%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ016-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:23:09 AM UTC 2025
% Result : Unsatisfiable 1.52s 1.72s
% Output : Proof 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 46
% Syntax : Number of formulae : 134 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 300 ( 61 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 302 ( 138 ~; 122 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-8 aty)
% Number of variables : 424 ( 408 !; 0 ?; 424 :)
% Comments :
%------------------------------------------------------------------------------
tff(achievable_type,type,
achievable: ( $i * $i ) > $o ).
tff(squares_type,type,
squares: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(not_covered_type,type,
not_covered: $i ).
tff(row_type,type,
row: $i > $i ).
tff(n5_type,type,
n5: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(covered_type,type,
covered: $i ).
tff(successor_type,type,
successor: $i > $i ).
tff(n4_type,type,
n4: $i ).
tff(n3_type,type,
n3: $i ).
tff(n2_type,type,
n2: $i ).
tff(n1_type,type,
n1: $i ).
tff(removed_type,type,
removed: $i ).
tff(n6_type,type,
n6: $i ).
tff(n7_type,type,
n7: $i ).
tff(n8_type,type,
n8: $i ).
tff(1,plain,
( ( complement(covered) = not_covered )
<=> ( complement(covered) = not_covered ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
complement(covered) = not_covered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_covered_is_not_covered) ).
tff(3,plain,
complement(covered) = not_covered,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
not_covered = complement(covered),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered) = squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)),
inference(monotonicity,[status(thm)],[4,4,4,4,4,4,4,4]) ).
tff(6,plain,
( ( successor(n4) = n5 )
<=> ( successor(n4) = n5 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
successor(n4) = n5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_4_is_5) ).
tff(8,plain,
successor(n4) = n5,
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
n5 = successor(n4),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
row(n5) = row(successor(n4)),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
<=> achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(monotonicity,[status(thm)],[10,5]) ).
tff(12,plain,
( achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))
<=> achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ( complement(not_covered) = covered )
<=> ( complement(not_covered) = covered ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
complement(not_covered) = covered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_not_covered_is_covered) ).
tff(15,plain,
complement(not_covered) = covered,
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,covered,covered,covered,covered,covered,covered,covered),
inference(monotonicity,[status(thm)],[15,15,15,15,15,15,15,15]) ).
tff(17,plain,
squares(covered,covered,covered,covered,covered,covered,covered,covered) = squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ( successor(n3) = n4 )
<=> ( successor(n3) = n4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
successor(n3) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_3_is_4) ).
tff(20,plain,
successor(n3) = n4,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
n4 = successor(n3),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
row(n4) = row(successor(n3)),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered))
<=> achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(monotonicity,[status(thm)],[22,17]) ).
tff(24,plain,
( achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))
<=> achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ( successor(n2) = n3 )
<=> ( successor(n2) = n3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
successor(n2) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_2_is_3) ).
tff(27,plain,
successor(n2) = n3,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
n3 = successor(n2),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
row(n3) = row(successor(n2)),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
<=> achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(monotonicity,[status(thm)],[29,5]) ).
tff(31,plain,
( achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered)))
<=> achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered),
inference(monotonicity,[status(thm)],[15,3,3,15,15,15,15,15]) ).
tff(33,plain,
squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered) = squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( successor(n1) = n2 )
<=> ( successor(n1) = n2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
successor(n1) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_1_is_2) ).
tff(36,plain,
successor(n1) = n2,
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
n2 = successor(n1),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
row(n2) = row(successor(n1)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered))
<=> achievable(row(successor(n1)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(monotonicity,[status(thm)],[38,33]) ).
tff(40,plain,
( achievable(row(successor(n1)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))
<=> achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered)) ),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ( complement(removed) = not_covered )
<=> ( complement(removed) = not_covered ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
complement(removed) = not_covered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_removed_is_not_covered) ).
tff(43,plain,
complement(removed) = not_covered,
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered),
inference(monotonicity,[status(thm)],[15,43,43,15,15,15,15,15]) ).
tff(45,plain,
squares(complement(not_covered),complement(removed),complement(removed),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)) = squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)),
inference(transitivity,[status(thm)],[44,33]) ).
tff(46,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)))
<=> achievable(row(successor(n1)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered))
<=> achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_row_initially) ).
tff(49,plain,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
^ [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
refl(( ( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
<=> ( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
<=> ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
<=> ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',place_vertical_pieces) ).
tff(54,plain,
! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered))
| 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))) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered))
| 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(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered))
| 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(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered))
| 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(modus_ponens,[status(thm)],[58,57]) ).
tff(60,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(unit_resolution,[status(thm)],[59,56,49]) ).
tff(61,plain,
achievable(row(successor(n1)),squares(complement(not_covered),complement(covered),complement(covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(modus_ponens,[status(thm)],[60,46]) ).
