TSTP Solution File: KLE131+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:25:07 EDT 2023
% Result : Theorem 13.97s 3.51s
% Output : Refutation 13.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 47
% Syntax : Number of formulae : 151 ( 93 unt; 18 typ; 0 def)
% Number of atoms : 197 ( 193 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 1047 ( 62 ~; 56 |; 1 &; 921 @)
% ( 1 <=>; 4 =>; 2 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 4 con; 0-2 aty)
% Number of variables : 177 ( 0 ^; 177 !; 0 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(divergence_type,type,
divergence: $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(forward_diamond_type,type,
forward_diamond: $i > $i > $i ).
thf(star_type,type,
star: $i > $i ).
thf(domain_difference_type,type,
domain_difference: $i > $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(codomain_type,type,
codomain: $i > $i ).
thf(coantidomain_type,type,
coantidomain: $i > $i ).
thf(backward_box_type,type,
backward_box: $i > $i > $i ).
thf(c_type,type,
c: $i > $i ).
thf(backward_diamond_type,type,
backward_diamond: $i > $i > $i ).
thf(antidomain_type,type,
antidomain: $i > $i ).
thf(forward_box_type,type,
forward_box: $i > $i > $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(14,axiom,
! [A: $i] :
( ( addition @ ( antidomain @ ( antidomain @ A ) ) @ ( antidomain @ A ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(69,plain,
! [A: $i] :
( ( addition @ ( antidomain @ ( antidomain @ A ) ) @ ( antidomain @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(42,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,axiom,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
thf(87,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(88,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(cnf,[status(esa)],[87]) ).
thf(89,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(lifteq,[status(thm)],[88]) ).
thf(43,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[43]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( multiplication @ A @ ( coantidomain @ A ) )
!= ( multiplication @ one @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89,44]) ).
thf(266,plain,
( ( coantidomain @ one )
= zero ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( one )),bind(B,$thf( coantidomain @ one ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
thf(45,plain,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,plain,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [A: $i] :
( ( coantidomain @ ( coantidomain @ A ) )
= ( codomain @ A ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(284,plain,
! [A: $i] :
( ( ( coantidomain @ zero )
= ( codomain @ A ) )
| ( ( coantidomain @ one )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[266,47]) ).
thf(285,plain,
( ( coantidomain @ zero )
= ( codomain @ one ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( one ))]]) ).
thf(298,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ one ) )
= ( codomain @ A ) )
| ( ( coantidomain @ zero )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[285,47]) ).
thf(299,plain,
( ( coantidomain @ ( codomain @ one ) )
= ( codomain @ zero ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( zero ))]]) ).
thf(312,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ zero ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ one ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[299,47]) ).
thf(313,plain,
( ( coantidomain @ ( codomain @ zero ) )
= ( codomain @ ( codomain @ one ) ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( codomain @ one ))]]) ).
thf(331,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ zero ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[313,47]) ).
thf(332,plain,
( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
= ( codomain @ ( codomain @ zero ) ) ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( codomain @ zero ))]]) ).
thf(388,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[332,47]) ).
thf(389,plain,
( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
= ( codomain @ ( codomain @ ( codomain @ one ) ) ) ),
inference(pattern_uni,[status(thm)],[388:[bind(A,$thf( codomain @ ( codomain @ one ) ))]]) ).
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',left_distributivity) ).
thf(84,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(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( addition @ ( domain @ A ) @ ( addition @ ( forward_diamond @ B @ ( domain @ A ) ) @ ( domain @ C ) ) )
= ( addition @ ( forward_diamond @ B @ ( domain @ A ) ) @ ( domain @ C ) ) )
=> ( ( addition @ ( domain @ A ) @ ( addition @ ( divergence @ B ) @ ( forward_diamond @ ( star @ B ) @ ( domain @ C ) ) ) )
= ( addition @ ( divergence @ B ) @ ( forward_diamond @ ( star @ B ) @ ( domain @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence2) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
( ( ( addition @ ( domain @ A ) @ ( addition @ ( forward_diamond @ B @ ( domain @ A ) ) @ ( domain @ C ) ) )
= ( addition @ ( forward_diamond @ B @ ( domain @ A ) ) @ ( domain @ C ) ) )
=> ( ( addition @ ( domain @ A ) @ ( addition @ ( divergence @ B ) @ ( forward_diamond @ ( star @ B ) @ ( domain @ C ) ) ) )
= ( addition @ ( divergence @ B ) @ ( forward_diamond @ ( star @ B ) @ ( domain @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(4,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(39,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[40]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(72,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,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',right_distributivity) ).
