TSTP Solution File: PUZ016-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 : Sun Sep 18 14:10:51 EDT 2022
% Result : Unsatisfiable 0.62s 0.69s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 45
% Syntax : Number of formulae : 97 ( 27 unt; 10 typ; 0 def)
% Number of atoms : 255 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 319 ( 155 ~; 129 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 5 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-8 aty)
% Number of variables : 480 ( 450 !; 0 ?; 480 :)
% Comments :
%------------------------------------------------------------------------------
tff(achievable_type,type,
achievable: ( $i * $i ) > $o ).
tff(squares_type,type,
squares: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(removed_type,type,
removed: $i ).
tff(row_type,type,
row: $i > $i ).
tff(successor_type,type,
successor: $i > $i ).
tff(n1_type,type,
n1: $i ).
tff(not_covered_type,type,
not_covered: $i ).
tff(covered_type,type,
covered: $i ).
tff(n8_type,type,
n8: $i ).
tff(1,plain,
( ( complement(complement(not_covered)) = not_covered )
<=> ( complement(complement(complement(removed))) = complement(removed) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( complement(covered) = not_covered )
<=> ( complement(complement(not_covered)) = not_covered ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( complement(covered) = not_covered )
<=> ( complement(covered) = not_covered ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
complement(covered) = not_covered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_covered_is_not_covered) ).
tff(5,plain,
complement(covered) = not_covered,
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
complement(complement(not_covered)) = not_covered,
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
complement(complement(complement(removed))) = complement(removed),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed)))) = squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)),
inference(monotonicity,[status(thm)],[7,7,7,7,7,7,7,7]) ).
tff(9,plain,
( achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed)))))
<=> achievable(row(successor(successor(n1))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed))) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( achievable(row(successor(successor(n1))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
<=> achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ~ achievable(row(successor(successor(n1))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
<=> ~ achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed)))))
<=> achievable(row(successor(successor(successor(successor(n1))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed))) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(13,plain,
( achievable(row(successor(successor(successor(successor(n1))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
<=> achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ~ achievable(row(successor(successor(successor(successor(n1))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
<=> ~ achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed)))))
<=> achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed))) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(16,plain,
( achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
<=> achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( ~ achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
<=> ~ achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),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(successor(successor(successor(successor(successor(successor(successor(n1)))))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered))
<=> ~ achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),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(20,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(21,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(22,plain,
~ achievable(row(n8),squares(covered,covered,covered,covered,covered,covered,covered,covered)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),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)],[22,19]) ).
tff(24,plain,
~ achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))),
inference(modus_ponens,[status(thm)],[23,18]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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(28,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(29,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)],[28,27]) ).
tff(30,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)],[29]) ).
tff(31,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)],[30,26]) ).
tff(32,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(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) )
<=> ( ~ ! [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(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,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(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,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(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(successor(successor(successor(successor(n1)))))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed))),
inference(unit_resolution,[status(thm)],[34,31,24]) ).
tff(36,plain,
~ achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))),
inference(modus_ponens,[status(thm)],[35,17]) ).
tff(37,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(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) )
<=> ( ~ ! [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(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,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(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,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(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ achievable(row(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(successor(successor(n1))))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(unit_resolution,[status(thm)],[39,31]) ).
tff(41,plain,
~ achievable(row(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))),
inference(unit_resolution,[status(thm)],[40,36]) ).
tff(42,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(successor(successor(successor(successor(n1))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) )
<=> ( ~ ! [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(successor(successor(successor(successor(n1))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,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(successor(successor(successor(successor(n1))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,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(successor(successor(successor(successor(n1))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(successor(successor(n1)))))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ achievable(row(successor(successor(successor(successor(n1))))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed))),
inference(unit_resolution,[status(thm)],[44,31,41]) ).
tff(46,plain,
~ achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))),
inference(modus_ponens,[status(thm)],[45,14]) ).
tff(47,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(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) )
<=> ( ~ ! [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(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,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(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,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(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ achievable(row(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(successor(successor(n1))))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(unit_resolution,[status(thm)],[49,31]) ).
tff(51,plain,
~ achievable(row(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))),
inference(unit_resolution,[status(thm)],[50,46]) ).
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))) )
| ~ achievable(row(successor(successor(n1))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) )
<=> ( ~ ! [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(successor(successor(n1))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,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(successor(successor(n1))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(quant_inst,[status(thm)],]) ).
