
thf(67,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(68,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [A: $i] :
( ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one )
= ( strong_iteration @ A ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(10,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
thf(49,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(24,plain,
! [A: $i,B: $i,C: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ A ) @ B )
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[51,26]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( addition @ ( star @ B ) @ A )
= ( addition @ one @ ( addition @ ( multiplication @ B @ ( star @ B ) ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( multiplication @ G @ ( star @ G ) )),bind(D,$thf( one ))]]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( addition @ ( star @ B ) @ A )
= ( addition @ one @ ( addition @ ( multiplication @ B @ ( star @ B ) ) @ A ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(4,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
thf(27,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[28]) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ A @ A )
!= ( addition @ ( addition @ D @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,26]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ ( addition @ A @ B ) ) )
= ( addition @ A @ B ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( addition @ G @ H )),bind(B,$thf( addition @ G @ H )),bind(C,$thf( H )),bind(D,$thf( G ))]]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ ( addition @ A @ B ) ) )
= ( addition @ A @ B ) ),
inference(simp,[status(thm)],[128]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ A )
= ( star @ B ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,51]) ).
thf(148,plain,
( ( addition @ one @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[148,26]) ).
thf(196,plain,
! [A: $i] :
( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
= ( addition @ ( star @ one ) @ A ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( A )),bind(B,$thf( star @ one )),bind(C,$thf( one ))]]) ).
thf(4115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
= ( addition @ ( star @ one ) @ C ) )
| ( ( addition @ A @ ( addition @ B @ ( addition @ A @ B ) ) )
!= ( addition @ one @ ( addition @ ( star @ one ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[139,196]) ).
thf(4116,plain,
( ( addition @ ( star @ one ) @ ( addition @ one @ ( star @ one ) ) )
= ( addition @ one @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[4115:[bind(A,$thf( one )),bind(B,$thf( star @ one )),bind(C,$thf( addition @ one @ ( star @ one ) ))]]) ).
thf(4578,plain,
( ( addition @ ( star @ one ) @ ( star @ one ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[4116,148]) ).
thf(6251,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ ( multiplication @ B @ ( star @ B ) ) @ A ) )
= ( star @ one ) )
| ( ( addition @ ( star @ B ) @ A )
!= ( addition @ ( star @ one ) @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,4578]) ).
thf(6252,plain,
( ( addition @ one @ ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[6251:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(6728,plain,
( ( addition @ one @ ( addition @ ( star @ one ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[6252,58]) ).
thf(6862,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ one @ ( addition @ ( multiplication @ B @ ( star @ B ) ) @ A ) ) )
= ( star @ one ) )
| ( ( addition @ ( star @ B ) @ A )
!= ( addition @ ( star @ one ) @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,6728]) ).
thf(6863,plain,
( ( addition @ one @ ( addition @ one @ ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( star @ one ) ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[6862:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ A @ A )
!= ( addition @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,26]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( addition @ A @ ( addition @ A @ B ) )
= ( addition @ A @ B ) ),
inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(14341,plain,
( ( addition @ one @ ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[6863,130]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(14490,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ one ) )
| ( ( addition @ one @ ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( star @ one ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14341,35]) ).
thf(14491,plain,
( ( addition @ ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( star @ one ) ) @ one )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[14490:[bind(A,$thf( one )),bind(B,$thf( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( star @ one ) ))]]) ).
thf(16608,plain,
( ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( addition @ ( star @ one ) @ one ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[14491,26]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
=> ( ( addition @ A @ B )
= B ) )
& ( ( ( addition @ A @ B )
= B )
=> ( leq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
( ! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( ( addition @ A @ B )
= B ) )
& ! [A: $i,B: $i] :
( ( ( addition @ A @ B )
= B )
=> ( leq @ A @ B ) ) ),
inference(miniscope,[status(thm)],[36]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[37]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[40]) ).
thf(3852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= D )
| ( leq @ C @ D )
| ( ( addition @ A @ ( addition @ A @ B ) )
!= ( addition @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[130,41]) ).
thf(3853,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= ( addition @ A @ B ) )
| ( leq @ A @ ( addition @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[3852:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( addition @ E @ F ))]]) ).
thf(4015,plain,
! [B: $i,A: $i] : ( leq @ A @ ( addition @ A @ B ) ),
inference(simp,[status(thm)],[3853]) ).
thf(16631,plain,
! [B: $i,A: $i] :
( ( leq @ A @ ( star @ one ) )
| ( ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( addition @ ( star @ one ) @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16608,4015]) ).
thf(16632,plain,
leq @ ( multiplication @ one @ ( star @ one ) ) @ ( star @ one ),
inference(pattern_uni,[status(thm)],[16631:[bind(A,$thf( multiplication @ one @ ( star @ one ) )),bind(B,$thf( addition @ ( star @ one ) @ one ))]]) ).
thf(17094,plain,
leq @ ( star @ one ) @ ( star @ one ),
inference(rewrite,[status(thm)],[16632,58]) ).
thf(14,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
thf(59,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(60,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(61,plain,
! [A: $i] :
( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
= ( strong_iteration @ A ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ),
inference(cnf,[status(esa)],[37]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(5,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(30,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( B = C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[42,32]) ).
thf(462,plain,
! [A: $i] :
( ~ ( leq @ A @ zero )
| ( zero = A ) ),
inference(pattern_uni,[status(thm)],[461:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( star @ A )
!= C )
| ( leq @ B @ C )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[51,41]) ).
thf(427,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( star @ A ) )
!= ( star @ A ) )
| ( leq @ one @ ( multiplication @ A @ ( star @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[426:[bind(A,$thf( F )),bind(B,$thf( one )),bind(C,$thf( multiplication @ F @ ( star @ F ) ))]]) ).
thf(432,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( star @ A ) )
!= ( star @ A ) )
| ( leq @ one @ ( multiplication @ A @ ( star @ A ) ) ) ),
inference(simp,[status(thm)],[427]) ).
thf(17897,plain,
! [B: $i,A: $i] :
( ( A
!= ( star @ B ) )
| ( leq @ one @ ( multiplication @ B @ ( star @ B ) ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,432]) ).
thf(17898,plain,
( ( ( star @ one )
!= ( star @ one ) )
| ( leq @ one @ ( multiplication @ one @ ( star @ one ) ) ) ),
inference(pattern_uni,[status(thm)],[17897:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(17909,plain,
leq @ one @ ( multiplication @ one @ ( star @ one ) ),
inference(simp,[status(thm)],[17898]) ).
thf(17917,plain,
leq @ one @ ( star @ one ),
inference(rewrite,[status(thm)],[17909,58]) ).
thf(19931,plain,
! [A: $i] :
( ~ ( leq @ A @ zero )
| ( A != one ) ),
inference(paramod_ordered,[status(thm)],[462,2954]) ).
thf(19932,plain,
~ ( leq @ one @ zero ),
inference(pattern_uni,[status(thm)],[19931:[bind(A,$thf( one ))]]) ).
thf(21113,plain,
( ( leq @ one @ ( star @ one ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[17917,19932]) ).
thf(21145,plain,
( ( one != one )
| ( ( star @ one )
!= zero ) ),
inference(simp,[status(thm)],[21113]) ).
thf(21168,plain,
( ( star @ one )
!= zero ),
inference(simp,[status(thm)],[21145]) ).
thf(21243,plain,
! [A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( star @ one ) ) ),
inference(paramod_ordered,[status(thm)],[462,21168]) ).
thf(21244,plain,
~ ( leq @ ( star @ one ) @ zero ),
inference(pattern_uni,[status(thm)],[21243:[bind(A,$thf( star @ one ))]]) ).
thf(21271,plain,
! [B: $i,A: $i] :
( ( leq @ A @ ( addition @ A @ B ) )
!= ( leq @ ( star @ one ) @ zero ) ),
inference(paramod_ordered,[status(thm)],[4015,21244]) ).
thf(21325,plain,
! [B: $i,A: $i] :
( ( A
!= ( star @ one ) )
| ( ( addition @ A @ B )
!= zero ) ),
inference(simp,[status(thm)],[21271]) ).
thf(21340,plain,
! [A: $i] :
( ( addition @ ( star @ one ) @ A )
!= zero ),
inference(simp,[status(thm)],[21325]) ).
thf(23254,plain,
! [B: $i,A: $i] :
( ( ( strong_iteration @ A )
!= zero )
| ( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,21340]) ).
thf(23255,plain,
( ( strong_iteration @ one )
!= zero ),
inference(pattern_uni,[status(thm)],[23254:[bind(A,$thf( one )),bind(B,$thf( multiplication @ ( strong_iteration @ one ) @ zero ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(64,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(65,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[65]) ).
thf(93,plain,
! [A: $i] :
( ( A
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,23]) ).
thf(100,plain,
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one ) ),
inference(simp,[status(thm)],[93]) ).
thf(870,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,100]) ).
thf(877,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one )
| ( A
!= ( star @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[870]) ).
thf(893,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[877]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ zero )
= ( star @ B ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[45,51]) ).
thf(152,plain,
( ( addition @ one @ zero )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( star @ zero )),bind(B,$thf( zero ))]]) ).
thf(172,plain,
( ( star @ zero )
= one ),
inference(rewrite,[status(thm)],[152,32]) ).
thf(6189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ C @ ( addition @ ( star @ B ) @ A ) )
| ( ( addition @ one @ ( addition @ ( multiplication @ B @ ( star @ B ) ) @ A ) )
!= ( addition @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[168,4015]) ).
thf(6190,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( star @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[6189:[bind(A,$thf( F )),bind(B,$thf( I )),bind(C,$thf( one )),bind(D,$thf( addition @ ( multiplication @ I @ ( star @ I ) ) @ F ))]]) ).
thf(6562,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( star @ B ) @ A ) ),
inference(simp,[status(thm)],[6190]) ).
thf(8768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ B @ A ) )
| ( ( addition @ A @ B )
!= ( addition @ ( star @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,6562]) ).
thf(8769,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( star @ B ) ) ),
inference(pattern_uni,[status(thm)],[8768:[bind(A,$thf( star @ E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E ))]]) ).
thf(8807,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( star @ B ) ) ),
inference(simp,[status(thm)],[8769]) ).
thf(9723,plain,
! [B: $i,A: $i] :
( ( leq @ one @ ( addition @ A @ one ) )
| ( ( star @ zero )
!= ( star @ B ) ) ),
inference(paramod_ordered,[status(thm)],[172,8807]) ).
thf(9724,plain,
! [A: $i] : ( leq @ one @ ( addition @ A @ one ) ),
inference(pattern_uni,[status(thm)],[9723:[bind(A,$thf( A )),bind(B,$thf( zero ))]]) ).
thf(9851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ D @ one ) ) ),
inference(paramod_ordered,[status(thm)],[26,9724]) ).
thf(9852,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( addition @ B @ one ) ) ),
inference(pattern_uni,[status(thm)],[9851:[bind(A,$thf( one )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( addition @ E @ F ))]]) ).
thf(9919,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( addition @ B @ one ) ) ),
inference(simp,[status(thm)],[9852]) ).
thf(10645,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ B @ ( strong_iteration @ A ) ) )
| ( ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one )
!= ( addition @ C @ one ) ) ),
inference(paramod_ordered,[status(thm)],[69,9919]) ).
thf(10646,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( strong_iteration @ B ) ) ),
inference(pattern_uni,[status(thm)],[10645:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( multiplication @ F @ ( strong_iteration @ F ) ))]]) ).
thf(10812,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( strong_iteration @ B ) ) ),
inference(simp,[status(thm)],[10646]) ).
thf(651,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ A @ B ) )
= ( addition @ ( star @ one ) @ C ) )
| ( ( addition @ B @ A )
!= ( addition @ ( star @ one ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,196]) ).
thf(652,plain,
! [A: $i] :
( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
= ( addition @ ( star @ one ) @ A ) ),
inference(pattern_uni,[status(thm)],[651:[bind(A,$thf( A )),bind(B,$thf( star @ one )),bind(C,$thf( A ))]]) ).
thf(21110,plain,
! [A: $i] :
( ( leq @ one @ ( addition @ A @ one ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[9724,19932]) ).
thf(21134,plain,
! [A: $i] :
( ( one != one )
| ( ( addition @ A @ one )
!= zero ) ),
inference(simp,[status(thm)],[21110]) ).
thf(21158,plain,
! [A: $i] :
( ( addition @ A @ one )
!= zero ),
inference(simp,[status(thm)],[21134]) ).
thf(21530,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( addition @ B @ one ) ) ),
inference(paramod_ordered,[status(thm)],[462,21158]) ).
thf(21531,plain,
! [A: $i] :
~ ( leq @ ( addition @ A @ one ) @ zero ),
inference(pattern_uni,[status(thm)],[21530:[bind(A,$thf( addition @ C @ one )),bind(B,$thf( C ))]]) ).
thf(21594,plain,
! [A: $i] :
~ ( leq @ ( addition @ A @ one ) @ zero ),
inference(simp,[status(thm)],[21531]) ).
thf(23660,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( ( leq @ A @ B )
!= ( leq @ ( addition @ C @ one ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[41,21594]) ).
thf(23661,plain,
! [A: $i] :
( ( addition @ ( addition @ A @ one ) @ zero )
!= zero ),
inference(pattern_uni,[status(thm)],[23660:[bind(A,$thf( addition @ D @ one )),bind(B,$thf( zero )),bind(C,$thf( D ))]]) ).
thf(23829,plain,
! [A: $i] :
( ( addition @ ( addition @ A @ one ) @ zero )
!= zero ),
inference(simp,[status(thm)],[23661]) ).
thf(28257,plain,
! [A: $i] :
( ( addition @ A @ ( addition @ one @ zero ) )
!= zero ),
inference(rewrite,[status(thm)],[23829,26]) ).
