TSTP Solution File: LCL276-3 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL276-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:30:00 EDT 2023
% Result : Unsatisfiable 11.16s 3.09s
% Output : Refutation 11.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 108 ( 75 unt; 10 typ; 0 def)
% Number of atoms : 157 ( 54 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1318 ( 59 ~; 31 |; 0 &;1228 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 195 ( 0 ^; 195 !; 0 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_type,type,
theorem: $i > $o ).
thf(equivalent_type,type,
equivalent: $i > $i > $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(r_type,type,
r: $i ).
thf(p_type,type,
p: $i ).
thf(q_type,type,
q: $i ).
thf(axiom_type,type,
axiom: $i > $o ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( equivalent @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalent_defn) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equivalent @ A @ B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( not @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
= ( equivalent @ A @ B ) ),
inference(rewrite,[status(thm)],[28,26]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
thf(16,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(41,plain,
! [B: $i,A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) ),
inference(rewrite,[status(thm)],[16,20]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( axiom @ ( or @ ( equivalent @ A @ B ) @ ( or @ D @ C ) ) )
| ( ( not @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
!= ( not @ ( or @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,41]) ).
thf(102,plain,
! [B: $i,A: $i] : ( axiom @ ( or @ ( equivalent @ B @ A ) @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( not @ ( implies @ J @ I ) )),bind(D,$thf( not @ ( implies @ I @ J ) ))]]) ).
thf(110,plain,
! [B: $i,A: $i] : ( axiom @ ( or @ ( equivalent @ B @ A ) @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(646,plain,
! [B: $i,A: $i] : ( axiom @ ( or @ ( equivalent @ B @ A ) @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( not @ ( or @ ( not @ B ) @ A ) ) ) ) ),
inference(rewrite,[status(thm)],[110,20]) ).
thf(8,axiom,
! [A: $i] :
( ( theorem @ A )
| ~ ( axiom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(21,plain,
! [A: $i] :
( ( theorem @ A )
| ~ ( axiom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,plain,
! [A: $i] :
( ( theorem @ A )
| ~ ( axiom @ A ) ),
inference(cnf,[status(esa)],[21]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ C )
| ( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[41,22]) ).
thf(43,plain,
! [B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( or @ ( not @ ( or @ J @ I ) ) @ ( or @ I @ J ) ))]]) ).
thf(44,plain,
! [B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(1,negated_conjecture,
~ ( theorem @ ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(12,plain,
~ ( theorem @ ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
~ ( theorem @ ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,13]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( or @ ( equivalent @ A @ B ) @ ( or @ C @ D ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) )
| ( ( not @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
!= ( not @ ( or @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,74]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( or @ ( equivalent @ B @ A ) @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( not @ ( implies @ I @ J ) )),bind(D,$thf( not @ ( implies @ J @ I ) ))]]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( or @ ( equivalent @ B @ A ) @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( or @ ( equivalent @ B @ A ) @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( not @ ( or @ ( not @ B ) @ A ) ) ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(rewrite,[status(thm)],[121,20]) ).
thf(2,axiom,
! [A: $i] : ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
thf(14,plain,
! [A: $i] : ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,plain,
! [A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ),
inference(rewrite,[status(thm)],[14,20]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( theorem @ B )
| ( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
!= ( axiom @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,22]) ).
thf(36,plain,
! [A: $i] : ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( D )),bind(B,$thf( or @ ( not @ ( or @ D @ D ) ) @ D ))]]) ).
thf(37,plain,
! [A: $i] : ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ),
inference(simp,[status(thm)],[36]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( theorem @ ( not @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) ) )
| ( ( equivalent @ A @ B )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,13]) ).
thf(100,plain,
~ ( theorem @ ( not @ ( or @ ( not @ ( implies @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) @ ( not @ ( implies @ ( or @ p @ ( or @ q @ r ) ) @ ( or @ r @ ( or @ p @ q ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( or @ r @ ( or @ p @ q ) )),bind(B,$thf( or @ p @ ( or @ q @ r ) ))]]) ).
thf(180,plain,
~ ( theorem @ ( not @ ( or @ ( not @ ( or @ ( not @ ( or @ r @ ( or @ p @ q ) ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) @ ( not @ ( or @ ( not @ ( or @ p @ ( or @ q @ r ) ) ) @ ( or @ r @ ( or @ p @ q ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[100,20]) ).
thf(181,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
!= ( theorem @ ( not @ ( or @ ( not @ ( or @ ( not @ ( or @ r @ ( or @ p @ q ) ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) @ ( not @ ( or @ ( not @ ( or @ p @ ( or @ q @ r ) ) ) @ ( or @ r @ ( or @ p @ q ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,180]) ).
