TSTP Solution File: HWC002-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : HWC002-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 11:17:02 EDT 2023
% Result : Unsatisfiable 3.41s 1.80s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 50
% Syntax : Number of formulae : 89 ( 47 unt; 12 typ; 0 def)
% Number of atoms : 107 ( 40 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1002 ( 32 ~; 30 |; 0 &; 940 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 198 ( 0 ^; 198 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(circuit_type,type,
circuit: $i > $i > $i > $o ).
thf(top_type,type,
top: $i > $i ).
thf(connect_type,type,
connect: $i > $i > $i ).
thf(table_type,type,
table: $i > $i > $i > $i > $i ).
thf(n0_type,type,
n0: $i ).
thf(n1_type,type,
n1: $i ).
thf(nil_type,type,
nil: $i ).
thf(bottom_type,type,
bottom: $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(middle_type,type,
middle: $i > $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(10,axiom,
! [A: $i] :
( ( connect @ nil @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connect_definition1) ).
thf(57,plain,
! [A: $i] :
( ( connect @ nil @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
( ( or @ n0 @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition2) ).
thf(61,plain,
( ( or @ n0 @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ ( or @ A @ C ) ) @ ( bottom @ ( connect @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_across_middle2) ).
thf(53,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ ( or @ A @ C ) ) @ ( bottom @ ( connect @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
( ( and @ n0 @ n1 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition2) ).
thf(41,plain,
( ( and @ n0 @ n1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ ( connect @ B @ C ) ) ) @ ( middle @ D ) @ ( bottom @ ( connect @ E @ ( connect @ F @ G ) ) ) )
| ( circuit @ ( top @ ( connect @ ( and @ A @ B ) @ C ) ) @ ( middle @ D ) @ ( bottom @ ( connect @ ( and @ E @ F ) @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_nearest_middle1) ).
thf(45,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ ( connect @ B @ C ) ) ) @ ( middle @ D ) @ ( bottom @ ( connect @ E @ ( connect @ F @ G ) ) ) )
| ( circuit @ ( top @ ( connect @ ( and @ A @ B ) @ C ) ) @ ( middle @ D ) @ ( bottom @ ( connect @ ( and @ E @ F ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
( ( table @ n1 @ n1 @ n1 @ n1 )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',full_table) ).
thf(59,plain,
( ( table @ n1 @ n1 @ n1 @ n1 )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i] :
( ( or @ nil @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition5) ).
thf(63,plain,
! [A: $i] :
( ( or @ nil @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( or @ C @ A ) @ B ) ) @ nil @ ( bottom @ ( connect @ ( or @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',split_and_omit_middle2) ).
thf(67,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( or @ C @ A ) @ B ) ) @ nil @ ( bottom @ ( connect @ ( or @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ ( and @ A @ C ) ) @ ( bottom @ ( connect @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_across_middle1) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ ( and @ A @ C ) ) @ ( bottom @ ( connect @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( not @ A ) @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ ( not @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invert_adjacent1) ).
thf(55,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( not @ A ) @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ ( not @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( not @ ( table @ A @ B @ C @ D ) )
= ( table @ ( not @ A ) @ ( not @ B ) @ ( not @ C ) @ ( not @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_table_definition) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( not @ ( table @ A @ B @ C @ D ) )
= ( table @ ( not @ A ) @ ( not @ B ) @ ( not @ C ) @ ( not @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
( ( or @ n1 @ n0 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition3) ).
thf(51,plain,
( ( or @ n1 @ n0 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( and @ C @ A ) @ B ) ) @ nil @ ( bottom @ ( connect @ ( and @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',split_and_omit_middle1) ).
thf(47,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( and @ C @ A ) @ B ) ) @ nil @ ( bottom @ ( connect @ ( and @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ B ) @ ( middle @ ( or @ A @ C ) ) @ ( bottom @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_across_empty_middle2) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ B ) @ ( middle @ ( or @ A @ C ) ) @ ( bottom @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ ( connect @ B @ C ) ) ) @ ( middle @ D ) @ ( bottom @ ( connect @ E @ ( connect @ F @ G ) ) ) )
| ( circuit @ ( top @ ( connect @ ( or @ A @ B ) @ C ) ) @ ( middle @ D ) @ ( bottom @ ( connect @ ( or @ E @ F ) @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_nearest_middle2) ).
