TSTP Solution File: KLE104-10 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE104-10 : TPTP v8.1.2. Released v7.3.0.
% 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 11:25:04 EDT 2023
% Result : Unsatisfiable 39.75s 6.78s
% Output : Refutation 39.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 52
% Syntax : Number of formulae : 140 ( 95 unt; 21 typ; 0 def)
% Number of atoms : 145 ( 144 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 672 ( 36 ~; 26 |; 0 &; 610 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 7 con; 0-4 aty)
% Number of variables : 147 ( 0 ^; 147 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
thf(addition_type,type,
addition: $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(sK2_goals_X1_type,type,
sK2_goals_X1: $i ).
thf(backward_box_type,type,
backward_box: $i > $i > $i ).
thf(sK3_goals_X0_type,type,
sK3_goals_X0: $i ).
thf(sK1_goals_X2_type,type,
sK1_goals_X2: $i ).
thf(one_type,type,
one: $i ).
thf(forward_box_type,type,
forward_box: $i > $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(backward_diamond_type,type,
backward_diamond: $i > $i > $i ).
thf(codomain_type,type,
codomain: $i > $i ).
thf(coantidomain_type,type,
coantidomain: $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(ifeq2_type,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(antidomain_type,type,
antidomain: $i > $i ).
thf(domain_difference_type,type,
domain_difference: $i > $i > $i ).
thf(c_type,type,
c: $i > $i ).
thf(forward_diamond_type,type,
forward_diamond: $i > $i > $i ).
thf(leq_type,type,
leq: $i > $i > $i ).
thf(true_type,type,
true: $i ).
thf(19,axiom,
! [B: $i,A: $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(69,plain,
! [B: $i,A: $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)],[19]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[51]) ).
thf(26,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(83,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(84,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[83]) ).
thf(17,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(65,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
thf(41,plain,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(87,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(24,axiom,
! [A: $i] :
( ( domain @ A )
= ( antidomain @ ( antidomain @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(79,plain,
! [A: $i] :
( ( domain @ A )
= ( antidomain @ ( antidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
thf(47,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,plain,
! [A: $i] :
( ( coantidomain @ ( coantidomain @ A ) )
= ( codomain @ A ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(45,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(46,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[45]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( forward_diamond @ A @ B )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( forward_diamond @ A @ B )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( domain_difference @ A @ B )
= ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_difference) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( domain_difference @ A @ B )
= ( multiplication @ ( domain @ A ) @ ( antidomain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( forward_box @ A @ B )
= ( c @ ( forward_diamond @ A @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_box) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( forward_box @ A @ B )
= ( c @ ( forward_diamond @ A @ ( c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(89,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(48,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(lifteq,[status(thm)],[47]) ).
thf(90,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[89]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( multiplication @ A @ ( coantidomain @ A ) )
!= ( multiplication @ one @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48,90]) ).
thf(193,plain,
( ( coantidomain @ one )
= zero ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( one )),bind(B,$thf( coantidomain @ one ))]]) ).
thf(205,plain,
! [A: $i] :
( ( ( coantidomain @ zero )
= ( codomain @ A ) )
| ( ( coantidomain @ one )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[193,42]) ).
thf(206,plain,
( ( coantidomain @ zero )
= ( codomain @ one ) ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( one ))]]) ).
thf(313,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ one ) )
= ( codomain @ A ) )
| ( ( coantidomain @ zero )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[206,42]) ).
thf(314,plain,
( ( coantidomain @ ( codomain @ one ) )
= ( codomain @ zero ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( zero ))]]) ).
thf(327,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ zero ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ one ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[314,42]) ).
thf(328,plain,
( ( coantidomain @ ( codomain @ zero ) )
= ( codomain @ ( codomain @ one ) ) ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( codomain @ one ))]]) ).
thf(345,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ zero ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[328,42]) ).
thf(346,plain,
( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
= ( codomain @ ( codomain @ zero ) ) ),
inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( codomain @ zero ))]]) ).
thf(393,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[346,42]) ).
thf(394,plain,
( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
= ( codomain @ ( codomain @ ( codomain @ one ) ) ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( codomain @ ( codomain @ one ) ))]]) ).
thf(451,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[394,48]) ).
thf(452,plain,
( ( multiplication @ ( codomain @ ( codomain @ zero ) ) @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[451:[bind(A,$thf( codomain @ ( codomain @ zero ) ))]]) ).
thf(2,negated_conjecture,
( ( addition @ ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) ) @ ( domain @ sK1_goals_X2 ) )
!= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_1) ).