thf(36045,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
!= zero )
| ( ( addition @ ( star @ one ) @ A )
!= ( addition @ B @ ( addition @ one @ zero ) ) ) ),
inference(paramod_ordered,[status(thm)],[652,28257]) ).
thf(36046,plain,
( ( addition @ one @ ( addition @ ( addition @ one @ zero ) @ ( star @ one ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[36045:[bind(A,$thf( addition @ one @ zero )),bind(B,$thf( star @ one ))]]) ).
thf(137,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( addition @ C @ ( addition @ B @ A ) ) @ D )
= ( addition @ F @ ( addition @ E @ D ) ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[26,26]) ).
thf(138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ ( addition @ D @ A ) ) @ B )
= ( addition @ ( addition @ C @ D ) @ ( addition @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( addition @ G @ H ))]]) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ ( addition @ D @ A ) ) @ B )
= ( addition @ ( addition @ C @ D ) @ ( addition @ A @ B ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(4761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ ( addition @ D @ A ) @ B ) )
= ( addition @ C @ ( addition @ D @ ( addition @ A @ B ) ) ) ),
inference(rewrite,[status(thm)],[142,26]) ).
thf(44391,plain,
( ( addition @ one @ ( addition @ one @ ( addition @ zero @ ( star @ one ) ) ) )
!= zero ),
inference(rewrite,[status(thm)],[36046,4761]) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
!= C )
| ( leq @ B @ C )
| ( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[196,41]) ).
thf(630,plain,
! [A: $i] :
( ( ( addition @ ( star @ one ) @ A )
!= ( addition @ ( star @ one ) @ A ) )
| ( leq @ one @ ( addition @ ( star @ one ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[629:[bind(A,$thf( E )),bind(B,$thf( one )),bind(C,$thf( addition @ ( star @ one ) @ E ))]]) ).
thf(712,plain,
! [A: $i] : ( leq @ one @ ( addition @ ( star @ one ) @ A ) ),
inference(simp,[status(thm)],[630]) ).
thf(1229,plain,
! [B: $i,A: $i] :
( ( leq @ one @ ( strong_iteration @ A ) )
| ( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,712]) ).
thf(1230,plain,
leq @ one @ ( strong_iteration @ one ),
inference(pattern_uni,[status(thm)],[1229:[bind(A,$thf( one )),bind(B,$thf( multiplication @ ( strong_iteration @ one ) @ zero ))]]) ).
thf(1301,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ( ( leq @ one @ ( strong_iteration @ one ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1230,42]) ).
thf(1302,plain,
( ( addition @ one @ ( strong_iteration @ one ) )
= ( strong_iteration @ one ) ),
inference(pattern_uni,[status(thm)],[1301:[bind(A,$thf( one )),bind(B,$thf( strong_iteration @ one ))]]) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( strong_iteration @ one ) )
| ( ( addition @ one @ ( strong_iteration @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1302,35]) ).
thf(1331,plain,
( ( addition @ ( strong_iteration @ one ) @ one )
= ( strong_iteration @ one ) ),
inference(pattern_uni,[status(thm)],[1330:[bind(A,$thf( one )),bind(B,$thf( strong_iteration @ one ))]]) ).
thf(4246,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ ( addition @ B @ ( strong_iteration @ one ) ) )
= ( addition @ A @ B ) )
| ( ( addition @ ( strong_iteration @ one ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1331,139]) ).
thf(4247,plain,
( ( addition @ ( strong_iteration @ one ) @ ( addition @ one @ ( strong_iteration @ one ) ) )
= ( addition @ ( strong_iteration @ one ) @ one ) ),
inference(pattern_uni,[status(thm)],[4246:[bind(A,$thf( strong_iteration @ one )),bind(B,$thf( one ))]]) ).
thf(5131,plain,
( ( addition @ ( strong_iteration @ one ) @ ( strong_iteration @ one ) )
= ( strong_iteration @ one ) ),
inference(rewrite,[status(thm)],[4247,1331,1302]) ).
thf(5378,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ B @ ( star @ A ) )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[51,4015]) ).
thf(5379,plain,
! [A: $i] : ( leq @ one @ ( star @ A ) ),
inference(pattern_uni,[status(thm)],[5378:[bind(A,$thf( F )),bind(B,$thf( one )),bind(C,$thf( multiplication @ F @ ( star @ F ) ))]]) ).
thf(5385,plain,
! [A: $i] : ( leq @ one @ ( star @ A ) ),
inference(simp,[status(thm)],[5379]) ).
thf(23281,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[462,21340]) ).
thf(23282,plain,
! [A: $i] :
~ ( leq @ ( addition @ ( star @ one ) @ A ) @ zero ),
inference(pattern_uni,[status(thm)],[23281:[bind(A,$thf( addition @ ( star @ one ) @ D )),bind(B,$thf( D ))]]) ).
thf(23375,plain,
! [A: $i] :
~ ( leq @ ( addition @ ( star @ one ) @ A ) @ zero ),
inference(simp,[status(thm)],[23282]) ).
thf(26909,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( ( leq @ A @ B )
!= ( leq @ ( addition @ ( star @ one ) @ C ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[41,23375]) ).
thf(26910,plain,
! [A: $i] :
( ( addition @ ( addition @ ( star @ one ) @ A ) @ zero )
!= zero ),
inference(pattern_uni,[status(thm)],[26909:[bind(A,$thf( addition @ ( star @ one ) @ E )),bind(B,$thf( zero )),bind(C,$thf( E ))]]) ).
thf(27044,plain,
! [A: $i] :
( ( addition @ ( addition @ ( star @ one ) @ A ) @ zero )
!= zero ),
inference(simp,[status(thm)],[26910]) ).
thf(56771,plain,
! [A: $i] :
( ( addition @ ( star @ one ) @ ( addition @ A @ zero ) )
!= zero ),
inference(rewrite,[status(thm)],[27044,26]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
=> ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction1) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
=> ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
| ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
inference(cnf,[status(esa)],[52]) ).
thf(737,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( star @ one ) @ C )
| ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ( ( addition @ ( multiplication @ A @ C ) @ B )
!= ( addition @ one @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[148,53]) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ~ ( leq @ ( star @ one ) @ C )
| ( ( multiplication @ A @ C )
!= one )
| ( B
!= ( star @ one ) ) ),
inference(simp,[status(thm)],[737]) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ ( star @ one ) ) @ B )
| ~ ( leq @ ( star @ one ) @ B )
| ( ( multiplication @ A @ B )
!= one ) ),
inference(simp,[status(thm)],[759]) ).
thf(798,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ A @ B ) )
| ( ( addition @ B @ A )
!= ( addition @ ( star @ one ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,712]) ).
thf(799,plain,
! [A: $i] : ( leq @ one @ ( addition @ A @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( A )),bind(B,$thf( star @ one )),bind(C,$thf( A ))]]) ).
thf(841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ D @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,799]) ).
thf(842,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( addition @ B @ ( star @ one ) ) ) ),
inference(pattern_uni,[status(thm)],[841:[bind(A,$thf( star @ one )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( addition @ E @ F ))]]) ).
thf(854,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( addition @ B @ ( star @ one ) ) ) ),
inference(simp,[status(thm)],[842]) ).
thf(917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ B @ A ) )
| ( ( addition @ A @ B )
!= ( addition @ C @ ( addition @ D @ ( star @ one ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,854]) ).
thf(918,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( addition @ B @ ( star @ one ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[917:[bind(A,$thf( A )),bind(B,$thf( addition @ E @ ( star @ one ) )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(954,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( addition @ B @ ( star @ one ) ) @ A ) ),
inference(simp,[status(thm)],[918]) ).
thf(1097,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ B @ ( addition @ ( star @ one ) @ A ) ) ),
inference(rewrite,[status(thm)],[954,26]) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ C @ ( strong_iteration @ A ) ) )
| ( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,1097]) ).
thf(1246,plain,
! [A: $i] : ( leq @ one @ ( addition @ A @ ( strong_iteration @ one ) ) ),
inference(pattern_uni,[status(thm)],[1245:[bind(A,$thf( one )),bind(B,$thf( multiplication @ ( strong_iteration @ one ) @ zero )),bind(C,$thf( C ))]]) ).
thf(1279,plain,
! [A: $i] : ( leq @ one @ ( addition @ A @ ( strong_iteration @ one ) ) ),
inference(simp,[status(thm)],[1246]) ).
thf(1862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ D @ ( strong_iteration @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,1279]) ).
thf(1863,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( addition @ B @ ( strong_iteration @ one ) ) ) ),
inference(pattern_uni,[status(thm)],[1862:[bind(A,$thf( strong_iteration @ one )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( addition @ E @ F ))]]) ).
thf(1883,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ A @ ( addition @ B @ ( strong_iteration @ one ) ) ) ),
inference(simp,[status(thm)],[1863]) ).
thf(3464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ B @ A ) )
| ( ( addition @ A @ B )
!= ( addition @ C @ ( addition @ D @ ( strong_iteration @ one ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,1883]) ).
thf(3465,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( addition @ B @ ( strong_iteration @ one ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[3464:[bind(A,$thf( A )),bind(B,$thf( addition @ E @ ( strong_iteration @ one ) )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(3520,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( addition @ B @ ( strong_iteration @ one ) ) @ A ) ),
inference(simp,[status(thm)],[3465]) ).
thf(3566,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ B @ ( addition @ ( strong_iteration @ one ) @ A ) ) ),
inference(rewrite,[status(thm)],[3520,26]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( star @ D ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ one @ ( multiplication @ D @ ( star @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,51]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( star @ D ) )
| ( ( addition @ C @ B )
!= one )
| ( A
!= ( multiplication @ D @ ( star @ D ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ ( multiplication @ C @ ( star @ C ) ) ) )
= ( star @ C ) )
| ( ( addition @ B @ A )
!= one ) ),
inference(simp,[status(thm)],[158]) ).
thf(21087,plain,
! [B: $i,A: $i] :
( ( leq @ one @ ( addition @ ( star @ B ) @ A ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[6562,19932]) ).
thf(21124,plain,
! [B: $i,A: $i] :
( ( one != one )
| ( ( addition @ ( star @ B ) @ A )
!= zero ) ),
inference(simp,[status(thm)],[21087]) ).
thf(21149,plain,
! [B: $i,A: $i] :
( ( addition @ ( star @ B ) @ A )
!= zero ),
inference(simp,[status(thm)],[21124]) ).
thf(293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( addition @ E @ ( addition @ D @ C ) ) )
| ( ( addition @ A @ B )
!= ( addition @ ( addition @ E @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,26]) ).
thf(294,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ B @ ( addition @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( addition @ F @ G )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(311,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ B @ ( addition @ C @ A ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(14346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ ( addition @ B @ C ) )
= ( star @ one ) )
| ( ( addition @ one @ ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( star @ one ) ) )
!= ( addition @ B @ ( addition @ C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[14341,311]) ).
thf(14347,plain,
( ( addition @ ( star @ one ) @ ( addition @ one @ ( multiplication @ one @ ( star @ one ) ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[14346:[bind(A,$thf( star @ one )),bind(B,$thf( one )),bind(C,$thf( multiplication @ one @ ( star @ one ) ))]]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ one ) )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[148,35]) ).
thf(282,plain,
( ( addition @ ( star @ one ) @ one )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( one )),bind(B,$thf( star @ one ))]]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ ( star @ one ) @ one )
!= ( addition @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[282,26]) ).
thf(382,plain,
! [A: $i] :
( ( addition @ ( star @ one ) @ ( addition @ one @ A ) )
= ( addition @ ( star @ one ) @ A ) ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( star @ one ))]]) ).
thf(15263,plain,
( ( addition @ ( star @ one ) @ ( multiplication @ one @ ( star @ one ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[14347,382]) ).
thf(874,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[58,100]) ).
thf(883,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one )
| ( ( star @ sk1 )
!= one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[874]) ).
thf(890,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one )
| ( ( star @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[883]) ).
thf(10558,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[172,890]) ).
thf(10570,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= one )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[10558]) ).
thf(10621,plain,
! [A: $i] :
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ A )
!= one )
| ( sk1 != zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,10570]) ).
thf(10627,plain,
! [A: $i] :
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ A )
!= one )
| ( sk1 != zero )
| ( A
!= ( star @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[10621]) ).
thf(10633,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= one )
| ( sk1 != zero )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[10627]) ).
thf(10859,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ one )
!= one )
| ( sk1 != zero )
| ( sk2 != one )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[172,10633]) ).
thf(10862,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ one )
!= one )
| ( sk1 != zero )
| ( sk2 != one )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[10859]) ).
thf(10864,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ one )
!= one )
| ( sk1 != zero )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[10862]) ).
thf(738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ zero @ C ) @ D )
| ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[45,53]) ).
thf(739,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( addition @ zero @ B ) @ A )
| ( leq @ ( multiplication @ ( star @ zero ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[738:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(764,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( addition @ zero @ B ) @ A )
| ( leq @ ( multiplication @ ( star @ zero ) @ B ) @ A ) ),
inference(simp,[status(thm)],[739]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[35,32]) ).
thf(272,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(52152,plain,
! [B: $i,A: $i] :
( ~ ( leq @ B @ A )
| ( leq @ ( multiplication @ one @ B ) @ A ) ),
inference(rewrite,[status(thm)],[764,272,172]) ).
thf(173,plain,
( ( star @ sk2 )
!= ( star @ zero ) ),
inference(paramod_ordered,[status(thm)],[172,110]) ).
thf(183,plain,
sk2 != zero,
inference(simp,[status(thm)],[173]) ).
thf(20659,plain,
! [A: $i] :
( ~ ( leq @ A @ zero )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[462,183]) ).
thf(20660,plain,
~ ( leq @ sk2 @ zero ),
inference(pattern_uni,[status(thm)],[20659:[bind(A,$thf( sk2 ))]]) ).