thf(88,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ ( connect @ B @ C ) ) ) @ ( middle @ D ) @ ( bottom @ ( connect @ E @ ( connect @ F @ G ) ) ) )
| ( circuit @ ( top @ ( connect @ ( or @ A @ B ) @ C ) ) @ ( middle @ D ) @ ( bottom @ ( connect @ ( or @ E @ F ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ ( connect @ ( not @ A ) @ B ) ) @ nil @ ( bottom @ ( connect @ ( not @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invert_adjacent2) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ ( connect @ ( not @ A ) @ B ) ) @ nil @ ( bottom @ ( connect @ ( not @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( and @ ( table @ A @ B @ C @ D ) @ ( table @ E @ F @ G @ H ) )
= ( table @ ( and @ A @ E ) @ ( and @ B @ F ) @ ( and @ C @ G ) @ ( and @ D @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_table_definition) ).
thf(102,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( and @ ( table @ A @ B @ C @ D ) @ ( table @ E @ F @ G @ H ) )
= ( table @ ( and @ A @ E ) @ ( and @ B @ F ) @ ( and @ C @ G ) @ ( and @ D @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
( ( not @ n1 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition2) ).
thf(92,plain,
( ( not @ n1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
( ( table @ n0 @ n0 @ n0 @ n0 )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_table) ).
thf(65,plain,
( ( table @ n0 @ n0 @ n0 @ n0 )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(37,axiom,
( ( and @ n1 @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition3) ).
thf(109,plain,
( ( and @ n1 @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(20,axiom,
( ( not @ n0 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition1) ).
thf(77,plain,
( ( not @ n0 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( and @ C @ A ) @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ ( and @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',split_and_keep_middle1) ).
thf(96,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( and @ C @ A ) @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ ( and @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( or @ C @ A ) @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ ( or @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',split_and_keep_middle2) ).
thf(73,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( or @ C @ A ) @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ ( or @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ B ) @ ( middle @ ( and @ A @ C ) ) @ ( bottom @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_across_empty_middle1) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ nil @ ( bottom @ ( connect @ C @ D ) ) )
| ( circuit @ ( top @ B ) @ ( middle @ ( and @ A @ C ) ) @ ( bottom @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(17,axiom,
( ( not @ nil )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition3) ).
thf(71,plain,
( ( not @ nil )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
( ( or @ n0 @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition1) ).
thf(49,plain,
( ( or @ n0 @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
! [A: $i] :
( ( and @ nil @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition5) ).
thf(81,plain,
! [A: $i] :
( ( and @ nil @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,negated_conjecture,
~ ( circuit @ ( top @ ( connect @ ( table @ n0 @ n1 @ n0 @ n1 ) @ nil ) ) @ nil @ ( bottom @ ( connect @ ( table @ n0 @ n0 @ n1 @ n1 ) @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_output_configuration) ).
thf(39,plain,
~ ( circuit @ ( top @ ( connect @ ( table @ n0 @ n1 @ n0 @ n1 ) @ nil ) ) @ nil @ ( bottom @ ( connect @ ( table @ n0 @ n0 @ n1 @ n1 ) @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(31,axiom,
( ( and @ n0 @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition1) ).
thf(98,plain,
( ( and @ n0 @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [B: $i,A: $i] : ( circuit @ ( top @ A ) @ B @ ( bottom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsume_symmetric) ).
thf(87,plain,
! [B: $i,A: $i] : ( circuit @ ( top @ A ) @ B @ ( bottom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(34,axiom,
circuit @ ( top @ ( connect @ ( table @ n0 @ n0 @ n1 @ n1 ) @ nil ) ) @ nil @ ( bottom @ ( connect @ ( table @ n0 @ n1 @ n0 @ n1 ) @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',input_configuration) ).
thf(104,plain,
circuit @ ( top @ ( connect @ ( table @ n0 @ n0 @ n1 @ n1 ) @ nil ) ) @ nil @ ( bottom @ ( connect @ ( table @ n0 @ n1 @ n0 @ n1 ) @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( and @ C @ A ) @ ( connect @ A @ B ) ) ) @ nil @ ( bottom @ ( connect @ ( and @ C @ D ) @ ( connect @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_to_middle1) ).