tff(62,plain,
achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered)),
inference(modus_ponens,[status(thm)],[61,40]) ).
tff(63,plain,
^ [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
refl(( ( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) )
<=> ( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) )
<=> ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) )
<=> ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cover_columns_2_and_3) ).
tff(67,plain,
! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) )
| ~ achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered))
| achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered)) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) )
| ~ achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered))
| achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) )
| ~ achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered))
| achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,covered,covered,Y4,Y5,Y6,Y7,Y8)) )
| ~ achievable(row(n2),squares(covered,not_covered,not_covered,covered,covered,covered,covered,covered))
| achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(unit_resolution,[status(thm)],[72,69,62]) ).
tff(74,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ achievable(row(n2),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(unit_resolution,[status(thm)],[76,56]) ).
tff(78,plain,
achievable(row(successor(n2)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))),
inference(unit_resolution,[status(thm)],[77,73]) ).
tff(79,plain,
achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(modus_ponens,[status(thm)],[78,31]) ).
tff(80,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ achievable(row(n3),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(unit_resolution,[status(thm)],[82,56]) ).
tff(84,plain,
achievable(row(successor(n3)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(unit_resolution,[status(thm)],[83,79]) ).
tff(85,plain,
achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(modus_ponens,[status(thm)],[84,24]) ).
tff(86,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ achievable(row(n4),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(unit_resolution,[status(thm)],[88,56]) ).
tff(90,plain,
achievable(row(successor(n4)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))),
inference(unit_resolution,[status(thm)],[89,85]) ).
tff(91,plain,
achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(modus_ponens,[status(thm)],[90,12]) ).
tff(92,plain,
( ( successor(n5) = n6 )
<=> ( successor(n5) = n6 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
successor(n5) = n6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_5_is_6) ).
tff(94,plain,
successor(n5) = n6,
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
n6 = successor(n5),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
row(n6) = row(successor(n5)),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered))
<=> achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(monotonicity,[status(thm)],[96,17]) ).
tff(98,plain,
( ~ achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered))
<=> ~ achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( successor(n6) = n7 )
<=> ( successor(n6) = n7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
successor(n6) = n7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_6_is_7) ).
tff(101,plain,
successor(n6) = n7,
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
n7 = successor(n6),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
row(n7) = row(successor(n6)),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
<=> achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(monotonicity,[status(thm)],[103,5]) ).
tff(105,plain,
( ~ achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
<=> ~ achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( successor(n7) = n8 )
<=> ( successor(n7) = n8 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,axiom,
successor(n7) = n8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_of_7_is_8) ).
tff(108,plain,
successor(n7) = n8,
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
row(successor(n7)) = row(n8),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered)))
<=> achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
inference(monotonicity,[status(thm)],[109,16]) ).
tff(111,plain,
( achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered))
<=> achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered))
<=> ~ achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered))
<=> ~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,axiom,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_row_8_can_be_covered) ).
tff(115,plain,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
~ achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(modus_ponens,[status(thm)],[115,112]) ).
tff(117,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
( ~ achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n7)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(unit_resolution,[status(thm)],[119,56]) ).
tff(121,plain,
~ achievable(row(n7),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(unit_resolution,[status(thm)],[120,116]) ).
tff(122,plain,
~ achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))),
inference(modus_ponens,[status(thm)],[121,105]) ).
tff(123,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ~ achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered))
| achievable(row(successor(n6)),squares(complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered),complement(covered))) ),
inference(unit_resolution,[status(thm)],[125,56]) ).
tff(127,plain,
~ achievable(row(n6),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(unit_resolution,[status(thm)],[126,122]) ).
tff(128,plain,
~ achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))),
inference(modus_ponens,[status(thm)],[127,98]) ).
tff(129,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [Y4: $i,Y8: $i,Y2: $i,Y1: $i,Y5: $i,Y3: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8))
| achievable(row(successor(X)),squares(complement(Y1),complement(Y2),complement(Y3),complement(Y4),complement(Y5),complement(Y6),complement(Y7),complement(Y8))) )
| ~ achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
( ~ achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered))
| achievable(row(successor(n5)),squares(complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered),complement(not_covered))) ),
inference(unit_resolution,[status(thm)],[131,56]) ).
tff(133,plain,
~ achievable(row(n5),squares(not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(unit_resolution,[status(thm)],[132,128]) ).
tff(134,plain,
$false,
inference(unit_resolution,[status(thm)],[133,91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ016-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 02:39:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.52/1.72 % SZS status Unsatisfiable
% 1.52/1.72 % SZS output start Proof
% See solution above
% 1.52/1.75 % E exiting
%------------------------------------------------------------------------------