thf(33,plain,
( ( addition @ ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) ) @ ( domain @ sK1_goals_X2 ) )
!= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,plain,
( ( addition @ ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) ) @ ( domain @ sK1_goals_X2 ) )
!= one ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(36,plain,
( ( addition @ ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) ) @ ( domain @ sK1_goals_X2 ) )
!= one ),
inference(lifteq,[status(thm)],[35]) ).
thf(113,plain,
! [A: $i] :
( ( A != one )
| ( ( addition @ A @ zero )
!= ( addition @ ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) ) @ ( domain @ sK1_goals_X2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,36]) ).
thf(117,plain,
( ( ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) )
!= one )
| ( ( domain @ sK1_goals_X2 )
!= zero ) ),
inference(simp,[status(thm)],[113]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
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(11,axiom,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(53,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(lifteq,[status(thm)],[53]) ).
thf(66,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[65]) ).
thf(577,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( multiplication @ ( antidomain @ A ) @ A )
!= ( multiplication @ B @ one ) ) ),
inference(paramod_ordered,[status(thm)],[54,66]) ).
thf(578,plain,
( ( antidomain @ one )
= zero ),
inference(pattern_uni,[status(thm)],[577:[bind(A,$thf( one )),bind(B,$thf( antidomain @ one ))]]) ).
thf(80,plain,
! [A: $i] :
( ( antidomain @ ( antidomain @ A ) )
= ( domain @ A ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(692,plain,
! [A: $i] :
( ( ( antidomain @ zero )
= ( domain @ A ) )
| ( ( antidomain @ one )
!= ( antidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[578,80]) ).
thf(693,plain,
( ( antidomain @ zero )
= ( domain @ one ) ),
inference(pattern_uni,[status(thm)],[692:[bind(A,$thf( one ))]]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [A: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ A ) ) @ ( coantidomain @ A ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
thf(73,plain,
! [A: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ A ) ) @ ( coantidomain @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ B @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[66,46]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( A != B )
| ( zero != one ) ),
inference(simp,[status(thm)],[101]) ).
thf(109,plain,
! [A: $i] :
( ( A = zero )
| ( zero != one ) ),
inference(simp,[status(thm)],[107]) ).
thf(265,plain,
! [A: $i] :
( ( zero != one )
| ( A
!= ( addition @ ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) ) @ ( domain @ sK1_goals_X2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,36]) ).
thf(266,plain,
zero != one,
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( addition @ ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) ) @ ( domain @ sK1_goals_X2 ) ))]]) ).
thf(1,negated_conjecture,
( ( addition @ ( domain @ sK2_goals_X1 ) @ ( backward_box @ sK3_goals_X0 @ ( domain @ sK1_goals_X2 ) ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(32,plain,
( ( addition @ ( domain @ sK2_goals_X1 ) @ ( backward_box @ sK3_goals_X0 @ ( domain @ sK1_goals_X2 ) ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(34,plain,
( ( addition @ ( domain @ sK2_goals_X1 ) @ ( backward_box @ sK3_goals_X0 @ ( domain @ sK1_goals_X2 ) ) )
= one ),
inference(lifteq,[status(thm)],[32]) ).
thf(6,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)],[6]) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[43]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(111,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ A @ zero )
!= ( addition @ ( domain @ sK2_goals_X1 ) @ ( backward_box @ sK3_goals_X0 @ ( domain @ sK1_goals_X2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,34]) ).
thf(114,plain,
! [A: $i] :
( ( A = one )
| ( A
!= ( domain @ sK2_goals_X1 ) )
| ( ( backward_box @ sK3_goals_X0 @ ( domain @ sK1_goals_X2 ) )
!= zero ) ),
inference(simp,[status(thm)],[111]) ).
thf(118,plain,
( ( ( domain @ sK2_goals_X1 )
= one )
| ( ( backward_box @ sK3_goals_X0 @ ( domain @ sK1_goals_X2 ) )
!= zero ) ),
inference(simp,[status(thm)],[114]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( ifeq2 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ifeq2 @ ( addition @ A @ B ) @ B @ ( leq @ A @ B ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(334,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ zero ) )
= zero )
| ( ( coantidomain @ ( codomain @ one ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[314,48]) ).
thf(335,plain,
( ( multiplication @ ( codomain @ one ) @ ( codomain @ zero ) )
= zero ),
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( codomain @ one ))]]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( leq @ A @ B ) @ true @ ( addition @ A @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_diamond) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
! [A: $i] :
( ( c @ A )
= ( antidomain @ ( domain @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(91,plain,
! [A: $i] :
( ( c @ A )
= ( antidomain @ ( domain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(398,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ zero ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[346,48]) ).
