TSTP Solution File: PUZ016-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : PUZ016-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 11:47:25 EDT 2023
% Result : Unsatisfiable 7.60s 2.45s
% Output : Refutation 7.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of formulae : 112 ( 51 unt; 17 typ; 0 def)
% Number of atoms : 174 ( 96 equ; 0 cnn)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 1220 ( 80 ~; 61 |; 0 &;1079 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 13 con; 0-8 aty)
% Number of variables : 203 ( 0 ^; 203 !; 0 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
thf(achievable_type,type,
achievable: $i > $i > $o ).
thf(row_type,type,
row: $i > $i ).
thf(n8_type,type,
n8: $i ).
thf(squares_type,type,
squares: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(covered_type,type,
covered: $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(n2_type,type,
n2: $i ).
thf(n3_type,type,
n3: $i ).
thf(n1_type,type,
n1: $i ).
thf(n4_type,type,
n4: $i ).
thf(n5_type,type,
n5: $i ).
thf(n6_type,type,
n6: $i ).
thf(n7_type,type,
n7: $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(removed_type,type,
removed: $i ).
thf(not_covered_type,type,
not_covered: $i ).
thf(n9_type,type,
n9: $i ).
thf(18,axiom,
achievable @ ( row @ n1 ) @ ( squares @ not_covered @ removed @ removed @ not_covered @ not_covered @ not_covered @ not_covered @ not_covered ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_row_initially) ).
thf(56,plain,
achievable @ ( row @ n1 ) @ ( squares @ not_covered @ removed @ removed @ not_covered @ not_covered @ not_covered @ not_covered @ not_covered ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ not_covered @ not_covered @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ covered @ covered @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_5_and_6) ).
thf(38,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ not_covered @ not_covered @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ covered @ covered @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ not_covered @ not_covered @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ covered @ covered @ F @ G ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(187,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ covered @ covered @ F @ G ) )
| ( ( achievable @ ( row @ n1 ) @ ( squares @ not_covered @ removed @ removed @ not_covered @ not_covered @ not_covered @ not_covered @ not_covered ) )
!= ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ not_covered @ not_covered @ F @ G ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,39]) ).
thf(188,plain,
achievable @ ( row @ n1 ) @ ( squares @ not_covered @ removed @ removed @ not_covered @ covered @ covered @ not_covered @ not_covered ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered ))]]) ).
thf(1,negated_conjecture,
~ ( achievable @ ( row @ n8 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_row_8_can_be_covered) ).
thf(22,plain,
~ ( achievable @ ( row @ n8 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,plain,
~ ( achievable @ ( row @ n8 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(199,plain,
( ( achievable @ ( row @ n1 ) @ ( squares @ not_covered @ removed @ removed @ not_covered @ covered @ covered @ not_covered @ not_covered ) )
!= ( achievable @ ( row @ n8 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(paramod_ordered,[status(thm)],[188,23]) ).
thf(202,plain,
( ( ( row @ n1 )
!= ( row @ n8 ) )
| ( ( squares @ not_covered @ removed @ removed @ not_covered @ covered @ covered @ not_covered @ not_covered )
!= ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(16,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ not_covered @ not_covered @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ covered @ covered @ E @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_4_and_5) ).
thf(52,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ not_covered @ not_covered @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ covered @ covered @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ not_covered @ not_covered ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ covered @ covered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_7_and_8) ).
thf(61,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ not_covered @ not_covered ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ covered @ covered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(20,axiom,
( ( complement @ covered )
= not_covered ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_covered_is_not_covered) ).
thf(59,plain,
( ( complement @ covered )
= not_covered ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,plain,
( ( complement @ covered )
= not_covered ),
inference(lifteq,[status(thm)],[59]) ).
thf(3,axiom,
( ( successor @ n1 )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_1_is_2) ).
thf(26,plain,
( ( successor @ n1 )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,plain,
( ( successor @ n1 )
= n2 ),
inference(lifteq,[status(thm)],[26]) ).
thf(2,axiom,
( ( successor @ n2 )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_2_is_3) ).
thf(24,plain,
( ( successor @ n2 )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
( ( successor @ n2 )
= n3 ),
inference(lifteq,[status(thm)],[24]) ).
thf(63,plain,
( ( n3 = n2 )
| ( ( successor @ n1 )
!= ( successor @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[27,25]) ).
thf(65,plain,
( ( n3 = n2 )
| ( n1 != n2 ) ),
inference(simp,[status(thm)],[63]) ).
thf(14,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ H @ I ) )
| ( achievable @ ( row @ ( successor @ A ) ) @ ( squares @ ( complement @ B ) @ ( complement @ C ) @ ( complement @ D ) @ ( complement @ E ) @ ( complement @ F ) @ ( complement @ G ) @ ( complement @ H ) @ ( complement @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',place_vertical_pieces) ).