thf(114,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)],[29]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( domain_difference @ A @ B )
= ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_difference) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( domain_difference @ A @ B )
= ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( domain_difference @ A @ B )
= ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) )
= ( domain_difference @ A @ B ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(537,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[389,47]) ).
thf(538,plain,
( ( coantidomain @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
= ( codomain @ ( codomain @ ( codomain @ zero ) ) ) ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( codomain @ ( codomain @ zero ) ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(57,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(58,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[58]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ B @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[41,59]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( A != B )
| ( one != zero ) ),
inference(simp,[status(thm)],[132]) ).
thf(136,plain,
! [A: $i] :
( ( A = zero )
| ( one != zero ) ),
inference(simp,[status(thm)],[134]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( divergence @ A )
= zero )
<= ! [B: $i] :
( ( addition @ ( domain @ B ) @ ( forward_diamond @ ( star @ A ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ A @ ( domain @ B ) ) ) ) )
= ( forward_diamond @ ( star @ A ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ A @ ( domain @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( divergence @ A )
= zero )
<= ! [B: $i] :
( ( addition @ ( domain @ B ) @ ( forward_diamond @ ( star @ A ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ A @ ( domain @ B ) ) ) ) )
= ( forward_diamond @ ( star @ A ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ A @ ( domain @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i] :
( ( ( divergence @ A )
= zero )
| ~ ! [B: $i] :
( ( addition @ ( domain @ B ) @ ( forward_diamond @ ( star @ A ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ A @ ( domain @ B ) ) ) ) )
= ( forward_diamond @ ( star @ A ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ A @ ( domain @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
( ( divergence @ sk1 )
!= zero ),
inference(cnf,[status(esa)],[31]) ).
thf(35,plain,
( ( divergence @ sk1 )
!= zero ),
inference(lifteq,[status(thm)],[33]) ).
thf(152,plain,
! [A: $i] :
( ( one != zero )
| ( A
!= ( divergence @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[136,35]) ).
thf(153,plain,
one != zero,
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( divergence @ sk1 ))]]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( addition @ ( coantidomain @ ( multiplication @ A @ B ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).
thf(93,plain,
! [A: $i,B: $i] :
( ( addition @ ( coantidomain @ ( multiplication @ A @ B ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(315,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ zero ) )
= zero )
| ( ( coantidomain @ ( codomain @ one ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[299,89]) ).
thf(316,plain,
( ( multiplication @ ( codomain @ one ) @ ( codomain @ zero ) )
= zero ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( codomain @ one ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(78,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(526,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[389,89]) ).
thf(527,plain,
( ( multiplication @ ( codomain @ ( codomain @ zero ) ) @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[526:[bind(A,$thf( codomain @ ( codomain @ zero ) ))]]) ).
thf(73,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(cnf,[status(esa)],[72]) ).
thf(74,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(lifteq,[status(thm)],[73]) ).
thf(25,axiom,
! [A: $i] :
( ( c @ A )
= ( antidomain @ ( domain @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(102,plain,
! [A: $i] :
( ( c @ A )
= ( antidomain @ ( domain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(60,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(117,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)],[30]) ).
thf(3,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(36,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)],[3]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(433,plain,
! [B: $i,A: $i] :
( ( ( domain_difference @ A @ B )
= zero )
| ( ( multiplication @ ( codomain @ one ) @ ( codomain @ zero ) )
!= ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[316,56]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( ( domain_difference @ A @ B )
= zero )
| ( ( codomain @ one )
!= ( domain @ A ) )
| ( ( antidomain @ B )
!= ( codomain @ zero ) ) ),
inference(simp,[status(thm)],[433]) ).
thf(26,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(105,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(106,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[105]) ).
thf(107,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[106]) ).
thf(32,plain,
! [A: $i] :
( ( addition @ ( domain @ A ) @ ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ A ) @ ( forward_diamond @ sk1 @ ( domain @ A ) ) ) ) )
= ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ A ) @ ( forward_diamond @ sk1 @ ( domain @ A ) ) ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(34,plain,
! [A: $i] :
( ( addition @ ( domain @ A ) @ ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ A ) @ ( forward_diamond @ sk1 @ ( domain @ A ) ) ) ) )
= ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ A ) @ ( forward_diamond @ sk1 @ ( domain @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A
= ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ sk1 @ ( domain @ B ) ) ) ) )
| ( ( addition @ A @ zero )
!= ( addition @ ( domain @ B ) @ ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ sk1 @ ( domain @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,34]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A
= ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ sk1 @ ( domain @ B ) ) ) ) )
| ( A
!= ( domain @ B ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ B ) @ ( forward_diamond @ sk1 @ ( domain @ B ) ) ) )
!= zero ) ),
inference(simp,[status(thm)],[210]) ).