thf(21173,plain,
! [B: $i,A: $i] :
( ( leq @ A @ ( addition @ A @ B ) )
!= ( leq @ sk2 @ zero ) ),
inference(paramod_ordered,[status(thm)],[4015,20660]) ).
thf(21226,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( ( addition @ A @ B )
!= zero ) ),
inference(simp,[status(thm)],[21173]) ).
thf(21239,plain,
! [A: $i] :
( ( addition @ sk2 @ A )
!= zero ),
inference(simp,[status(thm)],[21226]) ).
thf(21692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= zero )
| ( ( addition @ B @ A )
!= ( addition @ sk2 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,21239]) ).
thf(21693,plain,
! [A: $i] :
( ( addition @ A @ sk2 )
!= zero ),
inference(pattern_uni,[status(thm)],[21692:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(22610,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( addition @ B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[462,21693]) ).
thf(22611,plain,
! [A: $i] :
~ ( leq @ ( addition @ A @ sk2 ) @ zero ),
inference(pattern_uni,[status(thm)],[22610:[bind(A,$thf( addition @ C @ sk2 )),bind(B,$thf( C ))]]) ).
thf(22702,plain,
! [A: $i] :
~ ( leq @ ( addition @ A @ sk2 ) @ zero ),
inference(simp,[status(thm)],[22611]) ).
thf(25328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( ( leq @ A @ B )
!= ( leq @ ( addition @ C @ sk2 ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[41,22702]) ).
thf(25329,plain,
! [A: $i] :
( ( addition @ ( addition @ A @ sk2 ) @ zero )
!= zero ),
inference(pattern_uni,[status(thm)],[25328:[bind(A,$thf( addition @ D @ sk2 )),bind(B,$thf( zero )),bind(C,$thf( D ))]]) ).
thf(25509,plain,
! [A: $i] :
( ( addition @ ( addition @ A @ sk2 ) @ zero )
!= zero ),
inference(simp,[status(thm)],[25329]) ).
thf(30707,plain,
! [A: $i] :
( ( addition @ A @ ( addition @ sk2 @ zero ) )
!= zero ),
inference(rewrite,[status(thm)],[25509,26]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( ( star @ one )
!= B )
| ( leq @ A @ B )
| ( ( addition @ ( star @ one ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[282,41]) ).
thf(413,plain,
( ( ( star @ one )
!= one )
| ( leq @ ( star @ one ) @ one ) ),
inference(pattern_uni,[status(thm)],[412:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(455,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( B
= ( star @ one ) )
| ( ( addition @ A @ B )
!= ( addition @ ( star @ one ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[42,282]) ).
thf(456,plain,
( ~ ( leq @ ( star @ one ) @ one )
| ( ( star @ one )
= one ) ),
inference(pattern_uni,[status(thm)],[455:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(18551,plain,
( ~ ( leq @ ( star @ one ) @ one )
| ( ( star @ sk2 )
!= ( star @ one ) ) ),
inference(paramod_ordered,[status(thm)],[456,110]) ).
thf(18792,plain,
( ~ ( leq @ ( star @ one ) @ one )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[18551]) ).
thf(19026,plain,
( ( ( star @ one )
!= one )
| ( sk2 != one )
| ( ( leq @ ( star @ one ) @ one )
!= ( leq @ ( star @ one ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[413,18792]) ).
thf(19027,plain,
( ( ( star @ one )
!= one )
| ( sk2 != one ) ),
inference(pattern_uni,[status(thm)],[19026:[]]) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( addition @ ( star @ one ) @ A ) @ B )
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
!= ( addition @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[196,26]) ).
thf(659,plain,
! [B: $i,A: $i] :
( ( addition @ one @ ( addition @ ( addition @ ( star @ one ) @ B ) @ A ) )
= ( addition @ ( addition @ ( star @ one ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[658:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( addition @ ( star @ one ) @ F )),bind(D,$thf( one ))]]) ).
thf(692,plain,
! [B: $i,A: $i] :
( ( addition @ one @ ( addition @ ( addition @ ( star @ one ) @ B ) @ A ) )
= ( addition @ ( addition @ ( star @ one ) @ B ) @ A ) ),
inference(simp,[status(thm)],[659]) ).
thf(39016,plain,
! [B: $i,A: $i] :
( ( addition @ one @ ( addition @ ( star @ one ) @ ( addition @ B @ A ) ) )
= ( addition @ ( star @ one ) @ ( addition @ B @ A ) ) ),
inference(rewrite,[status(thm)],[692,4761,26]) ).
thf(6819,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ one ) )
| ( ( addition @ one @ ( addition @ ( star @ one ) @ ( star @ one ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6728,35]) ).
thf(6820,plain,
( ( addition @ ( addition @ ( star @ one ) @ ( star @ one ) ) @ one )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[6819:[bind(A,$thf( one )),bind(B,$thf( addition @ ( star @ one ) @ ( star @ one ) ))]]) ).
thf(7980,plain,
( ( addition @ ( star @ one ) @ ( addition @ ( star @ one ) @ one ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[6820,26]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( star @ one ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ ( star @ one ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[26,282]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( star @ one ) )
| ( ( addition @ C @ B )
!= ( star @ one ) )
| ( A != one ) ),
inference(simp,[status(thm)],[383]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ one ) )
= ( star @ one ) )
| ( ( addition @ B @ A )
!= ( star @ one ) ) ),
inference(simp,[status(thm)],[392]) ).
thf(15672,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ one ) )
= ( star @ one ) )
| ( ( addition @ ( star @ one ) @ ( addition @ ( star @ one ) @ one ) )
!= ( addition @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7980,402]) ).
thf(15673,plain,
( ( addition @ ( star @ one ) @ ( addition @ ( addition @ ( star @ one ) @ one ) @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[15672:[bind(A,$thf( addition @ ( star @ one ) @ one )),bind(B,$thf( star @ one ))]]) ).
thf(17934,plain,
( ( addition @ ( star @ one ) @ ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[15673,4761]) ).
thf(17939,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ ( addition @ B @ C ) )
= ( star @ one ) )
| ( ( addition @ ( star @ one ) @ ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) )
!= ( addition @ B @ ( addition @ C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[17934,311]) ).
thf(17940,plain,
( ( addition @ ( addition @ one @ one ) @ ( addition @ ( star @ one ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[17939:[bind(A,$thf( addition @ one @ one )),bind(B,$thf( star @ one )),bind(C,$thf( star @ one ))]]) ).
thf(34633,plain,
( ( addition @ one @ ( addition @ one @ ( addition @ ( star @ one ) @ ( star @ one ) ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[17940,26]) ).
thf(654,plain,
! [A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( star @ one ) )
| ( ( addition @ ( star @ one ) @ one )
!= ( addition @ one @ ( addition @ ( star @ one ) @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,196]) ).
thf(670,plain,
! [A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( star @ one ) )
| ( ( star @ one )
!= one )
| ( ( addition @ ( star @ one ) @ A )
!= one ) ),
inference(simp,[status(thm)],[654]) ).
thf(295,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( addition @ B @ A ) @ C )
= ( addition @ E @ ( addition @ D @ C ) ) )
| ( ( addition @ A @ B )
!= ( addition @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35,26]) ).
thf(296,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ B @ A ) @ C )
= ( addition @ A @ ( addition @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(11382,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ B @ ( addition @ A @ C ) )
= ( addition @ A @ ( addition @ B @ C ) ) ),
inference(rewrite,[status(thm)],[296,26]) ).
thf(35521,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
!= zero )
| ( ( addition @ ( star @ one ) @ A )
!= ( addition @ B @ ( addition @ sk2 @ zero ) ) ) ),
inference(paramod_ordered,[status(thm)],[652,30707]) ).
thf(35522,plain,
( ( addition @ one @ ( addition @ ( addition @ sk2 @ zero ) @ ( star @ one ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[35521:[bind(A,$thf( addition @ sk2 @ zero )),bind(B,$thf( star @ one ))]]) ).
thf(38268,plain,
( ( addition @ one @ ( addition @ sk2 @ ( addition @ zero @ ( star @ one ) ) ) )
!= zero ),
inference(rewrite,[status(thm)],[35522,4761]) ).
thf(38274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ B @ ( addition @ C @ A ) ) )
!= zero )
| ( ( addition @ A @ ( addition @ B @ C ) )
!= ( addition @ sk2 @ ( addition @ zero @ ( star @ one ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,38268]) ).
thf(38275,plain,
( ( addition @ one @ ( addition @ zero @ ( addition @ ( star @ one ) @ sk2 ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[38274:[bind(A,$thf( sk2 )),bind(B,$thf( zero )),bind(C,$thf( star @ one ))]]) ).
thf(44885,plain,
( ( addition @ one @ ( addition @ ( star @ one ) @ sk2 ) )
!= zero ),
inference(rewrite,[status(thm)],[38275,272]) ).
thf(871,plain,
! [A: $i] :
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ A )
!= one )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,100]) ).
thf(882,plain,
! [A: $i] :
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ A )
!= one )
| ( A
!= ( star @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[871]) ).
thf(889,plain,
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= one )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[882]) ).
thf(10237,plain,
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ one )
!= one )
| ( sk2 != one )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[172,889]) ).
thf(10251,plain,
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ one )
!= one )
| ( sk2 != one )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[10237]) ).
thf(21683,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( addition @ sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[462,21239]) ).
thf(21684,plain,
! [A: $i] :
~ ( leq @ ( addition @ sk2 @ A ) @ zero ),
inference(pattern_uni,[status(thm)],[21683:[bind(A,$thf( addition @ sk2 @ D )),bind(B,$thf( D ))]]) ).
thf(21751,plain,
! [A: $i] :
~ ( leq @ ( addition @ sk2 @ A ) @ zero ),
inference(simp,[status(thm)],[21684]) ).
thf(23884,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( ( leq @ A @ B )
!= ( leq @ ( addition @ sk2 @ C ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[41,21751]) ).
thf(23885,plain,
! [A: $i] :
( ( addition @ ( addition @ sk2 @ A ) @ zero )
!= zero ),
inference(pattern_uni,[status(thm)],[23884:[bind(A,$thf( addition @ sk2 @ E )),bind(B,$thf( zero )),bind(C,$thf( E ))]]) ).
thf(24047,plain,
! [A: $i] :
( ( addition @ ( addition @ sk2 @ A ) @ zero )
!= zero ),
inference(simp,[status(thm)],[23885]) ).
thf(28583,plain,
! [A: $i] :
( ( addition @ sk2 @ ( addition @ A @ zero ) )
!= zero ),
inference(rewrite,[status(thm)],[24047,26]) ).
thf(35677,plain,
! [B: $i,A: $i] :
( ( ( addition @ sk2 @ ( addition @ one @ ( addition @ A @ ( star @ one ) ) ) )
!= zero )
| ( ( addition @ ( star @ one ) @ A )
!= ( addition @ B @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[652,28583]) ).
thf(35678,plain,
( ( addition @ sk2 @ ( addition @ one @ ( addition @ zero @ ( star @ one ) ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[35677:[bind(A,$thf( zero )),bind(B,$thf( star @ one ))]]) ).
thf(41969,plain,
( ( addition @ sk2 @ ( addition @ one @ ( star @ one ) ) )
!= zero ),
inference(rewrite,[status(thm)],[35678,272]) ).
thf(41973,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ C @ A ) )
!= zero )
| ( ( addition @ A @ ( addition @ B @ C ) )
!= ( addition @ sk2 @ ( addition @ one @ ( star @ one ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,41969]) ).
thf(41974,plain,
( ( addition @ one @ ( addition @ ( star @ one ) @ sk2 ) )
!= zero ),
inference(pattern_uni,[status(thm)],[41973:[bind(A,$thf( sk2 )),bind(B,$thf( one )),bind(C,$thf( star @ one ))]]) ).
thf(42458,plain,
( ( addition @ ( star @ one ) @ sk2 )
!= zero ),
inference(rewrite,[status(thm)],[41974,196]) ).
thf(660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( star @ one ) @ D ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ one @ ( addition @ ( star @ one ) @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,196]) ).
thf(678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( star @ one ) @ D ) )
| ( ( addition @ C @ B )
!= one )
| ( A
!= ( addition @ ( star @ one ) @ D ) ) ),
inference(simp,[status(thm)],[660]) ).
thf(702,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ ( addition @ ( star @ one ) @ C ) ) )
= ( addition @ ( star @ one ) @ C ) )
| ( ( addition @ B @ A )
!= one ) ),
inference(simp,[status(thm)],[678]) ).
thf(21083,plain,
! [B: $i,A: $i] :
( ( leq @ A @ ( addition @ A @ B ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[4015,19932]) ).
thf(21121,plain,
! [B: $i,A: $i] :
( ( A != one )
| ( ( addition @ A @ B )
!= zero ) ),
inference(simp,[status(thm)],[21083]) ).
thf(21146,plain,
! [A: $i] :
( ( addition @ one @ A )
!= zero ),
inference(simp,[status(thm)],[21121]) ).
thf(21399,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( addition @ one @ B ) ) ),
inference(paramod_ordered,[status(thm)],[462,21146]) ).
thf(21400,plain,
! [A: $i] :
~ ( leq @ ( addition @ one @ A ) @ zero ),
inference(pattern_uni,[status(thm)],[21399:[bind(A,$thf( addition @ one @ D )),bind(B,$thf( D ))]]) ).
thf(21452,plain,
! [A: $i] :
~ ( leq @ ( addition @ one @ A ) @ zero ),
inference(simp,[status(thm)],[21400]) ).
thf(23446,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( ( leq @ A @ B )
!= ( leq @ ( addition @ one @ C ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[41,21452]) ).
thf(23447,plain,
! [A: $i] :
( ( addition @ ( addition @ one @ A ) @ zero )
!= zero ),
inference(pattern_uni,[status(thm)],[23446:[bind(A,$thf( addition @ one @ E )),bind(B,$thf( zero )),bind(C,$thf( E ))]]) ).