thf(48,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ H @ I ) )
| ( achievable @ ( row @ ( successor @ A ) ) @ ( squares @ ( complement @ B ) @ ( complement @ C ) @ ( complement @ D ) @ ( complement @ E ) @ ( complement @ F ) @ ( complement @ G ) @ ( complement @ H ) @ ( complement @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(49,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ H @ I ) )
| ( achievable @ ( row @ ( successor @ A ) ) @ ( squares @ ( complement @ B ) @ ( complement @ C ) @ ( complement @ D ) @ ( complement @ E ) @ ( complement @ F ) @ ( complement @ G ) @ ( complement @ H ) @ ( complement @ I ) ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(222,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( achievable @ ( row @ ( successor @ A ) ) @ ( squares @ ( complement @ B ) @ ( complement @ C ) @ ( complement @ D ) @ ( complement @ E ) @ ( complement @ F ) @ ( complement @ G ) @ ( complement @ H ) @ ( complement @ I ) ) )
| ( ( achievable @ ( row @ n1 ) @ ( squares @ not_covered @ removed @ removed @ not_covered @ not_covered @ not_covered @ not_covered @ not_covered ) )
!= ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,49]) ).
thf(223,plain,
achievable @ ( row @ ( successor @ n1 ) ) @ ( squares @ ( complement @ not_covered ) @ ( complement @ removed ) @ ( complement @ removed ) @ ( complement @ not_covered ) @ ( complement @ not_covered ) @ ( complement @ not_covered ) @ ( complement @ not_covered ) @ ( complement @ not_covered ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( not_covered )),bind(G,$thf( not_covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(7,axiom,
( ( complement @ removed )
= not_covered ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_removed_is_not_covered) ).
thf(34,plain,
( ( complement @ removed )
= not_covered ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,plain,
( ( complement @ removed )
= not_covered ),
inference(lifteq,[status(thm)],[34]) ).
thf(10,axiom,
( ( complement @ not_covered )
= covered ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_not_covered_is_covered) ).
thf(40,plain,
( ( complement @ not_covered )
= covered ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,plain,
( ( complement @ not_covered )
= covered ),
inference(lifteq,[status(thm)],[40]) ).
thf(328,plain,
achievable @ ( row @ n2 ) @ ( squares @ covered @ not_covered @ not_covered @ covered @ covered @ covered @ covered @ covered ),
inference(rewrite,[status(thm)],[223,35,41,27]) ).
thf(4,axiom,
( ( successor @ n4 )
= n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_4_is_5) ).
thf(28,plain,
( ( successor @ n4 )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
( ( successor @ n4 )
= n5 ),
inference(lifteq,[status(thm)],[28]) ).
thf(69,plain,
( ( n5 = n2 )
| ( ( successor @ n4 )
!= ( successor @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[29,27]) ).
thf(73,plain,
( ( n5 = n2 )
| ( n4 != n1 ) ),
inference(simp,[status(thm)],[69]) ).
thf(13,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ not_covered @ not_covered @ C @ D @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ covered @ covered @ C @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_2_and_3) ).
thf(46,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ not_covered @ not_covered @ C @ D @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ covered @ covered @ C @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(47,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ not_covered @ not_covered @ C @ D @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ covered @ covered @ C @ D @ E @ F @ G ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(330,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( achievable @ ( row @ A ) @ ( squares @ B @ covered @ covered @ C @ D @ E @ F @ G ) )
| ( ( achievable @ ( row @ n2 ) @ ( squares @ covered @ not_covered @ not_covered @ covered @ covered @ covered @ covered @ covered ) )
!= ( achievable @ ( row @ A ) @ ( squares @ B @ not_covered @ not_covered @ C @ D @ E @ F @ G ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,47]) ).
thf(331,plain,
achievable @ ( row @ n2 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( covered )),bind(E,$thf( covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(337,plain,
( ( achievable @ ( row @ n2 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) )
!= ( achievable @ ( row @ n8 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(paramod_ordered,[status(thm)],[331,23]) ).
thf(342,plain,
( ( ( row @ n2 )
!= ( row @ n8 ) )
| ( ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered )
!= ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(345,plain,
( ( row @ n2 )
!= ( row @ n8 ) ),
inference(simp,[status(thm)],[342]) ).
thf(189,plain,
( ( achievable @ ( row @ n1 ) @ ( squares @ not_covered @ removed @ removed @ not_covered @ not_covered @ not_covered @ not_covered @ not_covered ) )
!= ( achievable @ ( row @ n8 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(paramod_ordered,[status(thm)],[56,23]) ).