thf(214,plain,
! [A: $i] :
( ( ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ A ) @ ( forward_diamond @ sk1 @ ( domain @ A ) ) ) )
= ( domain @ A ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ A ) @ ( forward_diamond @ sk1 @ ( domain @ A ) ) ) )
!= zero ) ),
inference(simp,[status(thm)],[212]) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( ( codomain @ one )
!= ( domain @ A ) )
| ( ( antidomain @ B )
!= ( codomain @ zero ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ C ) @ ( forward_diamond @ sk1 @ ( domain @ C ) ) ) )
= ( domain @ C ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
!= zero )
| ( ( domain_difference @ A @ B )
!= ( domain_difference @ ( domain @ C ) @ ( forward_diamond @ sk1 @ ( domain @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[463,214]) ).
thf(626,plain,
! [A: $i] :
( ( ( codomain @ one )
!= ( domain @ ( domain @ A ) ) )
| ( ( antidomain @ ( forward_diamond @ sk1 @ ( domain @ A ) ) )
!= ( codomain @ zero ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ A ) @ ( forward_diamond @ sk1 @ ( domain @ A ) ) ) )
= ( domain @ A ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
!= zero ) ),
inference(pattern_uni,[status(thm)],[625:[bind(A,$thf( domain @ G )),bind(B,$thf( forward_diamond @ sk1 @ ( domain @ G ) )),bind(C,$thf( G ))]]) ).
thf(630,plain,
! [A: $i] :
( ( ( codomain @ one )
!= ( domain @ ( domain @ A ) ) )
| ( ( antidomain @ ( forward_diamond @ sk1 @ ( domain @ A ) ) )
!= ( codomain @ zero ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ ( domain_difference @ ( domain @ A ) @ ( forward_diamond @ sk1 @ ( domain @ A ) ) ) )
= ( domain @ A ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
!= zero ) ),
inference(simp,[status(thm)],[626]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( multiplication @ ( antidomain @ A ) @ A )
!= ( multiplication @ B @ one ) ) ),
inference(paramod_ordered,[status(thm)],[74,41]) ).
thf(224,plain,
( ( antidomain @ one )
= zero ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( one )),bind(B,$thf( antidomain @ one ))]]) ).
thf(634,plain,
! [C: $i,B: $i,A: $i] :
( ( ( codomain @ one )
!= ( domain @ A ) )
| ( ( antidomain @ B )
!= ( codomain @ zero ) )
| ( ( codomain @ one )
!= ( domain @ ( domain @ C ) ) )
| ( ( antidomain @ ( forward_diamond @ sk1 @ ( domain @ C ) ) )
!= ( codomain @ zero ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
= ( domain @ C ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
!= zero )
| ( ( domain_difference @ A @ B )
!= ( domain_difference @ ( domain @ C ) @ ( forward_diamond @ sk1 @ ( domain @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[463,630]) ).
thf(635,plain,
! [A: $i] :
( ( ( codomain @ one )
!= ( domain @ ( domain @ A ) ) )
| ( ( antidomain @ ( forward_diamond @ sk1 @ ( domain @ A ) ) )
!= ( codomain @ zero ) )
| ( ( codomain @ one )
!= ( domain @ ( domain @ A ) ) )
| ( ( antidomain @ ( forward_diamond @ sk1 @ ( domain @ A ) ) )
!= ( codomain @ zero ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
= ( domain @ A ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
!= zero ) ),
inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( domain @ G )),bind(B,$thf( forward_diamond @ sk1 @ ( domain @ G ) )),bind(C,$thf( G ))]]) ).
thf(650,plain,
! [A: $i] :
( ( ( codomain @ one )
!= ( domain @ ( domain @ A ) ) )
| ( ( antidomain @ ( forward_diamond @ sk1 @ ( domain @ A ) ) )
!= ( codomain @ zero ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
= ( domain @ A ) )
| ( ( forward_diamond @ ( star @ sk1 ) @ zero )
!= zero ) ),
inference(simp,[status(thm)],[635]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_diamond) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(334,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ one ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ zero ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[313,89]) ).
thf(335,plain,
( ( multiplication @ ( codomain @ zero ) @ ( codomain @ ( codomain @ one ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( codomain @ zero ))]]) ).
