TSTP Solution File: KLE147+2 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE147+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:25:10 EDT 2023
% Result : Theorem 179.90s 36.26s
% Output : Refutation 179.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 30
% Syntax : Number of formulae : 149 ( 74 unt; 11 typ; 0 def)
% Number of atoms : 295 ( 204 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1341 ( 164 ~; 136 |; 6 &;1024 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 181 ( 0 ^; 181 !; 0 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $o ).
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(one_type,type,
one: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(14,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(55,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)],[14]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
| ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
inference(cnf,[status(esa)],[55]) ).
thf(13,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
thf(52,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,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(39,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)],[8]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(19,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(73,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)],[19]) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(36,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[37]) ).
thf(9,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
thf(42,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ zero )
= ( star @ B ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,44]) ).
thf(260,plain,
( ( addition @ one @ zero )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( star @ zero )),bind(B,$thf( zero ))]]) ).
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(285,plain,
( ( star @ zero )
= one ),
inference(rewrite,[status(thm)],[260,32]) ).
thf(290,plain,
! [A: $i] :
( ( ( addition @ one @ ( multiplication @ A @ one ) )
= ( star @ A ) )
| ( ( star @ zero )
!= ( star @ A ) ) ),
inference(paramod_ordered,[status(thm)],[285,44]) ).
thf(291,plain,
( ( addition @ one @ ( multiplication @ zero @ one ) )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( zero ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(67,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(68,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[68]) ).
thf(352,plain,
( ( addition @ one @ zero )
= one ),
inference(rewrite,[status(thm)],[291,69,285]) ).
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(364,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ one @ A )
= ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ one @ zero )
!= ( addition @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[352,26]) ).
thf(365,plain,
! [A: $i] :
( ( addition @ one @ ( addition @ zero @ A ) )
= ( addition @ one @ A ) ),
inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( one ))]]) ).
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(524,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ one @ A )
= ( addition @ C @ B ) )
| ( ( addition @ one @ ( addition @ zero @ A ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[365,35]) ).
thf(525,plain,
! [A: $i] :
( ( addition @ ( addition @ zero @ A ) @ one )
= ( addition @ one @ A ) ),
inference(pattern_uni,[status(thm)],[524:[bind(A,$thf( E )),bind(B,$thf( one )),bind(C,$thf( addition @ zero @ E ))]]) ).
thf(555,plain,
! [A: $i] :
( ( addition @ ( addition @ zero @ A ) @ one )
= ( addition @ one @ A ) ),
inference(simp,[status(thm)],[525]) ).
thf(887,plain,
! [A: $i] :
( ( addition @ zero @ ( addition @ A @ one ) )
= ( addition @ one @ A ) ),
inference(rewrite,[status(thm)],[555,26]) ).
thf(924,plain,
! [A: $i] :
( ( ( addition @ zero @ ( addition @ A @ one ) )
= one )
| ( ( addition @ one @ A )
!= ( addition @ one @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[887,352]) ).
thf(925,plain,
( ( addition @ zero @ ( addition @ zero @ one ) )
= one ),
inference(pattern_uni,[status(thm)],[924:[bind(A,$thf( zero ))]]) ).
thf(528,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(529,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[528:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(1029,plain,
( ( addition @ zero @ one )
= one ),
inference(rewrite,[status(thm)],[925,529]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ A )
= B )
| ( ( addition @ zero @ ( addition @ A @ one ) )
!= ( addition @ zero @ B ) ) ),
inference(paramod_ordered,[status(thm)],[887,529]) ).
thf(889,plain,
! [A: $i] :
( ( addition @ one @ A )
= ( addition @ A @ one ) ),
inference(pattern_uni,[status(thm)],[888:[bind(A,$thf( C )),bind(B,$thf( addition @ C @ one ))]]) ).
thf(1023,plain,
! [A: $i] :
( ( addition @ one @ A )
= ( addition @ A @ one ) ),
inference(simp,[status(thm)],[889]) ).
thf(53,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [A: $i] :
( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
= ( strong_iteration @ A ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(1318,plain,
! [A: $i] :
( ( ( addition @ one @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
= ( strong_iteration @ A ) )
| ( ( star @ zero )
!= ( star @ A ) ) ),
inference(paramod_ordered,[status(thm)],[285,54]) ).
thf(1319,plain,
( ( addition @ one @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) )
= ( strong_iteration @ zero ) ),
inference(pattern_uni,[status(thm)],[1318:[bind(A,$thf( zero ))]]) ).
thf(10,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(45,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)],[10]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
| ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
inference(cnf,[status(esa)],[45]) ).
thf(15,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
thf(57,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
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(16,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(60,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)],[16]) ).
thf(61,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)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[61]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[64]) ).