thf(23564,plain,
! [A: $i] :
( ( addition @ ( addition @ one @ A ) @ zero )
!= zero ),
inference(simp,[status(thm)],[23447]) ).
thf(27092,plain,
! [A: $i] :
( ( addition @ one @ ( addition @ A @ zero ) )
!= zero ),
inference(rewrite,[status(thm)],[23564,26]) ).
thf(44507,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ B @ ( addition @ C @ A ) ) )
!= zero )
| ( ( addition @ A @ ( addition @ B @ C ) )
!= ( addition @ one @ ( addition @ zero @ ( star @ one ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,44391]) ).
thf(44508,plain,
( ( addition @ one @ ( addition @ zero @ ( addition @ ( star @ one ) @ one ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[44507:[bind(A,$thf( one )),bind(B,$thf( zero )),bind(C,$thf( star @ one ))]]) ).
thf(48170,plain,
( ( addition @ one @ ( addition @ ( star @ one ) @ one ) )
!= zero ),
inference(rewrite,[status(thm)],[44508,272]) ).
thf(5426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ C )
= C )
| ( ( leq @ one @ ( star @ A ) )
!= ( leq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5385,42]) ).
thf(5427,plain,
! [A: $i] :
( ( addition @ one @ ( star @ A ) )
= ( star @ A ) ),
inference(pattern_uni,[status(thm)],[5426:[bind(A,$thf( D )),bind(B,$thf( one )),bind(C,$thf( star @ D ))]]) ).
thf(5436,plain,
! [A: $i] :
( ( addition @ one @ ( star @ A ) )
= ( star @ A ) ),
inference(simp,[status(thm)],[5427]) ).
thf(5771,plain,
! [C: $i,B: $i,A: $i] :
( ( ( star @ A )
= ( addition @ C @ B ) )
| ( ( addition @ one @ ( star @ A ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5436,35]) ).
thf(5772,plain,
! [A: $i] :
( ( addition @ ( star @ A ) @ one )
= ( star @ A ) ),
inference(pattern_uni,[status(thm)],[5771:[bind(A,$thf( D )),bind(B,$thf( one )),bind(C,$thf( star @ D ))]]) ).
thf(5866,plain,
! [A: $i] :
( ( addition @ ( star @ A ) @ one )
= ( star @ A ) ),
inference(simp,[status(thm)],[5772]) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
!= D )
| ( leq @ C @ D )
| ( ( addition @ A @ B )
!= ( addition @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35,41]) ).
thf(421,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
!= B )
| ( leq @ A @ B ) ),
inference(pattern_uni,[status(thm)],[420:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(2001,plain,
! [B: $i,A: $i] :
( ( ( addition @ zero @ one )
= ( strong_iteration @ B ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ B @ ( strong_iteration @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[45,69]) ).
thf(2002,plain,
( ( addition @ zero @ one )
= ( strong_iteration @ zero ) ),
inference(pattern_uni,[status(thm)],[2001:[bind(A,$thf( strong_iteration @ zero )),bind(B,$thf( zero ))]]) ).
thf(2116,plain,
( ( strong_iteration @ zero )
= one ),
inference(rewrite,[status(thm)],[2002,272]) ).
thf(2157,plain,
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( strong_iteration @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[2116,100]) ).
thf(2159,plain,
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[2157]) ).
thf(8693,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,2159]) ).
thf(8712,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero )
| ( A
!= ( star @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[8693]) ).
thf(8717,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[8712]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( multiplication @ A @ ( multiplication @ B @ C ) ) )
= ( star @ D ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ D @ ( star @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,51]) ).
thf(593,plain,
! [B: $i,A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( multiplication @ B @ ( star @ ( multiplication @ A @ B ) ) ) ) )
= ( star @ ( multiplication @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[592:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( star @ ( multiplication @ H @ I ) )),bind(D,$thf( multiplication @ H @ I ))]]) ).
thf(606,plain,
! [B: $i,A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( multiplication @ B @ ( star @ ( multiplication @ A @ B ) ) ) ) )
= ( star @ ( multiplication @ A @ B ) ) ),
inference(simp,[status(thm)],[593]) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,41]) ).
thf(409,plain,
! [A: $i] :
( ( A != A )
| ( leq @ A @ A ) ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(429,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[409]) ).
thf(734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( leq @ A @ A )
!= ( leq @ ( addition @ ( multiplication @ B @ D ) @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[429,53]) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( A
!= ( addition @ ( multiplication @ B @ D ) @ C ) )
| ( A != D ) ),
inference(simp,[status(thm)],[734]) ).
thf(770,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ( ( addition @ ( multiplication @ A @ C ) @ B )
!= C ) ),
inference(simp,[status(thm)],[754]) ).
thf(20,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
thf(76,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( A
= ( star @ B ) )
| ( ( addition @ A @ A )
!= ( addition @ one @ ( multiplication @ B @ ( star @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,51]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( A
= ( star @ B ) )
| ( A != one )
| ( A
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(164,plain,
! [A: $i] :
( ( ( star @ A )
= one )
| ( ( multiplication @ A @ ( star @ A ) )
!= one ) ),
inference(simp,[status(thm)],[160]) ).
thf(96,plain,
! [A: $i] :
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ A ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[58,23]) ).
thf(102,plain,
! [A: $i] :
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ A ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( star @ sk1 )
!= one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[96]) ).
thf(108,plain,
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ sk2 ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( star @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[102]) ).
thf(974,plain,
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ sk2 ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[172,108]) ).
thf(981,plain,
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ sk2 ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[974]) ).
thf(10703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ A @ B )
!= ( addition @ D @ one ) ) ),
inference(paramod_ordered,[status(thm)],[35,9919]) ).
thf(10704,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ B @ ( addition @ one @ A ) ) ),
inference(pattern_uni,[status(thm)],[10703:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(10833,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ B @ ( addition @ one @ A ) ) ),
inference(simp,[status(thm)],[10704]) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ D )
| ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( addition @ zero @ A )
!= ( addition @ ( multiplication @ B @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[272,53]) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ~ ( leq @ A @ D )
| ( ( multiplication @ B @ D )
!= zero )
| ( A != C ) ),
inference(simp,[status(thm)],[751]) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ~ ( leq @ B @ C )
| ( ( multiplication @ A @ C )
!= zero ) ),
inference(simp,[status(thm)],[757]) ).
thf(55084,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ( ( star @ one )
!= C )
| ( ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( addition @ ( star @ one ) @ one ) )
!= ( addition @ ( multiplication @ A @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16608,770]) ).
thf(55085,plain,
( ( leq @ ( multiplication @ ( star @ one ) @ ( addition @ ( star @ one ) @ one ) ) @ ( star @ one ) )
| ( ( star @ one )
!= ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[55084:[bind(A,$thf( one )),bind(B,$thf( addition @ ( star @ one ) @ one )),bind(C,$thf( star @ one ))]]) ).
thf(55377,plain,
leq @ ( multiplication @ ( star @ one ) @ ( addition @ ( star @ one ) @ one ) ) @ ( star @ one ),
inference(simp,[status(thm)],[55085]) ).
thf(1206,plain,
! [A: $i] :
( ( ( addition @ one @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
= ( strong_iteration @ A ) )
| ( ( star @ zero )
!= ( star @ A ) ) ),
inference(paramod_ordered,[status(thm)],[172,61]) ).
thf(1207,plain,
( ( addition @ one @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) )
= ( strong_iteration @ zero ) ),
inference(pattern_uni,[status(thm)],[1206:[bind(A,$thf( zero ))]]) ).
thf(1530,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( strong_iteration @ zero ) )
| ( ( addition @ one @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1207,35]) ).
thf(1531,plain,
( ( addition @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) @ one )
= ( strong_iteration @ zero ) ),
inference(pattern_uni,[status(thm)],[1530:[bind(A,$thf( one )),bind(B,$thf( multiplication @ ( strong_iteration @ zero ) @ zero ))]]) ).
thf(2127,plain,
( ( addition @ ( multiplication @ one @ zero ) @ one )
= one ),
inference(rewrite,[status(thm)],[1531,2116]) ).
thf(2179,plain,
( ( addition @ zero @ one )
= one ),
inference(rewrite,[status(thm)],[2127,58]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( star @ one ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ one @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,148]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( star @ one ) )
| ( ( addition @ C @ B )
!= one )
| ( A
!= ( star @ one ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ ( star @ one ) ) )
= ( star @ one ) )
| ( ( addition @ B @ A )
!= one ) ),
inference(simp,[status(thm)],[202]) ).
thf(8947,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ ( star @ one ) ) )
= ( star @ one ) )
| ( ( addition @ zero @ one )
!= ( addition @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2179,212]) ).
thf(8948,plain,
( ( addition @ zero @ ( addition @ one @ ( star @ one ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[8947:[bind(A,$thf( one )),bind(B,$thf( zero ))]]) ).
thf(9348,plain,
( ( addition @ one @ ( star @ one ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[8948,272]) ).
thf(15818,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ one ) )
= ( star @ one ) )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9348,402]) ).
thf(15819,plain,
( ( addition @ one @ ( addition @ ( star @ one ) @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[15818:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(16234,plain,
( ( addition @ ( star @ one ) @ one )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[15819,196]) ).
thf(57516,plain,
leq @ ( multiplication @ ( star @ one ) @ ( star @ one ) ) @ ( star @ one ),
inference(rewrite,[status(thm)],[55377,16234]) ).
thf(57520,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ( ( leq @ ( multiplication @ ( star @ one ) @ ( star @ one ) ) @ ( star @ one ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57516,42]) ).
thf(57521,plain,
( ( addition @ ( multiplication @ ( star @ one ) @ ( star @ one ) ) @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[57520:[bind(A,$thf( multiplication @ ( star @ one ) @ ( star @ one ) )),bind(B,$thf( star @ one ))]]) ).
thf(667,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( star @ A ) )
= ( addition @ ( star @ one ) @ B ) )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51,196]) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( star @ A ) )
= ( addition @ ( star @ one ) @ B ) )
| ( ( star @ one )
!= one )
| ( ( multiplication @ A @ ( star @ A ) )
!= B ) ),
inference(simp,[status(thm)],[667]) ).
thf(698,plain,
! [A: $i] :
( ( ( addition @ ( star @ one ) @ ( multiplication @ A @ ( star @ A ) ) )
= ( addition @ one @ ( star @ A ) ) )
| ( ( star @ one )
!= one ) ),
inference(simp,[status(thm)],[674]) ).
thf(42635,plain,
! [A: $i] :
( ( ( addition @ ( star @ one ) @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) )
| ( ( star @ one )
!= one ) ),
inference(rewrite,[status(thm)],[698,5436]) ).
thf(875,plain,
! [A: $i] :
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ A )
!= one )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[58,100]) ).
thf(879,plain,
! [A: $i] :
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ A )
!= one )
| ( ( star @ sk1 )
!= one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[875]) ).
thf(894,plain,
( ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one )
| ( ( star @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[879]) ).
thf(94,plain,
! [A: $i] :
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ A ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,23]) ).
thf(106,plain,
! [A: $i] :
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ A ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( A
!= ( star @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[94]) ).
thf(111,plain,
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( star @ sk1 ) ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[106]) ).
thf(3817,plain,
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ one ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( sk2 != one )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[172,111]) ).
thf(3827,plain,
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ one ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( sk2 != one )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[3817]) ).
thf(416,plain,
! [B: $i,A: $i] :
( ( ( star @ one )
!= B )
| ( leq @ A @ B )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[148,41]) ).
thf(417,plain,
( ( ( star @ one )
!= ( star @ one ) )
| ( leq @ one @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[416:[bind(A,$thf( one )),bind(B,$thf( star @ one ))]]) ).
thf(428,plain,
leq @ one @ ( star @ one ),
inference(simp,[status(thm)],[417]) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
!= ( leq @ one @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[428,53]) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ( ( addition @ ( multiplication @ A @ C ) @ B )
!= one )
| ( C
!= ( star @ one ) ) ),
inference(simp,[status(thm)],[727]) ).
thf(778,plain,
! [B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ ( star @ one ) )
| ( ( addition @ ( multiplication @ A @ ( star @ one ) ) @ B )
!= one ) ),
inference(simp,[status(thm)],[760]) ).
thf(729,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ ( multiplication @ ( star @ C ) @ D ) @ E )
| ( ( leq @ A @ B )
!= ( leq @ ( addition @ ( multiplication @ C @ E ) @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[41,53]) ).
thf(730,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( addition @ ( multiplication @ C @ A ) @ B ) @ A )
!= A )
| ( leq @ ( multiplication @ ( star @ C ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[729:[bind(A,$thf( addition @ ( multiplication @ H @ B ) @ G )),bind(B,$thf( B )),bind(C,$thf( H )),bind(D,$thf( G )),bind(E,$thf( B ))]]) ).
thf(780,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( addition @ ( multiplication @ C @ A ) @ B ) @ A )
!= A )
| ( leq @ ( multiplication @ ( star @ C ) @ B ) @ A ) ),
inference(simp,[status(thm)],[730]) ).
thf(63613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ C @ A ) @ ( addition @ B @ A ) )
!= A )
| ( leq @ ( multiplication @ ( star @ C ) @ B ) @ A ) ),
inference(rewrite,[status(thm)],[780,26]) ).
thf(174,plain,
! [A: $i] :
( ( ( addition @ one @ ( multiplication @ A @ one ) )
= ( star @ A ) )
| ( ( star @ zero )
!= ( star @ A ) ) ),
inference(paramod_ordered,[status(thm)],[172,51]) ).
thf(175,plain,
( ( addition @ one @ ( multiplication @ zero @ one ) )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( zero ))]]) ).
thf(223,plain,
( ( addition @ one @ zero )
= one ),
inference(rewrite,[status(thm)],[175,66,172]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ A @ B )
!= ( addition @ one @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[35,223]) ).