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))) )
| ~ achievable(row(successor(successor(n1))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(successor(successor(n1)))),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ achievable(row(successor(successor(n1))),squares(complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed),complement(removed))),
inference(unit_resolution,[status(thm)],[54,31,51]) ).
tff(56,plain,
~ achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))),
inference(modus_ponens,[status(thm)],[55,11]) ).
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(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) )
<=> ( ~ ! [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(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ) ),
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(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
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(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ achievable(row(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(successor(n1))),squares(complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))),complement(complement(complement(removed))))) ),
inference(unit_resolution,[status(thm)],[59,31]) ).
tff(61,plain,
~ achievable(row(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))),
inference(unit_resolution,[status(thm)],[60,56]) ).
tff(62,plain,
^ [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
refl(
( ( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) )
<=> ( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) )
<=> ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
^ [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
rewrite(
( ( ~ achievable(row(X),squares(Y1,not_covered,not_covered,Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(not_covered),complement(not_covered),Y4,Y5,Y6,Y7,Y8)) )
<=> ( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) ) )),
inference(bind,[status(th)],]) ).
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,complement(not_covered),complement(not_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,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
^ [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
rewrite(
( ( ~ 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,complement(not_covered),complement(not_covered),Y4,Y5,Y6,Y7,Y8)) ) )),
inference(bind,[status(th)],]) ).
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)) )
<=> ! [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,complement(not_covered),complement(not_covered),Y4,Y5,Y6,Y7,Y8)) ) ),
inference(quant_intro,[status(thm)],[66]) ).
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)) )
<=> ! [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(69,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(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)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
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,complement(not_covered),complement(not_covered),Y4,Y5,Y6,Y7,Y8)) ),
inference(modus_ponens,[status(thm)],[70,67]) ).
tff(72,plain,
! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) ),
inference(modus_ponens,[status(thm)],[71,65]) ).
tff(73,plain,
! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) ),
inference(modus_ponens,[status(thm)],[73,63]) ).
tff(75,plain,
( ( ~ ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) )
| ~ achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) )
<=> ( ~ ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) )
| ~ achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ~ ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) )
| ~ achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [Y4: $i,Y8: $i,Y1: $i,Y5: $i,Y7: $i,X: $i,Y6: $i] :
( ~ achievable(row(X),squares(Y1,complement(removed),complement(removed),Y4,Y5,Y6,Y7,Y8))
| achievable(row(X),squares(Y1,complement(complement(removed)),complement(complement(removed)),Y4,Y5,Y6,Y7,Y8)) )
| ~ achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed))))
| achievable(row(successor(n1)),squares(complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
~ achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))),
inference(unit_resolution,[status(thm)],[77,74,61]) ).
tff(79,plain,
( achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered))
<=> achievable(row(n1),squares(complement(removed),removed,removed,complement(removed),complement(removed),complement(removed),complement(removed),complement(removed))) ),
inference(rewrite,[status(thm)],]) ).
tff(80,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(81,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(82,plain,
achievable(row(n1),squares(not_covered,removed,removed,not_covered,not_covered,not_covered,not_covered,not_covered)),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
achievable(row(n1),squares(complement(removed),removed,removed,complement(removed),complement(removed),complement(removed),complement(removed),complement(removed))),
inference(modus_ponens,[status(thm)],[82,79]) ).
tff(84,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(complement(removed),removed,removed,complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) )
<=> ( ~ ! [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(complement(removed),removed,removed,complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,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(complement(removed),removed,removed,complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(quant_inst,[status(thm)],]) ).
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(n1),squares(complement(removed),removed,removed,complement(removed),complement(removed),complement(removed),complement(removed),complement(removed)))
| achievable(row(successor(n1)),squares(complement(complement(removed)),complement(removed),complement(removed),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)),complement(complement(removed)))) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
$false,
inference(unit_resolution,[status(thm)],[86,31,83,78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : PUZ016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.37 % Computer : n005.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Fri Sep 2 18:17:18 EDT 2022
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.37 Usage: tptp [options] [-file:]file
% 0.13/0.37 -h, -? prints this message.
% 0.13/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.37 -m, -model generate model.
% 0.13/0.37 -p, -proof generate proof.
% 0.13/0.37 -c, -core generate unsat core of named formulas.
% 0.13/0.37 -st, -statistics display statistics.
% 0.13/0.37 -t:timeout set timeout (in second).
% 0.13/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.37 -<param>:<value> configuration parameter and value.
% 0.13/0.37 -o:<output-file> file to place output in.
% 0.62/0.69 % SZS status Unsatisfiable
% 0.62/0.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------