thf(399,plain,
( ( multiplication @ ( codomain @ ( codomain @ one ) ) @ ( codomain @ ( codomain @ zero ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( codomain @ ( codomain @ one ) ))]]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[49]) ).
thf(18,axiom,
! [A: $i] :
( ( addition @ ( antidomain @ ( antidomain @ A ) ) @ ( antidomain @ A ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(67,plain,
! [A: $i] :
( ( addition @ ( antidomain @ ( antidomain @ A ) ) @ ( antidomain @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( backward_diamond @ A @ B )
= ( codomain @ ( multiplication @ ( codomain @ B ) @ A ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(350,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ one ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ zero ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[328,48]) ).
thf(351,plain,
( ( multiplication @ ( codomain @ zero ) @ ( codomain @ ( codomain @ one ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( codomain @ zero ))]]) ).
thf(12,axiom,
! [B: $i,A: $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(55,plain,
! [B: $i,A: $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)],[12]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( backward_box @ A @ B )
= ( c @ ( backward_diamond @ A @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_box) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( backward_box @ A @ B )
= ( c @ ( backward_diamond @ A @ ( c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(446,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[394,42]) ).
thf(447,plain,
( ( coantidomain @ ( codomain @ ( codomain @ ( codomain @ one ) ) ) )
= ( codomain @ ( codomain @ ( codomain @ zero ) ) ) ),
inference(pattern_uni,[status(thm)],[446:[bind(A,$thf( codomain @ ( codomain @ zero ) ))]]) ).
thf(707,plain,
! [A: $i] :
( ( ( antidomain @ ( domain @ one ) )
= ( domain @ A ) )
| ( ( antidomain @ zero )
!= ( antidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[693,80]) ).
thf(708,plain,
( ( antidomain @ ( domain @ one ) )
= ( domain @ zero ) ),
inference(pattern_uni,[status(thm)],[707:[bind(A,$thf( zero ))]]) ).
thf(99,plain,
( ( addition @ ( domain @ sK2_goals_X1 ) @ ( backward_box @ sK3_goals_X0 @ ( domain @ sK1_goals_X2 ) ) )
!= ( addition @ ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) ) @ ( domain @ sK1_goals_X2 ) ) ),
inference(paramod_ordered,[status(thm)],[34,36]) ).
thf(100,plain,
( ( ( forward_box @ sK3_goals_X0 @ ( domain @ sK2_goals_X1 ) )
!= ( domain @ sK2_goals_X1 ) )
| ( ( backward_box @ sK3_goals_X0 @ ( domain @ sK1_goals_X2 ) )
!= ( domain @ sK1_goals_X2 ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(11315,plain,
$false,
inference(e,[status(thm)],[69,52,84,65,41,87,79,47,42,37,46,93,57,61,89,206,452,117,85,38,693,33,578,53,328,77,193,73,266,45,32,34,44,59,118,71,54,49,335,81,39,91,66,399,394,80,48,63,50,67,314,43,40,351,55,75,346,447,36,51,90,83,708,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : KLE104-10 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 03:29:22 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.85/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.95 % [INFO] Parsing done (121ms).
% 1.23/0.96 % [INFO] Running in sequential loop mode.
% 1.58/1.16 % [INFO] eprover registered as external prover.
% 1.58/1.16 % [INFO] cvc4 registered as external prover.
% 1.58/1.16 % [INFO] Scanning for conjecture ...
% 1.75/1.22 % [INFO] Found a conjecture and 29 axioms. Running axiom selection ...
% 1.75/1.26 % [INFO] Axiom selection finished. Selected 29 axioms (removed 0 axioms).
% 2.08/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.29 % [INFO] Type checking passed.
% 2.08/1.29 % [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 ...
% 39.75/6.77 % External prover 'e' found a proof!
% 39.75/6.77 % [INFO] Killing All external provers ...
% 39.75/6.78 % Time passed: 6270ms (effective reasoning time: 5815ms)
% 39.75/6.78 % 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)>
% 39.75/6.78 % Axioms used in derivation (29): forward_box, additive_identity, domain3, multiplicative_right_identity, codomain2, right_annihilation, domain1, backward_diamond, ifeq_axiom_001, domain4, forward_diamond, codomain4, backward_box, ifeq_axiom, left_annihilation, codomain1, additive_idempotence, additive_associativity, right_distributivity, domain2, order, additive_commutativity, domain_difference, order_1, complement, multiplicative_left_identity, codomain3, multiplicative_associativity, left_distributivity
% 39.75/6.78 % No. of inferences in proof: 119
% 39.75/6.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6270 ms resp. 5815 ms w/o parsing
% 39.83/6.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 39.83/6.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------