thf(286,plain,
( ( addition @ zero @ one )
= one ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( one )),bind(B,$thf( zero ))]]) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= one )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ zero @ one ) ) ),
inference(paramod_ordered,[status(thm)],[286,26]) ).
thf(339,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= one )
| ( ( addition @ C @ B )
!= zero )
| ( A != one ) ),
inference(simp,[status(thm)],[333]) ).
thf(349,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ one ) )
= one )
| ( ( addition @ B @ A )
!= zero ) ),
inference(simp,[status(thm)],[339]) ).
thf(991,plain,
! [A: $i] :
( ( A
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( sk1 != zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,981]) ).
thf(999,plain,
( ( sk1 != zero )
| ( ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[991]) ).
thf(1181,plain,
( ( sk1 != zero )
| ( ( strong_iteration @ ( multiplication @ one @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[172,999]) ).
thf(1190,plain,
( ( sk1 != zero )
| ( ( strong_iteration @ ( multiplication @ one @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[1181]) ).
thf(1195,plain,
( ( sk1 != zero )
| ( ( strong_iteration @ ( multiplication @ one @ sk2 ) )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[1190]) ).
thf(1502,plain,
( ( sk1 != zero )
| ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one ) ),
inference(rewrite,[status(thm)],[1195,58]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(70,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( A
= ( star @ B ) )
| ( ( addition @ A @ zero )
!= ( addition @ one @ ( multiplication @ B @ ( star @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,51]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( A
= ( star @ B ) )
| ( A != one )
| ( ( multiplication @ B @ ( star @ B ) )
!= zero ) ),
inference(simp,[status(thm)],[150]) ).
thf(165,plain,
! [A: $i] :
( ( ( star @ A )
= one )
| ( ( multiplication @ A @ ( star @ A ) )
!= zero ) ),
inference(simp,[status(thm)],[161]) ).
thf(23292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= zero )
| ( ( addition @ B @ A )
!= ( addition @ ( star @ one ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,21340]) ).
thf(23293,plain,
! [A: $i] :
( ( addition @ A @ ( star @ one ) )
!= zero ),
inference(pattern_uni,[status(thm)],[23292:[bind(A,$thf( A )),bind(B,$thf( star @ one )),bind(C,$thf( A ))]]) ).
thf(25555,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( addition @ B @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[462,23293]) ).
thf(25556,plain,
! [A: $i] :
~ ( leq @ ( addition @ A @ ( star @ one ) ) @ zero ),
inference(pattern_uni,[status(thm)],[25555:[bind(A,$thf( addition @ C @ ( star @ one ) )),bind(B,$thf( C ))]]) ).
thf(25656,plain,
! [A: $i] :
~ ( leq @ ( addition @ A @ ( star @ one ) ) @ zero ),
inference(simp,[status(thm)],[25556]) ).
thf(31084,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( ( leq @ A @ B )
!= ( leq @ ( addition @ C @ ( star @ one ) ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[41,25656]) ).
thf(31085,plain,
! [A: $i] :
( ( addition @ ( addition @ A @ ( star @ one ) ) @ zero )
!= zero ),
inference(pattern_uni,[status(thm)],[31084:[bind(A,$thf( addition @ D @ ( star @ one ) )),bind(B,$thf( zero )),bind(C,$thf( D ))]]) ).
thf(31271,plain,
! [A: $i] :
( ( addition @ ( addition @ A @ ( star @ one ) ) @ zero )
!= zero ),
inference(simp,[status(thm)],[31085]) ).
thf(58607,plain,
! [A: $i] :
( ( addition @ A @ ( addition @ ( star @ one ) @ zero ) )
!= zero ),
inference(rewrite,[status(thm)],[31271,26]) ).
thf(483,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( B
= ( addition @ E @ ( addition @ D @ C ) ) )
| ( ( addition @ A @ B )
!= ( addition @ ( addition @ E @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[42,26]) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ B @ C ) @ A )
| ( ( addition @ B @ ( addition @ C @ A ) )
= A ) ),
inference(pattern_uni,[status(thm)],[483:[bind(A,$thf( addition @ F @ G )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ B @ C ) @ A )
| ( ( addition @ B @ ( addition @ C @ A ) )
= A ) ),
inference(simp,[status(thm)],[484]) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ zero @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[272,41]) ).
thf(508,plain,
! [A: $i] :
( ( A != A )
| ( leq @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[507:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(551,plain,
! [A: $i] : ( leq @ zero @ A ),
inference(simp,[status(thm)],[508]) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( star @ A )
= ( addition @ C @ B ) )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[51,35]) ).
thf(308,plain,
! [A: $i] :
( ( addition @ ( multiplication @ A @ ( star @ A ) ) @ one )
= ( star @ A ) ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( F )),bind(B,$thf( one )),bind(C,$thf( multiplication @ F @ ( star @ F ) ))]]) ).
thf(317,plain,
! [A: $i] :
( ( addition @ ( multiplication @ A @ ( star @ A ) ) @ one )
= ( star @ A ) ),
inference(simp,[status(thm)],[308]) ).
thf(17935,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ C @ A ) )
= ( star @ one ) )
| ( ( addition @ ( star @ one ) @ ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) )
!= ( addition @ A @ ( addition @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[17934,311]) ).
thf(17936,plain,
( ( addition @ ( star @ one ) @ ( addition @ ( addition @ one @ one ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[17935:[bind(A,$thf( star @ one )),bind(B,$thf( star @ one )),bind(C,$thf( addition @ one @ one ))]]) ).
thf(32607,plain,
( ( addition @ ( star @ one ) @ ( addition @ one @ ( addition @ one @ ( star @ one ) ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[17936,4761]) ).
thf(422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
!= D )
| ( leq @ C @ D )
| ( ( addition @ B @ A )
!= ( addition @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35,41]) ).
thf(423,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= A )
| ( leq @ B @ A ) ),
inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(32834,plain,
! [B: $i,A: $i] :
( ( ( star @ one )
!= A )
| ( leq @ B @ A )
| ( ( addition @ ( star @ one ) @ ( addition @ one @ ( addition @ one @ ( star @ one ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[32607,423]) ).
thf(32835,plain,
( ( ( star @ one )
!= ( star @ one ) )
| ( leq @ ( addition @ one @ ( addition @ one @ ( star @ one ) ) ) @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[32834:[bind(A,$thf( star @ one )),bind(B,$thf( addition @ one @ ( addition @ one @ ( star @ one ) ) ))]]) ).
thf(33246,plain,
leq @ ( addition @ one @ ( addition @ one @ ( star @ one ) ) ) @ ( star @ one ),
inference(simp,[status(thm)],[32835]) ).
thf(33644,plain,
leq @ ( addition @ one @ ( star @ one ) ) @ ( star @ one ),
inference(rewrite,[status(thm)],[33246,130]) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( star @ A )
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ ( addition @ D @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51,26]) ).
thf(157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( star @ A )
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ D @ C )
!= one )
| ( ( multiplication @ A @ ( star @ A ) )
!= B ) ),
inference(simp,[status(thm)],[153]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ ( multiplication @ A @ ( star @ A ) ) ) )
= ( star @ A ) )
| ( ( addition @ C @ B )
!= one ) ),
inference(simp,[status(thm)],[157]) ).
thf(36181,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
!= zero )
| ( ( addition @ ( star @ one ) @ A )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[652,21340]) ).
thf(36182,plain,
! [A: $i] :
( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[36181:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(63148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ B ) @ A )
!= zero )
| ( ( addition @ one @ ( addition @ ( multiplication @ B @ ( star @ B ) ) @ A ) )
!= ( addition @ one @ ( addition @ C @ ( star @ one ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,36182]) ).
thf(63149,plain,
! [A: $i] :
( ( addition @ ( star @ A ) @ ( star @ one ) )
!= zero ),
inference(pattern_uni,[status(thm)],[63148:[bind(A,$thf( star @ one )),bind(B,$thf( F )),bind(C,$thf( multiplication @ F @ ( star @ F ) ))]]) ).
thf(63317,plain,
! [A: $i] :
( ( addition @ ( star @ A ) @ ( star @ one ) )
!= zero ),
inference(simp,[status(thm)],[63149]) ).
thf(4147,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ ( addition @ B @ one ) )
= ( addition @ A @ B ) )
| ( ( addition @ zero @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2179,139]) ).
thf(4148,plain,
( ( addition @ zero @ ( addition @ one @ one ) )
= ( addition @ zero @ one ) ),
inference(pattern_uni,[status(thm)],[4147:[bind(A,$thf( zero )),bind(B,$thf( one ))]]) ).
thf(4389,plain,
( ( addition @ one @ one )
= one ),
inference(rewrite,[status(thm)],[4148,272,2179]) ).
thf(475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( B
= ( addition @ D @ C ) )
| ( ( addition @ A @ B )
!= ( addition @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[42,35]) ).
thf(476,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ B @ A )
= B ) ),
inference(pattern_uni,[status(thm)],[475:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(18155,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ one ) )
| ( ( addition @ ( star @ one ) @ ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17934,35]) ).
thf(18156,plain,
( ( addition @ ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[18155:[bind(A,$thf( star @ one )),bind(B,$thf( addition @ ( star @ one ) @ ( addition @ one @ one ) ))]]) ).
thf(46852,plain,
( ( addition @ ( star @ one ) @ ( addition @ ( addition @ one @ one ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[18156,26]) ).
thf(47129,plain,
! [B: $i,A: $i] :
( ( ( star @ one )
!= A )
| ( leq @ B @ A )
| ( ( addition @ ( star @ one ) @ ( addition @ ( addition @ one @ one ) @ ( star @ one ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46852,423]) ).
thf(47130,plain,
( ( ( star @ one )
!= ( star @ one ) )
| ( leq @ ( addition @ ( addition @ one @ one ) @ ( star @ one ) ) @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[47129:[bind(A,$thf( star @ one )),bind(B,$thf( addition @ ( addition @ one @ one ) @ ( star @ one ) ))]]) ).
thf(47651,plain,
leq @ ( addition @ ( addition @ one @ one ) @ ( star @ one ) ) @ ( star @ one ),
inference(simp,[status(thm)],[47130]) ).
thf(48522,plain,
leq @ ( addition @ one @ ( addition @ one @ ( star @ one ) ) ) @ ( star @ one ),
inference(rewrite,[status(thm)],[47651,26]) ).
thf(35600,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ one @ ( addition @ A @ ( star @ one ) ) ) )
!= zero )
| ( ( addition @ ( star @ one ) @ A )
!= ( addition @ B @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[652,27092]) ).
thf(35601,plain,
( ( addition @ one @ ( addition @ one @ ( addition @ zero @ ( star @ one ) ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[35600:[bind(A,$thf( zero )),bind(B,$thf( star @ one ))]]) ).
thf(38708,plain,
( ( addition @ one @ ( addition @ zero @ ( star @ one ) ) )
!= zero ),
inference(rewrite,[status(thm)],[35601,130]) ).
thf(8750,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ one @ ( strong_iteration @ A ) )
| ( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
!= ( addition @ ( star @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,6562]) ).
thf(8751,plain,
! [A: $i] : ( leq @ one @ ( strong_iteration @ A ) ),
inference(pattern_uni,[status(thm)],[8750:[bind(A,$thf( F )),bind(B,$thf( multiplication @ ( strong_iteration @ F ) @ zero )),bind(C,$thf( F ))]]) ).
thf(8836,plain,
! [A: $i] : ( leq @ one @ ( strong_iteration @ A ) ),
inference(simp,[status(thm)],[8751]) ).
thf(9333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ C )
= C )
| ( ( leq @ one @ ( strong_iteration @ A ) )
!= ( leq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8836,42]) ).
thf(9334,plain,
! [A: $i] :
( ( addition @ one @ ( strong_iteration @ A ) )
= ( strong_iteration @ A ) ),
inference(pattern_uni,[status(thm)],[9333:[bind(A,$thf( D )),bind(B,$thf( one )),bind(C,$thf( strong_iteration @ D ))]]) ).
thf(9343,plain,
! [A: $i] :
( ( addition @ one @ ( strong_iteration @ A ) )
= ( strong_iteration @ A ) ),
inference(simp,[status(thm)],[9334]) ).
thf(10034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( strong_iteration @ A )
= ( addition @ C @ B ) )
| ( ( addition @ one @ ( strong_iteration @ A ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9343,35]) ).
thf(10035,plain,
! [A: $i] :
( ( addition @ ( strong_iteration @ A ) @ one )
= ( strong_iteration @ A ) ),
inference(pattern_uni,[status(thm)],[10034:[bind(A,$thf( D )),bind(B,$thf( one )),bind(C,$thf( strong_iteration @ D ))]]) ).
thf(10163,plain,
! [A: $i] :
( ( addition @ ( strong_iteration @ A ) @ one )
= ( strong_iteration @ A ) ),
inference(simp,[status(thm)],[10035]) ).
thf(64412,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= ( addition @ ( star @ C ) @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,63317]) ).
thf(64413,plain,
! [A: $i] :
( ( addition @ ( star @ one ) @ ( star @ A ) )
!= zero ),
inference(pattern_uni,[status(thm)],[64412:[bind(A,$thf( star @ D )),bind(B,$thf( star @ one )),bind(C,$thf( D ))]]) ).
thf(64512,plain,
! [A: $i] :
( ( addition @ ( star @ one ) @ ( star @ A ) )
!= zero ),
inference(simp,[status(thm)],[64413]) ).
thf(16778,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ one ) )
| ( ( addition @ ( multiplication @ one @ ( star @ one ) ) @ ( addition @ ( star @ one ) @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16608,35]) ).
thf(16779,plain,
( ( addition @ ( addition @ ( star @ one ) @ one ) @ ( multiplication @ one @ ( star @ one ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[16778:[bind(A,$thf( multiplication @ one @ ( star @ one ) )),bind(B,$thf( addition @ ( star @ one ) @ one ))]]) ).