thf(190,plain,
( ( ( row @ n1 )
!= ( row @ n8 ) )
| ( ( squares @ not_covered @ removed @ removed @ not_covered @ not_covered @ not_covered @ not_covered @ not_covered )
!= ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(192,plain,
( ( ( row @ n1 )
!= ( row @ n8 ) )
| ( not_covered != covered )
| ( removed != covered )
| ( removed != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered ) ),
inference(simp,[status(thm)],[190]) ).
thf(194,plain,
( ( ( row @ n1 )
!= ( row @ n8 ) )
| ( not_covered != covered )
| ( removed != covered ) ),
inference(simp,[status(thm)],[192]) ).
thf(11,axiom,
( ( successor @ n7 )
= n8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_7_is_8) ).
thf(42,plain,
( ( successor @ n7 )
= n8 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(43,plain,
( ( successor @ n7 )
= n8 ),
inference(lifteq,[status(thm)],[42]) ).
thf(346,plain,
n2 != n8,
inference(simp,[status(thm)],[345]) ).
thf(193,plain,
( ( n1 != n8 )
| ( not_covered != covered )
| ( removed != covered )
| ( removed != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered )
| ( not_covered != covered ) ),
inference(simp,[status(thm)],[190]) ).
thf(195,plain,
( ( n1 != n8 )
| ( not_covered != covered )
| ( removed != covered ) ),
inference(simp,[status(thm)],[193]) ).
thf(8,axiom,
( ( successor @ n3 )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_3_is_4) ).
thf(36,plain,
( ( successor @ n3 )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,plain,
( ( successor @ n3 )
= n4 ),
inference(lifteq,[status(thm)],[36]) ).
thf(19,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ not_covered @ not_covered @ B @ C @ D @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ covered @ covered @ B @ C @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_1_and_2) ).
thf(57,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ not_covered @ not_covered @ B @ C @ D @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ covered @ covered @ B @ C @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
( ( successor @ n5 )
= n6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_5_is_6) ).
thf(32,plain,
( ( successor @ n5 )
= n6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
( ( successor @ n5 )
= n6 ),
inference(lifteq,[status(thm)],[32]) ).
thf(12,axiom,
( ( successor @ n8 )
= n9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_8_is_9) ).
thf(44,plain,
( ( successor @ n8 )
= n9 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(45,plain,
( ( successor @ n8 )
= n9 ),
inference(lifteq,[status(thm)],[44]) ).
thf(191,plain,
( ( n1 != n8 )
| ( ( squares @ not_covered @ removed @ removed @ not_covered @ not_covered @ not_covered @ not_covered @ not_covered )
!= ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(67,plain,
( ( n5 = n3 )
| ( ( successor @ n4 )
!= ( successor @ n2 ) ) ),
inference(paramod_ordered,[status(thm)],[29,25]) ).
thf(71,plain,
( ( n5 = n3 )
| ( n4 != n2 ) ),
inference(simp,[status(thm)],[67]) ).
thf(17,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ not_covered @ not_covered @ D @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ covered @ covered @ D @ E @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_3_and_4) ).
thf(54,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ not_covered @ not_covered @ D @ E @ F @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ covered @ covered @ D @ E @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
( ( successor @ n6 )
= n7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_of_6_is_7) ).
thf(30,plain,
( ( successor @ n6 )
= n7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
( ( successor @ n6 )
= n7 ),
inference(lifteq,[status(thm)],[30]) ).
thf(78,plain,
( ( n7 = n2 )
| ( ( successor @ n6 )
!= ( successor @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[27,31]) ).
thf(81,plain,
( ( n7 = n2 )
| ( n6 != n1 ) ),
inference(simp,[status(thm)],[78]) ).
thf(284,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ H @ I ) )
| ( ( achievable @ ( row @ ( successor @ A ) ) @ ( squares @ ( complement @ B ) @ ( complement @ C ) @ ( complement @ D ) @ ( complement @ E ) @ ( complement @ F ) @ ( complement @ G ) @ ( complement @ H ) @ ( complement @ I ) ) )
!= ( achievable @ ( row @ n8 ) @ ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,23]) ).
thf(295,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ H @ I ) )
| ( ( row @ ( successor @ A ) )
!= ( row @ n8 ) )
| ( ( squares @ ( complement @ B ) @ ( complement @ C ) @ ( complement @ D ) @ ( complement @ E ) @ ( complement @ F ) @ ( complement @ G ) @ ( complement @ H ) @ ( complement @ I ) )
!= ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(15,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ not_covered @ not_covered @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ covered @ covered @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cover_columns_6_and_7) ).
