TSTP Solution File: LCL039-1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : LCL039-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 : Tue May 7 07:53:52 EDT 2024
% Result : Unsatisfiable 9.14s 2.88s
% Output : Refutation 9.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 90 ( 51 unt; 5 typ; 0 def)
% Number of atoms : 172 ( 54 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 849 ( 78 ~; 43 |; 0 &; 728 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 128 ( 0 ^ 128 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(necessary_type,type,
necessary: $i > $i ).
thf(a_type,type,
a: $i ).
thf(not_type,type,
not: $i > $i ).
thf(1,negated_conjecture,
~ ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(9,plain,
~ ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,plain,
~ ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i] : ( is_a_theorem @ ( implies @ ( necessary @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation2) ).
thf(17,plain,
! [A: $i] : ( is_a_theorem @ ( implies @ ( necessary @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [A: $i] :
( ( is_a_theorem @ ( implies @ ( necessary @ A ) @ A ) )
!= ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,10]) ).
thf(21,plain,
! [A: $i] :
( ( implies @ ( necessary @ A ) @ A )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(24,plain,
! [A: $i] :
( ( ( necessary @ A )
!= ( necessary @ a ) )
| ( A
!= ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(25,plain,
( ( necessary @ ( not @ ( necessary @ ( not @ a ) ) ) )
!= ( necessary @ a ) ),
inference(simp,[status(thm)],[24]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( necessary @ ( implies @ A @ B ) ) @ ( implies @ ( necessary @ A ) @ ( necessary @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation1) ).
thf(16,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( necessary @ ( implies @ A @ B ) ) @ ( implies @ ( necessary @ A ) @ ( necessary @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ ( necessary @ ( implies @ A @ B ) ) @ ( implies @ ( necessary @ A ) @ ( necessary @ B ) ) ) )
!= ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,10]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( implies @ ( necessary @ ( implies @ A @ B ) ) @ ( implies @ ( necessary @ A ) @ ( necessary @ B ) ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( necessary @ ( implies @ A @ B ) )
!= ( necessary @ a ) )
| ( ( implies @ ( necessary @ A ) @ ( necessary @ B ) )
!= ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_49) ).
thf(15,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
!= ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,10]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( ( implies @ ( not @ A ) @ ( not @ B ) )
!= ( necessary @ a ) )
| ( ( implies @ B @ A )
!= ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( is_a_theorem @ ( necessary @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_of_necessitation) ).
thf(18,plain,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( is_a_theorem @ ( necessary @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,plain,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( is_a_theorem @ ( necessary @ A ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ B ) )
| ( ( is_a_theorem @ ( implies @ ( necessary @ A ) @ A ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17,19]) ).
thf(77,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( D )),bind(B,$thf( implies @ ( necessary @ D ) @ D ))]]) ).
thf(95,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ B ) )
| ( ( is_a_theorem @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[95,19]) ).
thf(163,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( E )),bind(B,$thf( necessary @ ( implies @ ( necessary @ E ) @ E ) ))]]) ).
thf(168,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ B ) )
| ( ( is_a_theorem @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[168,19]) ).
thf(181,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( F )),bind(B,$thf( necessary @ ( necessary @ ( implies @ ( necessary @ F ) @ F ) ) ))]]) ).
thf(186,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ B ) )
| ( ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[186,19]) ).
thf(199,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( G )),bind(B,$thf( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ G ) @ G ) ) ) ))]]) ).
thf(205,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ B ) )
| ( ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[205,19]) ).
thf(217,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( H )),bind(B,$thf( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ H ) @ H ) ) ) ) ))]]) ).
thf(224,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_18) ).
thf(13,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
inference(cnf,[status(esa)],[11]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ C ) )
| ( ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( is_a_theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13,19]) ).
thf(75,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( necessary @ ( implies @ B @ ( implies @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( implies @ G @ ( implies @ F @ G ) ))]]) ).
thf(94,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( necessary @ ( implies @ B @ ( implies @ A @ B ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ C ) )
| ( ( is_a_theorem @ ( necessary @ ( implies @ B @ ( implies @ A @ B ) ) ) )
!= ( is_a_theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[94,19]) ).
thf(358,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( implies @ B @ ( implies @ A @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( necessary @ ( implies @ H @ ( implies @ G @ H ) ) ))]]) ).
thf(365,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( implies @ B @ ( implies @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[358]) ).
thf(71,plain,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( necessary @ A ) )
!= ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,10]) ).
thf(88,plain,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( ( necessary @ A )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ A )
| ( ( necessary @ B )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) )
| ( ( is_a_theorem @ ( necessary @ A ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,88]) ).
thf(107,plain,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( ( necessary @ ( necessary @ A ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( C )),bind(B,$thf( necessary @ C ))]]) ).