thf(29188,plain,
( ( addition @ ( star @ one ) @ ( addition @ one @ ( multiplication @ one @ ( star @ one ) ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[16779,26]) ).
thf(28359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= ( addition @ C @ ( addition @ one @ zero ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,28257]) ).
thf(28360,plain,
! [A: $i] :
( ( addition @ ( addition @ one @ zero ) @ A )
!= zero ),
inference(pattern_uni,[status(thm)],[28359:[bind(A,$thf( A )),bind(B,$thf( addition @ one @ zero )),bind(C,$thf( A ))]]) ).
thf(32160,plain,
! [A: $i] :
( ( addition @ one @ ( addition @ zero @ A ) )
!= zero ),
inference(rewrite,[status(thm)],[28360,26]) ).
thf(728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( leq @ zero @ A )
!= ( leq @ ( addition @ ( multiplication @ B @ D ) @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[551,53]) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( addition @ ( multiplication @ B @ D ) @ C )
!= zero )
| ( A != D ) ),
inference(simp,[status(thm)],[728]) ).
thf(779,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ( ( addition @ ( multiplication @ A @ C ) @ B )
!= zero ) ),
inference(simp,[status(thm)],[761]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(73,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17948,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ ( addition @ A @ ( addition @ B @ C ) ) )
= ( star @ one ) )
| ( ( addition @ B @ ( addition @ C @ A ) )
!= ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,17934]) ).
thf(17949,plain,
( ( addition @ ( star @ one ) @ ( addition @ one @ ( addition @ ( star @ one ) @ one ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[17948:[bind(A,$thf( one )),bind(B,$thf( star @ one )),bind(C,$thf( one ))]]) ).
thf(43390,plain,
( ( addition @ ( star @ one ) @ ( addition @ ( star @ one ) @ one ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[17949,382]) ).
thf(741,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ B @ A ) @ E )
| ( leq @ ( multiplication @ ( star @ C ) @ D ) @ E )
| ( ( addition @ A @ B )
!= ( addition @ ( multiplication @ C @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35,53]) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ A @ ( multiplication @ B @ C ) ) @ C )
| ( leq @ ( multiplication @ ( star @ B ) @ A ) @ C ) ),
inference(pattern_uni,[status(thm)],[741:[bind(A,$thf( multiplication @ F @ G )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B )),bind(E,$thf( G ))]]) ).
thf(765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ A @ ( multiplication @ B @ C ) ) @ C )
| ( leq @ ( multiplication @ ( star @ B ) @ A ) @ C ) ),
inference(simp,[status(thm)],[742]) ).
thf(752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( star @ A ) @ D )
| ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ ( multiplication @ B @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[51,53]) ).
thf(756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ~ ( leq @ ( star @ A ) @ D )
| ( ( multiplication @ B @ D )
!= one )
| ( ( multiplication @ A @ ( star @ A ) )
!= C ) ),
inference(simp,[status(thm)],[752]) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ ( multiplication @ A @ ( star @ A ) ) ) @ C )
| ~ ( leq @ ( star @ A ) @ C )
| ( ( multiplication @ B @ C )
!= one ) ),
inference(simp,[status(thm)],[756]) ).
thf(36159,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
!= zero )
| ( ( addition @ ( star @ one ) @ A )
!= ( addition @ B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[652,21693]) ).
thf(36160,plain,
( ( addition @ one @ ( addition @ sk2 @ ( star @ one ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[36159:[bind(A,$thf( sk2 )),bind(B,$thf( star @ one ))]]) ).
thf(10562,plain,
! [A: $i] :
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ A )
!= one )
| ( ( star @ sk1 )
!= one )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[58,890]) ).
thf(10563,plain,
! [A: $i] :
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ A )
!= one )
| ( ( star @ sk1 )
!= one )
| ( ( star @ sk1 )
!= one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[10562]) ).
thf(10571,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one )
| ( ( star @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[10563]) ).
thf(424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
!= E )
| ( leq @ D @ E )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[26,41]) ).
thf(425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ C @ A ) )
!= A )
| ( leq @ ( addition @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[424:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( addition @ F @ G )),bind(E,$thf( A ))]]) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ C @ A ) )
!= A )
| ( leq @ ( addition @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[425]) ).
thf(38711,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ C @ A ) )
!= zero )
| ( ( addition @ A @ ( addition @ B @ C ) )
!= ( addition @ one @ ( addition @ zero @ ( star @ one ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,38708]) ).
thf(38712,plain,
( ( addition @ zero @ ( addition @ ( star @ one ) @ one ) )
!= zero ),
inference(pattern_uni,[status(thm)],[38711:[bind(A,$thf( one )),bind(B,$thf( zero )),bind(C,$thf( star @ one ))]]) ).
thf(39944,plain,
( ( addition @ ( star @ one ) @ one )
!= zero ),
inference(rewrite,[status(thm)],[38712,272]) ).
thf(8697,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[58,2159]) ).
thf(8705,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero )
| ( ( star @ sk1 )
!= one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[8697]) ).
thf(8713,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero )
| ( ( star @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[8705]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ A )
= ( star @ B ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,51]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ A )
= ( star @ B ) )
| ( A != B )
| ( ( star @ B )
!= one ) ),
inference(simp,[status(thm)],[146]) ).
thf(166,plain,
! [A: $i] :
( ( ( addition @ one @ A )
= ( star @ A ) )
| ( ( star @ A )
!= one ) ),
inference(simp,[status(thm)],[162]) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ D )
| ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( addition @ A @ zero )
!= ( addition @ ( multiplication @ B @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[32,53]) ).
thf(736,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( multiplication @ A @ B ) @ B )
| ( leq @ ( multiplication @ ( star @ A ) @ zero ) @ B ) ),
inference(pattern_uni,[status(thm)],[735:[bind(A,$thf( multiplication @ E @ F )),bind(B,$thf( E )),bind(C,$thf( zero )),bind(D,$thf( F ))]]) ).
thf(763,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( multiplication @ A @ B ) @ B )
| ( leq @ ( multiplication @ ( star @ A ) @ zero ) @ B ) ),
inference(simp,[status(thm)],[736]) ).
thf(57582,plain,
! [B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ zero ) @ B )
| ( ( leq @ ( multiplication @ ( star @ one ) @ ( star @ one ) ) @ ( star @ one ) )
!= ( leq @ ( multiplication @ A @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57516,763]) ).
thf(57583,plain,
leq @ ( multiplication @ ( star @ ( star @ one ) ) @ zero ) @ ( star @ one ),
inference(pattern_uni,[status(thm)],[57582:[bind(A,$thf( star @ one )),bind(B,$thf( star @ one ))]]) ).
thf(58153,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ( ( leq @ ( multiplication @ ( star @ ( star @ one ) ) @ zero ) @ ( star @ one ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57583,42]) ).
thf(58154,plain,
( ( addition @ ( multiplication @ ( star @ ( star @ one ) ) @ zero ) @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[58153:[bind(A,$thf( multiplication @ ( star @ ( star @ one ) ) @ zero )),bind(B,$thf( star @ one ))]]) ).
thf(661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ C @ ( addition @ B @ A ) ) )
= ( addition @ ( star @ one ) @ D ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ ( star @ one ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[26,196]) ).
thf(669,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ C @ ( addition @ B @ A ) ) )
= ( addition @ ( star @ one ) @ D ) )
| ( ( addition @ C @ B )
!= ( star @ one ) )
| ( A != D ) ),
inference(simp,[status(thm)],[661]) ).
thf(694,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ B @ ( addition @ A @ C ) ) )
= ( addition @ ( star @ one ) @ C ) )
| ( ( addition @ B @ A )
!= ( star @ one ) ) ),
inference(simp,[status(thm)],[669]) ).
thf(28679,plain,
! [A: $i] :
( ( ( addition @ sk2 @ one )
!= zero )
| ( ( addition @ one @ zero )
!= ( addition @ A @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[223,28583]) ).
thf(28680,plain,
( ( addition @ sk2 @ one )
!= zero ),
inference(pattern_uni,[status(thm)],[28679:[bind(A,$thf( one ))]]) ).
thf(28933,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= ( addition @ sk2 @ one ) ) ),
inference(paramod_ordered,[status(thm)],[35,28680]) ).
thf(28934,plain,
( ( addition @ one @ sk2 )
!= zero ),
inference(pattern_uni,[status(thm)],[28933:[bind(A,$thf( sk2 )),bind(B,$thf( one ))]]) ).
thf(5349,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ B @ ( strong_iteration @ A ) )
| ( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[61,4015]) ).
thf(5350,plain,
! [A: $i] : ( leq @ ( star @ A ) @ ( strong_iteration @ A ) ),
inference(pattern_uni,[status(thm)],[5349:[bind(A,$thf( G )),bind(B,$thf( star @ G )),bind(C,$thf( multiplication @ ( strong_iteration @ G ) @ zero ))]]) ).
thf(5395,plain,
! [A: $i] : ( leq @ ( star @ A ) @ ( strong_iteration @ A ) ),
inference(simp,[status(thm)],[5350]) ).
thf(623,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ one @ B )
= ( addition @ ( star @ one ) @ C ) )
| ( ( addition @ A @ B )
!= ( addition @ ( star @ one ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[42,196]) ).
thf(624,plain,
! [A: $i] :
( ~ ( leq @ ( star @ one ) @ A )
| ( ( addition @ ( star @ one ) @ A )
= ( addition @ one @ A ) ) ),
inference(pattern_uni,[status(thm)],[623:[bind(A,$thf( star @ one )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(711,plain,
! [A: $i] :
( ~ ( leq @ ( star @ one ) @ A )
| ( ( addition @ ( star @ one ) @ A )
= ( addition @ one @ A ) ) ),
inference(simp,[status(thm)],[624]) ).
thf(50639,plain,
! [B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ B )
= ( addition @ one @ B ) )
| ( ( leq @ ( star @ A ) @ ( strong_iteration @ A ) )
!= ( leq @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5395,711]) ).
thf(50640,plain,
( ( addition @ ( star @ one ) @ ( strong_iteration @ one ) )
= ( addition @ one @ ( strong_iteration @ one ) ) ),
inference(pattern_uni,[status(thm)],[50639:[bind(A,$thf( one )),bind(B,$thf( strong_iteration @ one ))]]) ).
thf(51439,plain,
( ( addition @ ( star @ one ) @ ( strong_iteration @ one ) )
= ( strong_iteration @ one ) ),
inference(rewrite,[status(thm)],[50640,9343]) ).
thf(51737,plain,
! [A: $i] :
( ( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
= ( strong_iteration @ one ) )
| ( ( addition @ ( star @ one ) @ ( strong_iteration @ one ) )
!= ( addition @ ( star @ one ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51439,652]) ).
thf(51738,plain,
( ( addition @ one @ ( addition @ ( strong_iteration @ one ) @ ( star @ one ) ) )
= ( strong_iteration @ one ) ),
inference(pattern_uni,[status(thm)],[51737:[bind(A,$thf( strong_iteration @ one ))]]) ).
thf(51695,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( strong_iteration @ one ) )
| ( ( addition @ ( star @ one ) @ ( strong_iteration @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51439,35]) ).
thf(51696,plain,
( ( addition @ ( strong_iteration @ one ) @ ( star @ one ) )
= ( strong_iteration @ one ) ),
inference(pattern_uni,[status(thm)],[51695:[bind(A,$thf( star @ one )),bind(B,$thf( strong_iteration @ one ))]]) ).
thf(54078,plain,
( ( addition @ one @ ( strong_iteration @ one ) )
= ( strong_iteration @ one ) ),
inference(rewrite,[status(thm)],[51738,51696]) ).
thf(527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ zero @ A )
!= ( addition @ ( addition @ D @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[272,26]) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ D @ C )
!= zero )
| ( A != B ) ),
inference(simp,[status(thm)],[527]) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= A )
| ( ( addition @ C @ B )
!= zero ) ),
inference(simp,[status(thm)],[534]) ).
thf(10904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ B @ A ) )
| ( ( addition @ A @ B )
!= ( addition @ C @ ( strong_iteration @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,10812]) ).
thf(10905,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( strong_iteration @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[10904:[bind(A,$thf( A )),bind(B,$thf( strong_iteration @ E )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(10963,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( strong_iteration @ B ) @ A ) ),
inference(simp,[status(thm)],[10905]) ).
thf(723,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ~ ( leq @ B @ E )
| ( leq @ ( multiplication @ ( star @ C ) @ D ) @ E )
| ( ( addition @ A @ B )
!= ( addition @ ( multiplication @ C @ E ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[42,53]) ).
thf(724,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( multiplication @ B @ C ) @ A )
| ~ ( leq @ A @ C )
| ( leq @ ( multiplication @ ( star @ B ) @ A ) @ C ) ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( multiplication @ F @ G )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B )),bind(E,$thf( G ))]]) ).
thf(772,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( multiplication @ B @ C ) @ A )
| ~ ( leq @ A @ C )
| ( leq @ ( multiplication @ ( star @ B ) @ A ) @ C ) ),
inference(simp,[status(thm)],[724]) ).
thf(59099,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ( ( star @ one )
!= C )
| ( ( addition @ ( multiplication @ ( star @ one ) @ ( star @ one ) ) @ ( star @ one ) )
!= ( addition @ ( multiplication @ A @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57521,770]) ).
thf(59100,plain,
( ( leq @ ( multiplication @ ( star @ ( star @ one ) ) @ ( star @ one ) ) @ ( star @ one ) )
| ( ( star @ one )
!= ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[59099:[bind(A,$thf( star @ one )),bind(B,$thf( star @ one )),bind(C,$thf( star @ one ))]]) ).