thf(50,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ not_covered @ not_covered @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ covered @ covered @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(51,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ not_covered @ not_covered @ G ) )
| ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ covered @ covered @ G ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(244,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( achievable @ ( row @ ( successor @ A ) ) @ ( squares @ ( complement @ B ) @ ( complement @ C ) @ ( complement @ D ) @ ( complement @ E ) @ ( complement @ F ) @ ( complement @ G ) @ ( complement @ H ) @ ( complement @ I ) ) )
| ( ( achievable @ ( row @ n1 ) @ ( squares @ not_covered @ removed @ removed @ not_covered @ covered @ covered @ not_covered @ not_covered ) )
!= ( achievable @ ( row @ A ) @ ( squares @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) ),
inference(paramod_ordered,[status(thm)],[188,49]) ).
thf(245,plain,
achievable @ ( row @ ( successor @ n1 ) ) @ ( squares @ ( complement @ not_covered ) @ ( complement @ removed ) @ ( complement @ removed ) @ ( complement @ not_covered ) @ ( complement @ covered ) @ ( complement @ covered ) @ ( complement @ not_covered ) @ ( complement @ not_covered ) ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( n1 )),bind(B,$thf( not_covered )),bind(C,$thf( removed )),bind(D,$thf( removed )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered )),bind(H,$thf( not_covered )),bind(I,$thf( not_covered ))]]) ).
thf(454,plain,
achievable @ ( row @ n2 ) @ ( squares @ covered @ not_covered @ not_covered @ covered @ not_covered @ not_covered @ covered @ covered ),
inference(rewrite,[status(thm)],[245,35,41,27,60]) ).
thf(458,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( achievable @ ( row @ A ) @ ( squares @ B @ covered @ covered @ C @ D @ E @ F @ G ) )
| ( ( achievable @ ( row @ n2 ) @ ( squares @ covered @ not_covered @ not_covered @ covered @ not_covered @ not_covered @ covered @ covered ) )
!= ( achievable @ ( row @ A ) @ ( squares @ B @ not_covered @ not_covered @ C @ D @ E @ F @ G ) ) ) ),
inference(paramod_ordered,[status(thm)],[454,47]) ).
thf(459,plain,
achievable @ ( row @ n2 ) @ ( squares @ covered @ covered @ covered @ covered @ not_covered @ not_covered @ covered @ covered ),
inference(pattern_uni,[status(thm)],[458:[bind(A,$thf( n2 )),bind(B,$thf( covered )),bind(C,$thf( covered )),bind(D,$thf( not_covered )),bind(E,$thf( not_covered )),bind(F,$thf( covered )),bind(G,$thf( covered ))]]) ).
thf(215,plain,
( ( n1 != n8 )
| ( ( squares @ not_covered @ removed @ removed @ not_covered @ covered @ covered @ not_covered @ not_covered )
!= ( squares @ covered @ covered @ covered @ covered @ covered @ covered @ covered @ covered ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(502,plain,
$false,
inference(e,[status(thm)],[202,56,52,61,60,65,188,328,41,73,345,35,194,43,346,195,42,24,37,25,46,57,29,33,28,38,45,32,34,191,22,44,59,27,71,54,49,81,39,48,295,50,331,31,40,26,23,36,30,51,190,459,47,215,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 19:57:49 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (124ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.69/1.17 % [INFO] eprover registered as external prover.
% 1.69/1.17 % [INFO] cvc4 registered as external prover.
% 1.69/1.17 % [INFO] Scanning for conjecture ...
% 1.69/1.22 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 1.87/1.26 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.01/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 2.01/1.29 % [INFO] Type checking passed.
% 2.01/1.29 % [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 ...
% 7.60/2.44 % External prover 'e' found a proof!
% 7.60/2.44 % [INFO] Killing All external provers ...
% 7.60/2.45 % Time passed: 1916ms (effective reasoning time: 1461ms)
% 7.60/2.45 % 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)>
% 7.60/2.45 % Axioms used in derivation (20): successor_of_2_is_3, successor_of_7_is_8, cover_columns_1_and_2, cover_columns_5_and_6, complement_of_covered_is_not_covered, successor_of_3_is_4, cover_columns_2_and_3, successor_of_6_is_7, complement_of_removed_is_not_covered, cover_columns_7_and_8, successor_of_1_is_2, cover_columns_4_and_5, first_row_initially, successor_of_8_is_9, complement_of_not_covered_is_covered, cover_columns_3_and_4, place_vertical_pieces, successor_of_4_is_5, successor_of_5_is_6, cover_columns_6_and_7
% 7.60/2.45 % No. of inferences in proof: 95
% 7.60/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1916 ms resp. 1461 ms w/o parsing
% 7.60/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.60/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------