thf(194,plain,
! [A: $i] :
( ( or @ ( not @ ( or @ A @ A ) ) @ A )
!= ( not @ ( or @ ( not @ ( or @ ( not @ ( or @ r @ ( or @ p @ q ) ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) @ ( not @ ( or @ ( not @ ( or @ p @ ( or @ q @ r ) ) ) @ ( or @ r @ ( or @ p @ q ) ) ) ) ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
inference(rewrite,[status(thm)],[17,20]) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( theorem @ D )
| ( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
!= ( axiom @ D ) ) ),
inference(paramod_ordered,[status(thm)],[131,22]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( or @ B @ ( or @ A @ C ) ) ) @ ( or @ A @ ( or @ B @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( N )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( or @ ( not @ ( or @ N @ ( or @ L @ O ) ) ) @ ( or @ L @ ( or @ N @ O ) ) ))]]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( or @ B @ ( or @ A @ C ) ) ) @ ( or @ A @ ( or @ B @ C ) ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(51,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
!= ( theorem @ ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,13]) ).
thf(52,plain,
! [A: $i] :
( ( or @ ( not @ ( or @ A @ A ) ) @ A )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] : ( axiom @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ),
inference(rewrite,[status(thm)],[18,20]) ).
thf(174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( theorem @ D )
| ( ( axiom @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) )
!= ( axiom @ D ) ) ),
inference(paramod_ordered,[status(thm)],[168,22]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( implies @ A @ C ) ) @ ( implies @ ( or @ B @ A ) @ ( or @ B @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( M )),bind(B,$thf( O )),bind(C,$thf( N )),bind(D,$thf( or @ ( not @ ( implies @ M @ O ) ) @ ( implies @ ( or @ N @ M ) @ ( or @ N @ O ) ) ))]]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( implies @ A @ C ) ) @ ( implies @ ( or @ B @ A ) @ ( or @ B @ C ) ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( or @ ( not @ A ) @ C ) ) @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ B @ C ) ) ) ),
inference(rewrite,[status(thm)],[179,20]) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ B @ ( or @ A @ C ) ) ) @ ( or @ A @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[136,13]) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( not @ ( or @ B @ ( or @ A @ C ) ) ) @ ( or @ A @ ( or @ B @ C ) ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( axiom @ ( implies @ A @ ( or @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
thf(15,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ A @ ( or @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,plain,
! [B: $i,A: $i] : ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) ),
inference(rewrite,[status(thm)],[15,20]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ C )
| ( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[30,22]) ).
thf(39,plain,
! [B: $i,A: $i] : ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( or @ ( not @ H ) @ ( or @ G @ H ) ))]]) ).
thf(40,plain,
! [B: $i,A: $i] : ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( not @ ( or @ ( not @ ( or @ ( not @ ( or @ r @ ( or @ p @ q ) ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) @ ( not @ ( or @ ( not @ ( or @ p @ ( or @ q @ r ) ) ) @ ( or @ r @ ( or @ p @ q ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,180]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( or @ ( not @ B ) @ ( or @ A @ B ) )
!= ( not @ ( or @ ( not @ ( or @ ( not @ ( or @ r @ ( or @ p @ q ) ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) @ ( not @ ( or @ ( not @ ( or @ p @ ( or @ q @ r ) ) ) @ ( or @ r @ ( or @ p @ q ) ) ) ) ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ ( implies @ B @ A ) )
| ~ ( theorem @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ ( implies @ B @ A ) )
| ~ ( theorem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ ( implies @ B @ A ) )
| ~ ( theorem @ B ) ),
inference(cnf,[status(esa)],[23]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ ( or @ ( not @ B ) @ A ) )
| ~ ( theorem @ B ) ),
inference(rewrite,[status(thm)],[24,20]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ B )
| ( ( theorem @ ( or @ ( not @ B ) @ A ) )
!= ( theorem @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[31]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ B )
| ( ( theorem @ ( or @ ( not @ B ) @ A ) )
!= ( theorem @ B ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( or @ ( equivalent @ A @ B ) @ C ) )
| ( ( not @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
!= ( not @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,29]) ).
thf(98,plain,
! [A: $i] : ( axiom @ ( or @ ( equivalent @ A @ A ) @ ( not @ ( implies @ A @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( not @ ( implies @ F @ F ) ))]]) ).
thf(109,plain,
! [A: $i] : ( axiom @ ( or @ ( equivalent @ A @ A ) @ ( not @ ( implies @ A @ A ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(137,plain,
! [A: $i] : ( axiom @ ( or @ ( equivalent @ A @ A ) @ ( not @ ( or @ ( not @ A ) @ A ) ) ) ),
inference(rewrite,[status(thm)],[109,20]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ B )
| ( ( or @ ( not @ B ) @ A )
!= B ) ),
inference(simp,[status(thm)],[32]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( equivalent @ A @ B ) @ C ) )
| ( ( not @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
!= ( not @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,37]) ).