thf(59758,plain,
leq @ ( multiplication @ ( star @ ( star @ one ) ) @ ( star @ one ) ) @ ( star @ one ),
inference(simp,[status(thm)],[59100]) ).
thf(665,plain,
! [B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( star @ B ) )
| ( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
!= ( addition @ one @ ( multiplication @ B @ ( star @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[196,51]) ).
thf(680,plain,
! [B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( star @ B ) )
| ( one != one )
| ( ( addition @ ( star @ one ) @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(simp,[status(thm)],[665]) ).
thf(704,plain,
! [B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( star @ B ) )
| ( ( addition @ ( star @ one ) @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(simp,[status(thm)],[680]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
=> ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
thf(54,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
=> ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21109,plain,
! [A: $i] :
( ( leq @ one @ ( strong_iteration @ A ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[8836,19932]) ).
thf(21137,plain,
! [A: $i] :
( ( one != one )
| ( ( strong_iteration @ A )
!= zero ) ),
inference(simp,[status(thm)],[21109]) ).
thf(21161,plain,
! [A: $i] :
( ( strong_iteration @ A )
!= zero ),
inference(simp,[status(thm)],[21137]) ).
thf(18022,plain,
! [B: $i,A: $i] :
( ( ( star @ one )
!= B )
| ( leq @ A @ B )
| ( ( addition @ ( star @ one ) @ ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) )
!= ( addition @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17934,421]) ).
thf(18023,plain,
( ( ( star @ one )
!= ( star @ one ) )
| ( leq @ ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[18022:[bind(A,$thf( addition @ ( star @ one ) @ ( addition @ one @ one ) )),bind(B,$thf( star @ one ))]]) ).
thf(18401,plain,
leq @ ( addition @ ( star @ one ) @ ( addition @ one @ one ) ) @ ( star @ one ),
inference(simp,[status(thm)],[18023]) ).
thf(18859,plain,
leq @ ( addition @ ( star @ one ) @ one ) @ ( star @ one ),
inference(rewrite,[status(thm)],[18401,382]) ).
thf(530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= D )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ zero @ D ) ) ),
inference(paramod_ordered,[status(thm)],[26,272]) ).
thf(540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= D )
| ( ( addition @ C @ B )
!= zero )
| ( A != D ) ),
inference(simp,[status(thm)],[530]) ).
thf(552,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ C ) )
= C )
| ( ( addition @ B @ A )
!= zero ) ),
inference(simp,[status(thm)],[540]) ).
thf(10242,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= one )
| ( sk2 != one )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[58,889]) ).
thf(10247,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= one )
| ( sk2 != one )
| ( ( star @ sk1 )
!= one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[10242]) ).
thf(10253,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= one )
| ( sk2 != one )
| ( ( star @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[10247]) ).
thf(586,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,23]) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ A @ B )
!= ( star @ sk2 ) )
| ( C
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) ),
inference(simp,[status(thm)],[586]) ).
thf(609,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ A @ B )
!= ( star @ sk2 ) ) ),
inference(simp,[status(thm)],[596]) ).
thf(643,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( addition @ C @ B ) )
| ( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[196,35]) ).
thf(644,plain,
! [A: $i] :
( ( addition @ ( addition @ ( star @ one ) @ A ) @ one )
= ( addition @ ( star @ one ) @ A ) ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( E )),bind(B,$thf( one )),bind(C,$thf( addition @ ( star @ one ) @ E ))]]) ).
thf(689,plain,
! [A: $i] :
( ( addition @ ( addition @ ( star @ one ) @ A ) @ one )
= ( addition @ ( star @ one ) @ A ) ),
inference(simp,[status(thm)],[644]) ).
thf(37496,plain,
! [A: $i] :
( ( addition @ ( star @ one ) @ ( addition @ A @ one ) )
= ( addition @ ( star @ one ) @ A ) ),
inference(rewrite,[status(thm)],[689,26]) ).
thf(21080,plain,
! [A: $i] :
( ( leq @ one @ ( star @ A ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[5385,19932]) ).
thf(21128,plain,
! [A: $i] :
( ( one != one )
| ( ( star @ A )
!= zero ) ),
inference(simp,[status(thm)],[21080]) ).
thf(21153,plain,
! [A: $i] :
( ( star @ A )
!= zero ),
inference(simp,[status(thm)],[21128]) ).
thf(21257,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( star @ B ) ) ),
inference(paramod_ordered,[status(thm)],[462,21153]) ).
thf(21258,plain,
! [A: $i] :
~ ( leq @ ( star @ A ) @ zero ),
inference(pattern_uni,[status(thm)],[21257:[bind(A,$thf( star @ C )),bind(B,$thf( C ))]]) ).
thf(21259,plain,
! [A: $i] :
~ ( leq @ ( star @ A ) @ zero ),
inference(simp,[status(thm)],[21258]) ).
thf(666,plain,
! [B: $i,A: $i] :
( ( ( star @ A )
= ( addition @ ( star @ one ) @ B ) )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ one @ ( addition @ ( star @ one ) @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,196]) ).
thf(676,plain,
! [B: $i,A: $i] :
( ( ( star @ A )
= ( addition @ ( star @ one ) @ B ) )
| ( one != one )
| ( ( multiplication @ A @ ( star @ A ) )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(simp,[status(thm)],[666]) ).
thf(700,plain,
! [B: $i,A: $i] :
( ( ( star @ A )
= ( addition @ ( star @ one ) @ B ) )
| ( ( multiplication @ A @ ( star @ A ) )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(simp,[status(thm)],[676]) ).
thf(749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ A @ C ) @ D )
| ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( multiplication @ one @ A )
!= ( multiplication @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[58,53]) ).
thf(750,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( addition @ A @ B ) @ A )
| ( leq @ ( multiplication @ ( star @ one ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[749:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(768,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( addition @ A @ B ) @ A )
| ( leq @ ( multiplication @ ( star @ one ) @ B ) @ A ) ),
inference(simp,[status(thm)],[750]) ).
thf(385,plain,
! [A: $i] :
( ( ( star @ A )
= ( star @ one ) )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ ( star @ one ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[51,282]) ).
thf(394,plain,
! [A: $i] :
( ( ( star @ A )
= ( star @ one ) )
| ( ( star @ one )
!= one )
| ( ( multiplication @ A @ ( star @ A ) )
!= one ) ),
inference(simp,[status(thm)],[385]) ).
thf(583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ B @ ( multiplication @ C @ D ) )
= zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( multiplication @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[45,48]) ).
thf(595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ B @ ( multiplication @ C @ D ) )
= zero )
| ( ( multiplication @ B @ C )
!= zero )
| ( A != D ) ),
inference(simp,[status(thm)],[583]) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ A @ B )
!= zero ) ),
inference(simp,[status(thm)],[595]) ).
thf(18868,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ( ( leq @ ( addition @ ( star @ one ) @ one ) @ ( star @ one ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18859,42]) ).
thf(18869,plain,
( ( addition @ ( addition @ ( star @ one ) @ one ) @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[18868:[bind(A,$thf( addition @ ( star @ one ) @ one )),bind(B,$thf( star @ one ))]]) ).
thf(19080,plain,
( ( addition @ ( star @ one ) @ ( addition @ one @ ( star @ one ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[18869,26]) ).
thf(9640,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[172,8713]) ).
thf(9646,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ sk2 ) )
| ( ( multiplication @ ( star @ sk1 ) @ sk2 )
!= zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[9640]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
| ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(9735,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ E @ ( multiplication @ ( strong_iteration @ C ) @ D ) )
| ( ( leq @ one @ ( addition @ A @ ( star @ B ) ) )
!= ( leq @ E @ ( addition @ ( multiplication @ C @ E ) @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[8807,55]) ).
thf(9736,plain,
! [B: $i,A: $i] : ( leq @ one @ ( multiplication @ ( strong_iteration @ A ) @ ( star @ B ) ) ),
inference(pattern_uni,[status(thm)],[9735:[bind(A,$thf( multiplication @ F @ one )),bind(B,$thf( H )),bind(C,$thf( F )),bind(D,$thf( star @ H )),bind(E,$thf( one ))]]) ).
thf(9777,plain,
! [B: $i,A: $i] : ( leq @ one @ ( multiplication @ ( strong_iteration @ A ) @ ( star @ B ) ) ),
inference(simp,[status(thm)],[9736]) ).
thf(44418,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ A @ ( addition @ B @ C ) ) )
!= zero )
| ( ( addition @ B @ ( addition @ A @ C ) )
!= ( addition @ one @ ( addition @ zero @ ( star @ one ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11382,44391]) ).
thf(44419,plain,
( ( addition @ one @ ( addition @ zero @ ( addition @ one @ ( star @ one ) ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[44418:[bind(A,$thf( zero )),bind(B,$thf( one )),bind(C,$thf( star @ one ))]]) ).
thf(47813,plain,
( ( addition @ one @ ( addition @ one @ ( star @ one ) ) )
!= zero ),
inference(rewrite,[status(thm)],[44419,272]) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( star @ one ) @ A ) @ D )
| ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
!= ( addition @ ( multiplication @ B @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[196,53]) ).
thf(758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ~ ( leq @ ( addition @ ( star @ one ) @ A ) @ D )
| ( ( multiplication @ B @ D )
!= one )
| ( ( addition @ ( star @ one ) @ A )
!= C ) ),
inference(simp,[status(thm)],[733]) ).
thf(776,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ B ) @ ( addition @ ( star @ one ) @ A ) ) @ C )
| ~ ( leq @ ( addition @ ( star @ one ) @ A ) @ C )
| ( ( multiplication @ B @ C )
!= one ) ),
inference(simp,[status(thm)],[758]) ).
thf(21095,plain,
! [B: $i,A: $i] :
( ( leq @ one @ ( addition @ A @ ( star @ B ) ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[8807,19932]) ).
thf(21122,plain,
! [B: $i,A: $i] :
( ( one != one )
| ( ( addition @ A @ ( star @ B ) )
!= zero ) ),
inference(simp,[status(thm)],[21095]) ).
thf(21147,plain,
! [B: $i,A: $i] :
( ( addition @ A @ ( star @ B ) )
!= zero ),
inference(simp,[status(thm)],[21122]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
=> ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction2) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
=> ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
| ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
inference(cnf,[status(esa)],[62]) ).
thf(30809,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= ( addition @ C @ ( addition @ sk2 @ zero ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,30707]) ).
thf(30810,plain,
! [A: $i] :
( ( addition @ ( addition @ sk2 @ zero ) @ A )
!= zero ),
inference(pattern_uni,[status(thm)],[30809:[bind(A,$thf( A )),bind(B,$thf( addition @ sk2 @ zero )),bind(C,$thf( A ))]]) ).
thf(33983,plain,
! [A: $i] :
( ( addition @ sk2 @ ( addition @ zero @ A ) )
!= zero ),
inference(rewrite,[status(thm)],[30810,26]) ).
thf(21099,plain,
! [B: $i,A: $i] :
( ( leq @ one @ ( addition @ ( strong_iteration @ B ) @ A ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[10963,19932]) ).
thf(21139,plain,
! [B: $i,A: $i] :
( ( one != one )
| ( ( addition @ ( strong_iteration @ B ) @ A )
!= zero ) ),
inference(simp,[status(thm)],[21099]) ).
thf(21163,plain,
! [B: $i,A: $i] :
( ( addition @ ( strong_iteration @ B ) @ A )
!= zero ),
inference(simp,[status(thm)],[21139]) ).
thf(42041,plain,
( ( ( addition @ sk2 @ ( star @ one ) )
!= zero )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ one @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[9348,41969]) ).
thf(42042,plain,
( ( addition @ sk2 @ ( star @ one ) )
!= zero ),
inference(pattern_uni,[status(thm)],[42041:[]]) ).
thf(10240,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= one )
| ( sk2 != one )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,889]) ).
thf(10249,plain,
! [A: $i] :
( ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= one )
| ( sk2 != one )
| ( A
!= ( star @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[10240]) ).
thf(10254,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= one )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[10249]) ).
thf(10257,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( strong_iteration @ one )
!= one )
| ( sk2 != one )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[172,10254]) ).
thf(10260,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( strong_iteration @ one )
!= one )
| ( sk2 != one )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[10257]) ).
thf(57533,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= B )
| ( ( leq @ ( multiplication @ ( star @ one ) @ ( star @ one ) ) @ ( star @ one ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57516,476]) ).
thf(57534,plain,
( ( addition @ ( star @ one ) @ ( multiplication @ ( star @ one ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[57533:[bind(A,$thf( multiplication @ ( star @ one ) @ ( star @ one ) )),bind(B,$thf( star @ one ))]]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) )
= ( multiplication @ A @ ( addition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= D )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ one @ D ) ) ),
inference(paramod_ordered,[status(thm)],[48,58]) ).
thf(599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= D )
| ( ( multiplication @ A @ B )
!= one )
| ( C != D ) ),
inference(simp,[status(thm)],[588]) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= C )
| ( ( multiplication @ A @ B )
!= one ) ),
inference(simp,[status(thm)],[599]) ).
thf(481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
= D )
| ~ ( leq @ C @ D )
| ( ( addition @ B @ A )
!= ( addition @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35,42]) ).
thf(482,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= A )
| ~ ( leq @ B @ A ) ),
inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(748,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ C @ ( addition @ B @ A ) ) @ F )
| ( leq @ ( multiplication @ ( star @ D ) @ E ) @ F )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ ( multiplication @ D @ F ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[26,53]) ).
thf(755,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ D ) @ E ) @ F )
| ~ ( leq @ ( addition @ C @ ( addition @ B @ A ) ) @ F )
| ( ( addition @ C @ B )
!= ( multiplication @ D @ F ) )
| ( A != E ) ),
inference(simp,[status(thm)],[748]) ).