thf(107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( and @ C @ A ) @ ( connect @ A @ B ) ) ) @ nil @ ( bottom @ ( connect @ ( and @ C @ D ) @ ( connect @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,axiom,
( ( and @ n1 @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition4) ).
thf(79,plain,
( ( and @ n1 @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ A ) @ ( middle @ B ) @ ( bottom @ C ) )
| ( circuit @ ( top @ A ) @ ( middle @ ( not @ B ) ) @ ( bottom @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invert_middle) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ A ) @ ( middle @ B ) @ ( bottom @ C ) )
| ( circuit @ ( top @ A ) @ ( middle @ ( not @ B ) ) @ ( bottom @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( connect @ A @ ( connect @ A @ B ) )
= ( connect @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connect_definition2) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( connect @ A @ ( connect @ A @ B ) )
= ( connect @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(32,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( or @ C @ A ) @ ( connect @ A @ B ) ) ) @ nil @ ( bottom @ ( connect @ ( or @ C @ D ) @ ( connect @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_to_middle2) ).
thf(100,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( circuit @ ( top @ ( connect @ A @ B ) ) @ ( middle @ C ) @ ( bottom @ ( connect @ D @ E ) ) )
| ( circuit @ ( top @ ( connect @ ( or @ C @ A ) @ ( connect @ A @ B ) ) ) @ nil @ ( bottom @ ( connect @ ( or @ C @ D ) @ ( connect @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(27,axiom,
( ( or @ n1 @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition4) ).
thf(90,plain,
( ( or @ n1 @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(38,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( or @ ( table @ A @ B @ C @ D ) @ ( table @ E @ F @ G @ H ) )
= ( table @ ( or @ A @ E ) @ ( or @ B @ F ) @ ( or @ C @ G ) @ ( or @ D @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_table_definition) ).
thf(111,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( or @ ( table @ A @ B @ C @ D ) @ ( table @ E @ F @ G @ H ) )
= ( table @ ( or @ A @ E ) @ ( or @ B @ F ) @ ( or @ C @ G ) @ ( or @ D @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(113,plain,
$false,
inference(e,[status(thm)],[57,61,53,41,45,59,63,67,43,55,75,51,47,69,88,85,102,92,65,109,77,96,73,105,71,49,81,39,98,87,104,107,79,94,83,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWC002-1 : TPTP v8.1.2. Released v1.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 23:57:20 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.90/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/0.98 % [INFO] Parsing done (135ms).
% 1.31/0.99 % [INFO] Running in sequential loop mode.
% 1.71/1.19 % [INFO] eprover registered as external prover.
% 1.71/1.19 % [INFO] cvc4 registered as external prover.
% 1.71/1.20 % [INFO] Scanning for conjecture ...
% 1.88/1.26 % [INFO] Found a conjecture and 37 axioms. Running axiom selection ...
% 2.08/1.31 % [INFO] Axiom selection finished. Selected 37 axioms (removed 0 axioms).
% 2.08/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.36 % [INFO] Type checking passed.
% 2.08/1.36 % [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 ...
% 3.41/1.80 % External prover 'e' found a proof!
% 3.41/1.80 % [INFO] Killing All external provers ...
% 3.41/1.80 % Time passed: 1275ms (effective reasoning time: 808ms)
% 3.41/1.80 % 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)>
% 3.41/1.80 % Axioms used in derivation (37): invert_adjacent2, and_definition1, connect_definition1, or_definition1, invert_adjacent1, join_nearest_middle2, join_across_middle1, not_definition1, connect_definition2, or_definition4, not_definition3, or_table_definition, join_to_middle2, input_configuration, split_and_keep_middle2, or_definition5, not_table_definition, join_to_middle1, and_definition2, join_across_empty_middle1, or_definition2, and_definition4, and_definition5, split_and_keep_middle1, and_definition3, and_table_definition, full_table, join_across_empty_middle2, empty_table, split_and_omit_middle1, or_definition3, split_and_omit_middle2, subsume_symmetric, invert_middle, join_nearest_middle1, join_across_middle2, not_definition2
% 3.41/1.80 % No. of inferences in proof: 77
% 3.41/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1275 ms resp. 808 ms w/o parsing
% 3.96/1.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.96/1.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------