thf(80,plain,
! [A: $i] : ( theorem @ ( or @ ( equivalent @ A @ A ) @ ( not @ ( implies @ A @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( not @ ( implies @ F @ F ) ))]]) ).
thf(113,plain,
! [A: $i] : ( theorem @ ( or @ ( equivalent @ A @ A ) @ ( not @ ( implies @ A @ A ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(149,plain,
! [A: $i] : ( theorem @ ( or @ ( equivalent @ A @ A ) @ ( not @ ( or @ ( not @ A ) @ A ) ) ) ),
inference(rewrite,[status(thm)],[113,20]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,13]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( or @ ( not @ B ) @ ( or @ A @ B ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( or @ ( not @ ( implies @ C @ D ) ) @ ( not @ ( or @ ( not @ A ) @ B ) ) ) )
= ( equivalent @ C @ D ) )
| ( ( implies @ A @ B )
!= ( implies @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,78]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( not @ ( or @ ( not @ ( implies @ B @ A ) ) @ ( not @ ( or @ ( not @ A ) @ B ) ) ) )
= ( equivalent @ B @ A ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( not @ ( or @ ( not @ ( or @ ( not @ B ) @ A ) ) @ ( not @ ( or @ ( not @ A ) @ B ) ) ) )
= ( equivalent @ B @ A ) ),
inference(rewrite,[status(thm)],[94,20]) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ ( not @ A ) @ C ) ) @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ B @ C ) ) ) )
!= ( theorem @ ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[280,13]) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( not @ ( or @ ( not @ A ) @ C ) ) @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ B @ C ) ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(simp,[status(thm)],[295]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( or @ ( equivalent @ A @ B ) @ C )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) )
| ( ( not @ ( or @ ( not @ ( implies @ A @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
!= ( not @ ( or @ C @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,52]) ).
thf(82,plain,
! [A: $i] :
( ( or @ ( equivalent @ A @ A ) @ ( not @ ( implies @ A @ A ) ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( not @ ( implies @ F @ F ) ))]]) ).
thf(114,plain,
! [A: $i] :
( ( or @ ( equivalent @ A @ A ) @ ( not @ ( implies @ A @ A ) ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(122,plain,
! [A: $i] :
( ( or @ ( equivalent @ A @ A ) @ ( not @ ( or @ ( not @ A ) @ A ) ) )
!= ( equivalent @ ( or @ r @ ( or @ p @ q ) ) @ ( or @ p @ ( or @ q @ r ) ) ) ),
inference(rewrite,[status(thm)],[114,20]) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( not @ ( implies @ D @ C ) ) ) )
= ( equivalent @ C @ D ) )
| ( ( implies @ A @ B )
!= ( implies @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,78]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( not @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( not @ ( implies @ B @ A ) ) ) )
= ( equivalent @ A @ B ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( not @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( not @ ( or @ ( not @ B ) @ A ) ) ) )
= ( equivalent @ A @ B ) ),
inference(rewrite,[status(thm)],[92,20]) ).
thf(1035,plain,
$false,
inference(e,[status(thm)],[646,229,12,194,136,37,25,52,14,20,78,29,280,221,74,192,33,21,137,13,41,34,180,17,149,22,44,27,63,18,16,463,31,40,26,23,300,168,30,19,131,15,122,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL276-3 : TPTP v8.1.2. Released v2.3.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n009.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 : Thu May 18 15:58:19 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.08/1.00 % [INFO] Parsing done (113ms).
% 1.08/1.00 % [INFO] Running in sequential loop mode.
% 1.72/1.19 % [INFO] eprover registered as external prover.
% 1.72/1.19 % [INFO] cvc4 registered as external prover.
% 1.72/1.20 % [INFO] Scanning for conjecture ...
% 1.87/1.24 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.87/1.26 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.87/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.28 % [INFO] Type checking passed.
% 1.87/1.28 % [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 ...
% 11.16/3.09 % External prover 'e' found a proof!
% 11.16/3.09 % [INFO] Killing All external provers ...
% 11.16/3.09 % Time passed: 2539ms (effective reasoning time: 2079ms)
% 11.16/3.09 % 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)>
% 11.16/3.09 % Axioms used in derivation (10): axiom_1_5, equivalent_defn, and_defn, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 11.16/3.09 % No. of inferences in proof: 98
% 11.16/3.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2539 ms resp. 2079 ms w/o parsing
% 11.16/3.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.16/3.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------