thf(381,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ zero ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[332,89]) ).
thf(382,plain,
( ( multiplication @ ( codomain @ ( codomain @ one ) ) @ ( codomain @ ( codomain @ zero ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( codomain @ ( codomain @ one ) ))]]) ).
thf(18,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(81,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)],[18]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( forward_diamond @ A @ B )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( forward_diamond @ A @ B )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
! [A: $i] :
( ( forward_diamond @ A @ ( divergence @ A ) )
= ( divergence @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
thf(108,plain,
! [A: $i] :
( ( forward_diamond @ A @ ( divergence @ A ) )
= ( divergence @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(79,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[78]) ).
thf(80,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[79]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( backward_box @ A @ B )
= ( c @ ( backward_diamond @ A @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_box) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( backward_box @ A @ B )
= ( c @ ( backward_diamond @ A @ ( c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( forward_box @ A @ B )
= ( c @ ( forward_diamond @ A @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_box) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( forward_box @ A @ B )
= ( c @ ( forward_diamond @ A @ ( c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
! [A: $i] :
( ( domain @ A )
= ( antidomain @ ( antidomain @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(99,plain,
! [A: $i] :
( ( domain @ A )
= ( antidomain @ ( antidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( addition @ ( antidomain @ ( multiplication @ A @ B ) ) @ ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) )
= ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( addition @ ( antidomain @ ( multiplication @ A @ B ) ) @ ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) )
= ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( antidomain @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44,74]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( antidomain @ B )
!= one )
| ( A != B ) ),
inference(simp,[status(thm)],[228]) ).
thf(239,plain,
! [A: $i] :
( ( A = zero )
| ( ( antidomain @ A )
!= one ) ),
inference(simp,[status(thm)],[235]) ).
thf(595,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ ( codomain @ zero ) ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[538,89]) ).
thf(596,plain,
( ( multiplication @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) @ ( codomain @ ( codomain @ ( codomain @ zero ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[595:[bind(A,$thf( codomain @ ( codomain @ ( codomain @ one ) ) ))]]) ).
thf(310,plain,
( ( ( codomain @ zero )
= zero )
| ( ( coantidomain @ ( codomain @ one ) )
!= ( coantidomain @ one ) ) ),
inference(paramod_ordered,[status(thm)],[266,299]) ).
thf(322,plain,
( ( ( codomain @ zero )
= zero )
| ( ( codomain @ one )
!= one ) ),
inference(simp,[status(thm)],[310]) ).
thf(21,axiom,
! [A: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ A ) ) @ ( coantidomain @ A ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
thf(90,plain,
! [A: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ A ) ) @ ( coantidomain @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1799,plain,
$false,
inference(e,[status(thm)],[69,42,389,84,96,41,72,114,56,538,153,93,57,316,78,89,527,74,102,60,117,38,630,285,224,650,53,105,266,34,45,44,59,313,335,382,54,81,39,66,108,299,80,35,48,63,463,31,99,87,75,214,36,51,107,239,332,596,47,322,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n014.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 19 02:56:28 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.98 % [INFO] Parsing done (132ms).
% 1.20/0.99 % [INFO] Running in sequential loop mode.
% 1.86/1.21 % [INFO] eprover registered as external prover.
% 1.86/1.21 % [INFO] cvc4 registered as external prover.
% 1.86/1.22 % [INFO] Scanning for conjecture ...
% 1.94/1.28 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ...
% 2.24/1.33 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.24/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.24/1.37 % [INFO] Type checking passed.
% 2.24/1.37 % [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 ...
% 13.97/3.51 % External prover 'e' found a proof!
% 13.97/3.51 % [INFO] Killing All external provers ...
% 13.97/3.51 % Time passed: 2987ms (effective reasoning time: 2517ms)
% 13.97/3.51 % 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)>
% 13.97/3.51 % Axioms used in derivation (28): forward_box, additive_identity, domain4, backward_box, domain3, codomain2, complement, right_annihilation, backward_diamond, forward_diamond, codomain4, left_annihilation, codomain1, additive_idempotence, additive_associativity, right_distributivity, domain2, divergence2, multiplicative_right_identity, order, additive_commutativity, domain_difference, multiplicative_left_identity, codomain3, domain1, divergence1, multiplicative_associativity, left_distributivity
% 13.97/3.51 % No. of inferences in proof: 133
% 13.97/3.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2987 ms resp. 2517 ms w/o parsing
% 13.97/3.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.97/3.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------