thf(2107,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ zero @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[529,65]) ).
thf(2108,plain,
! [A: $i] :
( ( A != A )
| ( leq @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[2107:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(2147,plain,
! [A: $i] : ( leq @ zero @ A ),
inference(simp,[status(thm)],[2108]) ).
thf(1486,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( strong_iteration @ zero ) )
| ( ( addition @ one @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1319,35]) ).
thf(1487,plain,
( ( addition @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) @ one )
= ( strong_iteration @ zero ) ),
inference(pattern_uni,[status(thm)],[1486:[bind(A,$thf( one )),bind(B,$thf( multiplication @ ( strong_iteration @ zero ) @ zero ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
thf(70,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( leq @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) @ ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) )
& ( leq @ ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( leq @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) @ ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) )
& ( leq @ ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i] :
( ( leq @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) @ ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) )
& ( leq @ ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(937,plain,
! [B: $i,A: $i] :
( ( A
= ( addition @ zero @ ( addition @ B @ one ) ) )
| ( ( addition @ A @ A )
!= ( addition @ one @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,887]) ).
thf(938,plain,
( ( addition @ zero @ ( addition @ one @ one ) )
= one ),
inference(pattern_uni,[status(thm)],[937:[bind(A,$thf( one )),bind(B,$thf( one ))]]) ).
thf(1157,plain,
( ( addition @ one @ one )
= one ),
inference(rewrite,[status(thm)],[938,529]) ).
thf(2133,plain,
! [B: $i,A: $i] :
( ( one != B )
| ( leq @ A @ B )
| ( ( addition @ one @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1157,65]) ).
thf(2134,plain,
( ( one != one )
| ( leq @ one @ one ) ),
inference(pattern_uni,[status(thm)],[2133:[bind(A,$thf( one )),bind(B,$thf( one ))]]) ).
thf(2144,plain,
leq @ one @ one,
inference(simp,[status(thm)],[2134]) ).
thf(12,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(49,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(50,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[50]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ A )
= ( star @ B ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,44]) ).
thf(264,plain,
( ( addition @ one @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(58,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(2111,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ zero )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[32,65]) ).
thf(2112,plain,
! [A: $i] :
( ( A != zero )
| ( leq @ A @ zero ) ),
inference(pattern_uni,[status(thm)],[2111:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(2137,plain,
leq @ zero @ zero,
inference(simp,[status(thm)],[2112]) ).
thf(22,plain,
~ ( ! [A: $i,B: $i] : ( leq @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) @ ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) )
& ! [A: $i,B: $i] : ( leq @ ( multiplication @ ( star @ B ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) @ ( strong_iteration @ ( multiplication @ ( star @ A ) @ B ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) )
| ~ ( leq @ ( multiplication @ ( star @ sk4 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) ) @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(102,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( star @ sk4 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,23]) ).
thf(116,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk4 )
!= zero )
| ( A
!= ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(138,plain,
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk4 )
!= zero ) ),
inference(simp,[status(thm)],[116]) ).
thf(150,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk4 )
!= zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( star @ sk2 ) @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,138]) ).
thf(173,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk4 )
!= zero )
| ( ( star @ sk2 )
!= zero )
| ( A
!= ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(185,plain,
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk4 )
!= zero )
| ( ( star @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[173]) ).
thf(200,plain,
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk2 )
!= zero )
| ( ( star @ sk4 )
!= ( star @ sk2 ) )
| ( zero != zero ) ),
inference(eqfactor_ordered,[status(thm)],[185]) ).
thf(210,plain,
( ~ ( leq @ ( strong_iteration @ ( multiplication @ ( star @ sk1 ) @ sk2 ) ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk2 )
!= zero )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[200]) ).
thf(217,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ zero ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk2 )
!= zero )
| ( sk4 != sk2 )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( star @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[38,210]) ).
thf(224,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ zero ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk2 )
!= zero )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[217]) ).
thf(232,plain,
( ~ ( leq @ ( strong_iteration @ zero ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( ( star @ sk2 )
!= zero )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[224]) ).
thf(390,plain,
( ~ ( leq @ ( strong_iteration @ zero ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( ( star @ sk2 )
!= ( star @ sk1 ) )
| ( zero != zero ) ),
inference(eqfactor_ordered,[status(thm)],[232]) ).
thf(397,plain,
( ~ ( leq @ ( strong_iteration @ zero ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ ( multiplication @ ( star @ sk3 ) @ sk4 ) ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[390]) ).
thf(404,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ zero ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ zero ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( star @ sk3 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[38,397]) ).
thf(411,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ zero ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ zero ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( star @ sk3 )
!= zero )
| ( A != sk4 ) ),
inference(simp,[status(thm)],[404]) ).