thf(113,plain,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( ( necessary @ ( necessary @ A ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ A )
| ( ( necessary @ ( necessary @ B ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) )
| ( ( is_a_theorem @ ( necessary @ A ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,113]) ).
thf(244,plain,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( ( necessary @ ( necessary @ ( necessary @ A ) ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( C )),bind(B,$thf( necessary @ C ))]]) ).
thf(249,plain,
! [A: $i] :
( ~ ( is_a_theorem @ A )
| ( ( necessary @ ( necessary @ ( necessary @ A ) ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(384,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ C ) )
| ( ( is_a_theorem @ ( necessary @ ( necessary @ ( implies @ B @ ( implies @ A @ B ) ) ) ) )
!= ( is_a_theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[365,19]) ).
thf(385,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( implies @ B @ ( implies @ A @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( necessary @ ( necessary @ ( implies @ I @ ( implies @ H @ I ) ) ) ))]]) ).
thf(389,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( implies @ B @ ( implies @ A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[385]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ B @ C ) ) @ ( implies @ ( implies @ A @ B ) @ ( implies @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_35) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ B @ C ) ) @ ( implies @ ( implies @ A @ B ) @ ( implies @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( necessary @ B )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) )
| ( ( is_a_theorem @ ( implies @ ( necessary @ A ) @ A ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17,88]) ).
thf(101,plain,
! [A: $i] :
( ( necessary @ ( implies @ ( necessary @ A ) @ A ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( D )),bind(B,$thf( implies @ ( necessary @ D ) @ D ))]]) ).
thf(110,plain,
! [A: $i] :
( ( necessary @ ( implies @ ( necessary @ A ) @ A ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ B ) )
| ( ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[224,19]) ).
thf(267,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( I )),bind(B,$thf( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ I ) @ I ) ) ) ) ) ))]]) ).
thf(275,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( necessary @ B ) )
| ( ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ) ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[275,19]) ).
thf(412,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[411:[bind(A,$thf( J )),bind(B,$thf( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ J ) @ J ) ) ) ) ) ) ))]]) ).
thf(421,plain,
! [A: $i] : ( is_a_theorem @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( ( necessary @ B )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) )
| ( ( is_a_theorem @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[95,88]) ).
thf(154,plain,
! [A: $i] :
( ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( E )),bind(B,$thf( necessary @ ( implies @ ( necessary @ E ) @ E ) ))]]) ).
thf(169,plain,
! [A: $i] :
( ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ ( is_a_theorem @ A )
| ( ( implies @ A @ B )
!= A ) ),
inference(simp,[status(thm)],[43]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( ( necessary @ B )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) )
| ( ( is_a_theorem @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) )
!= ( is_a_theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[168,88]) ).
thf(172,plain,
! [A: $i] :
( ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( F )),bind(B,$thf( necessary @ ( necessary @ ( implies @ ( necessary @ F ) @ F ) ) ))]]) ).
thf(187,plain,
! [A: $i] :
( ( necessary @ ( necessary @ ( necessary @ ( implies @ ( necessary @ A ) @ A ) ) ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(26,plain,
( ( not @ ( necessary @ ( not @ a ) ) )
!= a ),
inference(simp,[status(thm)],[25]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( is_a_theorem @ ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( implies @ ( necessary @ a ) @ ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A
!= ( necessary @ a ) )
| ( ( implies @ B @ A )
!= ( not @ ( necessary @ ( not @ a ) ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(30,plain,
! [A: $i] :
( ( implies @ A @ ( necessary @ a ) )
!= ( not @ ( necessary @ ( not @ a ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(555,plain,
$false,
inference(e,[status(thm)],[10,25,61,60,224,13,205,44,12,16,11,94,15,365,249,88,389,14,110,421,57,28,275,21,9,169,45,17,187,113,18,95,26,186,23,168,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL039-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n015.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 6 11:50:24 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/0.99 % [INFO] Parsing done (113ms).
% 1.15/1.00 % [INFO] Running in sequential loop mode.
% 1.66/1.22 % [INFO] eprover registered as external prover.
% 1.66/1.23 % [INFO] cvc4 registered as external prover.
% 1.66/1.23 % [INFO] Scanning for conjecture ...
% 1.74/1.29 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.74/1.31 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.74/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.74/1.32 % [INFO] Type checking passed.
% 1.74/1.32 % [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 ...
% 9.14/2.87 % External prover 'e' found a proof!
% 9.14/2.88 % [INFO] Killing All external provers ...
% 9.14/2.88 % Time passed: 2342ms (effective reasoning time: 1876ms)
% 9.14/2.88 % 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)>
% 9.14/2.88 % Axioms used in derivation (7): condensed_detachment, cn_18, cn_35, necessitation2, necessitation1, cn_49, axiom_of_necessitation
% 9.14/2.88 % No. of inferences in proof: 85
% 9.14/2.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2342 ms resp. 1876 ms w/o parsing
% 9.14/2.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.14/2.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------