thf(771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ C ) @ D ) @ E )
| ~ ( leq @ ( addition @ B @ ( addition @ A @ D ) ) @ E )
| ( ( addition @ B @ A )
!= ( multiplication @ C @ E ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( B
= ( star @ C ) )
| ( ( addition @ A @ B )
!= ( addition @ one @ ( multiplication @ C @ ( star @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,51]) ).
thf(490,plain,
! [A: $i] :
( ~ ( leq @ one @ ( multiplication @ A @ ( star @ A ) ) )
| ( ( multiplication @ A @ ( star @ A ) )
= ( star @ A ) ) ),
inference(pattern_uni,[status(thm)],[489:[bind(A,$thf( one )),bind(B,$thf( multiplication @ F @ ( star @ F ) )),bind(C,$thf( F ))]]) ).
thf(495,plain,
! [A: $i] :
( ~ ( leq @ one @ ( multiplication @ A @ ( star @ A ) ) )
| ( ( multiplication @ A @ ( star @ A ) )
= ( star @ A ) ) ),
inference(simp,[status(thm)],[490]) ).
thf(21262,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( strong_iteration @ B ) ) ),
inference(paramod_ordered,[status(thm)],[462,21161]) ).
thf(21263,plain,
! [A: $i] :
~ ( leq @ ( strong_iteration @ A ) @ zero ),
inference(pattern_uni,[status(thm)],[21262:[bind(A,$thf( strong_iteration @ C )),bind(B,$thf( C ))]]) ).
thf(21264,plain,
! [A: $i] :
~ ( leq @ ( strong_iteration @ A ) @ zero ),
inference(simp,[status(thm)],[21263]) ).
thf(11209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ one @ ( addition @ B @ A ) )
| ( ( addition @ A @ B )
!= ( addition @ D @ ( addition @ one @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,10833]) ).
thf(11210,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( addition @ one @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[11209:[bind(A,$thf( A )),bind(B,$thf( addition @ one @ F )),bind(C,$thf( F )),bind(D,$thf( A ))]]) ).
thf(11328,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ ( addition @ one @ B ) @ A ) ),
inference(simp,[status(thm)],[11210]) ).
thf(13128,plain,
! [B: $i,A: $i] : ( leq @ one @ ( addition @ one @ ( addition @ B @ A ) ) ),
inference(rewrite,[status(thm)],[11328,26]) ).
thf(584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ ( multiplication @ A @ ( multiplication @ B @ C ) ) @ F )
= ( multiplication @ D @ ( multiplication @ E @ F ) ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[48,48]) ).
thf(585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ C @ ( multiplication @ D @ A ) ) @ B )
= ( multiplication @ ( multiplication @ C @ D ) @ ( multiplication @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[584:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( multiplication @ G @ H )),bind(E,$thf( C ))]]) ).
thf(604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ C @ ( multiplication @ D @ A ) ) @ B )
= ( multiplication @ ( multiplication @ C @ D ) @ ( multiplication @ A @ B ) ) ),
inference(simp,[status(thm)],[585]) ).
thf(31287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ C @ ( multiplication @ ( multiplication @ D @ A ) @ B ) )
= ( multiplication @ C @ ( multiplication @ D @ ( multiplication @ A @ B ) ) ) ),
inference(rewrite,[status(thm)],[604,48]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) )
= ( multiplication @ ( addition @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(60621,plain,
! [B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ zero ) @ B )
| ( ( leq @ ( multiplication @ ( star @ ( star @ one ) ) @ ( star @ one ) ) @ ( star @ one ) )
!= ( leq @ ( multiplication @ A @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[59758,763]) ).
thf(60622,plain,
leq @ ( multiplication @ ( star @ ( star @ ( star @ one ) ) ) @ zero ) @ ( star @ one ),
inference(pattern_uni,[status(thm)],[60621:[bind(A,$thf( star @ ( star @ one ) )),bind(B,$thf( star @ one ))]]) ).
thf(198,plain,
! [A: $i] :
( ( ( star @ one )
= ( star @ A ) )
| ( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
!= ( addition @ one @ ( star @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[148,51]) ).
thf(205,plain,
! [A: $i] :
( ( ( star @ one )
= ( star @ A ) )
| ( one != one )
| ( ( multiplication @ A @ ( star @ A ) )
!= ( star @ one ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(214,plain,
! [A: $i] :
( ( ( star @ one )
= ( star @ A ) )
| ( ( multiplication @ A @ ( star @ A ) )
!= ( star @ one ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(11121,plain,
! [A: $i] :
( ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( strong_iteration @ A )
!= one )
| ( sk2 != one )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[58,893]) ).
thf(11124,plain,
! [A: $i] :
( ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( strong_iteration @ A )
!= one )
| ( sk2 != one )
| ( ( star @ sk1 )
!= one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[11121]) ).
thf(11131,plain,
( ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( strong_iteration @ sk2 )
!= one )
| ( sk2 != one )
| ( ( star @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[11124]) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( star @ one ) @ C )
| ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ( ( addition @ ( multiplication @ A @ C ) @ B )
!= ( addition @ ( star @ one ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[282,53]) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C )
| ~ ( leq @ ( star @ one ) @ C )
| ( ( multiplication @ A @ C )
!= ( star @ one ) )
| ( B != one ) ),
inference(simp,[status(thm)],[747]) ).
thf(769,plain,
! [B: $i,A: $i] :
( ( leq @ ( multiplication @ ( star @ A ) @ one ) @ B )
| ~ ( leq @ ( star @ one ) @ B )
| ( ( multiplication @ A @ B )
!= ( star @ one ) ) ),
inference(simp,[status(thm)],[753]) ).
thf(54827,plain,
! [B: $i,A: $i] :
( ( leq @ ( star @ A ) @ B )
| ~ ( leq @ ( star @ one ) @ B )
| ( ( multiplication @ A @ B )
!= ( star @ one ) ) ),
inference(rewrite,[status(thm)],[769,66]) ).
thf(745,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ ( multiplication @ B @ C ) ) @ E ) @ F )
| ( leq @ ( multiplication @ ( star @ D ) @ E ) @ F )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ D @ F ) ) ),
inference(paramod_ordered,[status(thm)],[48,53]) ).
thf(746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ C @ ( multiplication @ D @ A ) ) @ B ) @ A )
| ( leq @ ( multiplication @ ( star @ ( multiplication @ C @ D ) ) @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[745:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( multiplication @ G @ H )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ C @ ( multiplication @ D @ A ) ) @ B ) @ A )
| ( leq @ ( multiplication @ ( star @ ( multiplication @ C @ D ) ) @ B ) @ A ) ),
inference(simp,[status(thm)],[746]) ).
thf(1184,plain,
! [A: $i] :
( ( sk1 != zero )
| ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,999]) ).
thf(1192,plain,
! [A: $i] :
( ( sk1 != zero )
| ( ( strong_iteration @ A )
!= ( star @ sk2 ) )
| ( ( strong_iteration @ sk2 )
!= one )
| ( A
!= ( star @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[1184]) ).
thf(1197,plain,
( ( sk1 != zero )
| ( ( star @ sk2 )
!= ( strong_iteration @ ( star @ sk1 ) ) )
| ( ( strong_iteration @ sk2 )
!= one )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[1192]) ).
thf(10914,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( leq @ E @ ( multiplication @ ( strong_iteration @ C ) @ D ) )
| ( ( leq @ one @ ( addition @ A @ ( strong_iteration @ B ) ) )
!= ( leq @ E @ ( addition @ ( multiplication @ C @ E ) @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[10812,55]) ).
thf(10915,plain,
! [B: $i,A: $i] : ( leq @ one @ ( multiplication @ ( strong_iteration @ A ) @ ( strong_iteration @ B ) ) ),
inference(pattern_uni,[status(thm)],[10914:[bind(A,$thf( multiplication @ F @ one )),bind(B,$thf( H )),bind(C,$thf( F )),bind(D,$thf( strong_iteration @ H )),bind(E,$thf( one ))]]) ).
thf(10966,plain,
! [B: $i,A: $i] : ( leq @ one @ ( multiplication @ ( strong_iteration @ A ) @ ( strong_iteration @ B ) ) ),
inference(simp,[status(thm)],[10915]) ).
thf(5460,plain,
! [A: $i] :
( ( leq @ one @ ( strong_iteration @ A ) )
| ( ( star @ zero )
!= ( star @ A ) ) ),
inference(paramod_ordered,[status(thm)],[172,5395]) ).
thf(5461,plain,
leq @ one @ ( strong_iteration @ zero ),
inference(pattern_uni,[status(thm)],[5460:[bind(A,$thf( zero ))]]) ).
thf(5473,plain,
leq @ one @ one,
inference(rewrite,[status(thm)],[5461,2116]) ).
thf(587,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ A @ ( multiplication @ B @ C ) ) ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[48,23]) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ A @ ( multiplication @ B @ C ) ) ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ A @ B )
!= ( star @ sk1 ) )
| ( C != sk2 ) ),
inference(simp,[status(thm)],[587]) ).
thf(607,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ A @ ( multiplication @ B @ sk2 ) ) ) )
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) )
| ( ( multiplication @ A @ B )
!= ( star @ sk1 ) ) ),
inference(simp,[status(thm)],[594]) ).
thf(485,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ B @ C )
= ( addition @ E @ ( addition @ D @ C ) ) )
| ( ( addition @ A @ B )
!= ( addition @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[42,26]) ).
thf(486,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(36003,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
!= zero )
| ( ( addition @ ( star @ one ) @ A )
!= ( addition @ B @ one ) ) ),
inference(paramod_ordered,[status(thm)],[652,21158]) ).
thf(36004,plain,
( ( addition @ one @ ( addition @ one @ ( star @ one ) ) )
!= zero ),
inference(pattern_uni,[status(thm)],[36003:[bind(A,$thf( one )),bind(B,$thf( star @ one ))]]) ).
thf(36795,plain,
( ( addition @ one @ ( star @ one ) )
!= zero ),
inference(rewrite,[status(thm)],[36004,130]) ).
thf(725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ A @ D )
| ( leq @ ( multiplication @ ( star @ B ) @ C ) @ D )
| ( ( addition @ A @ A )
!= ( addition @ ( multiplication @ B @ D ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,53]) ).
thf(726,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( multiplication @ A @ B ) @ B )
| ( leq @ ( multiplication @ ( star @ A ) @ ( multiplication @ A @ B ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( multiplication @ G @ H )),bind(B,$thf( G )),bind(C,$thf( multiplication @ G @ H )),bind(D,$thf( H ))]]) ).
thf(775,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( multiplication @ A @ B ) @ B )
| ( leq @ ( multiplication @ ( star @ A ) @ ( multiplication @ A @ B ) ) @ B ) ),
inference(simp,[status(thm)],[726]) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
!= ( addition @ ( addition @ D @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[196,26]) ).
thf(684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ D @ C )
!= one )
| ( ( addition @ ( star @ one ) @ A )
!= B ) ),
inference(simp,[status(thm)],[657]) ).
thf(708,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ ( addition @ ( star @ one ) @ A ) ) )
= ( addition @ ( star @ one ) @ A ) )
| ( ( addition @ C @ B )
!= one ) ),
inference(simp,[status(thm)],[684]) ).
thf(141017,plain,
$false,
inference(cvc4,[status(thm)],[2954,69,17094,23255,893,10812,4015,44391,5131,5385,56771,777,3566,170,21149,56,15263,10864,52152,30707,19027,39016,19932,34633,670,42,11382,24,44885,21239,10633,52,10251,4761,110,42458,702,196,27092,48170,5866,421,8717,46,606,770,10570,78,29,18792,164,4578,16608,6562,981,61,10833,774,57521,21168,42635,894,3827,778,63613,349,1502,70,429,21,165,28583,33,1883,58607,21751,493,551,456,889,2179,6728,317,33644,53,169,63317,4389,476,48522,212,38708,10163,64512,9348,25656,29188,32160,21146,41,779,32607,73,43390,311,765,773,36160,10571,430,32,45,64,8807,39944,8713,166,58154,38268,423,694,402,28934,5395,711,54078,59,545,27,413,22702,10963,772,59758,49,704,14341,382,54,21161,18859,172,76,2116,890,46852,552,10253,609,37496,36182,108,462,21259,700,66,57583,130,768,20660,394,35,223,608,19080,9646,9777,8836,21452,47813,776,48,21147,63,33983,21163,67,16234,51439,21158,42042,10260,57516,57534,72,612,43,41969,23375,482,51696,771,28257,495,9724,21264,26,652,9343,55,139,13128,10254,23,31287,9919,17917,75,58,60622,763,272,23293,214,11131,999,432,36,30,51,854,183,54827,21594,1097,168,767,1197,10966,2159,62,21153,21693,5473,607,111,486,5436,21340,100,36795,775,28680,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE147+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 02:48:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.85/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (127ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.54/1.15 % [INFO] eprover registered as external prover.
% 1.54/1.16 % [INFO] cvc4 registered as external prover.
% 1.54/1.16 % [INFO] Scanning for conjecture ...
% 1.85/1.22 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.93/1.26 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.93/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 1.93/1.29 % [INFO] Type checking passed.
% 1.93/1.29 % [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 ...
% 153.73/36.98 % External prover 'cvc4' found a proof!
% 153.73/36.98 % [INFO] Killing All external provers ...
% 153.73/36.98 % Time passed: 36482ms (effective reasoning time: 36022ms)
% 153.73/36.99 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 153.73/36.99 % Axioms used in derivation (18): additive_identity, isolation, additive_associativity, multiplicative_right_identity, star_unfold2, multiplicative_left_identity, idempotence, multiplicative_associativity, infty_unfold1, star_induction2, distributivity2, star_induction1, star_unfold1, left_annihilation, infty_coinduction, order, additive_commutativity, distributivity1
% 153.73/36.99 % No. of inferences in proof: 709
% 153.73/36.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 36482 ms resp. 36022 ms w/o parsing
% 154.23/37.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 154.23/37.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------