thf(418,plain,
( ~ ( leq @ ( strong_iteration @ zero ) @ zero )
| ~ ( leq @ zero @ ( strong_iteration @ zero ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( star @ sk3 )
!= zero ) ),
inference(simp,[status(thm)],[411]) ).
thf(487,plain,
( ~ ( leq @ zero @ ( strong_iteration @ zero ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( star @ sk3 )
!= zero )
| ( ( leq @ ( strong_iteration @ zero ) @ zero )
!= ( leq @ zero @ ( strong_iteration @ zero ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[418]) ).
thf(492,plain,
( ~ ( leq @ zero @ ( strong_iteration @ zero ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( star @ sk3 )
!= zero )
| ( ( strong_iteration @ zero )
!= zero )
| ( ( strong_iteration @ zero )
!= zero ) ),
inference(simp,[status(thm)],[487]) ).
thf(495,plain,
( ~ ( leq @ zero @ ( strong_iteration @ zero ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( star @ sk3 )
!= zero )
| ( ( strong_iteration @ zero )
!= zero ) ),
inference(simp,[status(thm)],[492]) ).
thf(676,plain,
( ~ ( leq @ zero @ ( strong_iteration @ zero ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( strong_iteration @ zero )
!= zero )
| ( ( star @ sk3 )
!= ( star @ sk1 ) )
| ( zero != zero ) ),
inference(eqfactor_ordered,[status(thm)],[495]) ).
thf(679,plain,
( ~ ( leq @ zero @ ( strong_iteration @ zero ) )
| ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( strong_iteration @ zero )
!= zero )
| ( ( star @ sk3 )
!= ( star @ sk1 ) ) ),
inference(simp,[status(thm)],[676]) ).
thf(2153,plain,
( ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( strong_iteration @ zero )
!= zero )
| ( ( star @ sk3 )
!= ( star @ sk1 ) )
| ( ( leq @ zero @ ( strong_iteration @ zero ) )
!= ( leq @ zero @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[2137,679]) ).
thf(2224,plain,
( ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( strong_iteration @ zero )
!= zero )
| ( sk3 != sk1 )
| ( zero != zero )
| ( ( strong_iteration @ zero )
!= zero ) ),
inference(simp,[status(thm)],[2153]) ).
thf(2293,plain,
( ( sk4 != sk2 )
| ( ( star @ sk1 )
!= zero )
| ( sk2 != sk1 )
| ( ( strong_iteration @ zero )
!= zero )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[2224]) ).
thf(20,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(76,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)],[20]) ).
thf(11,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(47,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)],[11]) ).
thf(48,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)],[47]) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ one ) )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[264,35]) ).
thf(539,plain,
( ( addition @ ( star @ one ) @ one )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[538:[bind(A,$thf( one )),bind(B,$thf( star @ one ))]]) ).
thf(2113,plain,
! [B: $i,A: $i] :
( ( ( star @ one )
!= B )
| ( leq @ A @ B )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[264,65]) ).
thf(2114,plain,
( ( ( star @ one )
!= ( star @ one ) )
| ( leq @ one @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[2113:[bind(A,$thf( one )),bind(B,$thf( star @ one ))]]) ).
thf(2138,plain,
leq @ one @ ( star @ one ),
inference(simp,[status(thm)],[2114]) ).
thf(158569,plain,
$false,
inference(cvc4,[status(thm)],[56,52,41,73,1029,35,67,1023,69,352,42,24,1319,46,57,29,60,529,38,2147,1487,70,21,33,65,285,2144,32,264,45,44,59,27,54,2293,49,76,39,48,887,539,1157,26,55,23,36,30,51,47,2138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE147+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n027.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 03:19:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.92/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.02 % [INFO] Parsing done (134ms).
% 1.23/1.03 % [INFO] Running in sequential loop mode.
% 1.76/1.23 % [INFO] eprover registered as external prover.
% 1.76/1.23 % [INFO] cvc4 registered as external prover.
% 1.76/1.23 % [INFO] Scanning for conjecture ...
% 1.90/1.29 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.90/1.33 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.11/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.11/1.36 % [INFO] Type checking passed.
% 2.11/1.37 % [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 ...
% 179.90/36.25 % External prover 'cvc4' found a proof!
% 179.90/36.25 % [INFO] Killing All external provers ...
% 179.90/36.25 % Time passed: 35730ms (effective reasoning time: 35220ms)
% 179.90/36.25 % 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)>
% 179.90/36.26 % 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
% 179.90/36.26 % No. of inferences in proof: 138
% 179.90/36.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 35730 ms resp. 35220 ms w/o parsing
% 179.90/36.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 179.90/36.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------